Adaptive Estimation of Vector Autoregressive Models with Time-Varying Variance: Application to Testing Linear Causality in Mean
Adaptive Estimation of Vector Autoregressive Models with Time-Varying Variance: Application to Testing Linear Causality in Mean
By Valentin Patilea
IRMAR-INSA and CREST ENSAI (2010)
Abstract Paper

Hamdi  Raïssi

IRMAR-INSA

France

Coder Page  

The code provides Wald tests results for testing linear Granger causality in mean in the framework of VAR models with non constant variance. A summary on bandwidth selection and the minimum eigenvalues of the estimated volatilities is displayed. The series have to be centered before proceeding to the tests. Note that the adequacy of the VAR model has to be tested before using the modified portmanteau tests available on this companion website.
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Abstract
Linear Vector AutoRegressive (VAR) models where the innovations could be unconditionally heteroscedastic and serially dependent are considered. The volatility structure is deterministic and quite general, including breaks or trending variances as special cases. In this framework we propose Ordinary Least Squares (OLS), Generalized Least Squares (GLS) and Adaptive Least Squares (ALS) procedures. The GLS estimator requires the knowledge of the time-varying variance structure while in the ALS approach the unknown variance is estimated by kernel smoothing with the outer product of the OLS residuals vectors. Different bandwidths for the different cells of the time-varying variance matrix are also allowed. We derive the asymptotic distribution of the proposed estimators for the VAR model coefficients and compare their properties. In particular we show that the ALS estimator is asymptotically equivalent to the infeasible GLS estimator. This asymptotic equivalence is obtained uniformly with respect to the bandwidth(s) in a given range and hence justifies data-driven bandwidth rules. Using these results we build Wald tests for the linear Granger causality in mean which are adapted to VAR processes driven by errors with a non stationary volatility. It is also shown that the commonly used standard Wald test for the linear Granger causality in mean is potentially unreliable in our framework (incorrect level and lower asymptotic power). Monte Carlo and real-data experiments illustrate the use of the different estimation approaches for the analysis of VAR models with time-varying variance innovations.
Patilea, V., "Adaptive Estimation of Vector Autoregressive Models with Time-Varying Variance: Application to Testing Linear Causality in Mean", IRMAR-INSA and CREST ENSAI.
number of observations
number of observations
dimension of the process
dimension of the process
dimension of the first subvector X1
dimension of the first subvector X1
dimension of the subvector X2
dimension of the subvector X2
autoregressive order
autoregressive order
number of grid points
number of grid points
sup bound for the grid
sup bound for the grid
min bound for the grid
min bound for the grid
data
data
Waiting time

Please cite the publication as :

Patilea, V., "Adaptive Estimation of Vector Autoregressive Models with Time-Varying Variance: Application to Testing Linear Causality in Mean", IRMAR-INSA and CREST ENSAI.

Please cite the companion website as :

Patilea, V., "Adaptive Estimation of Vector Autoregressive Models with Time-Varying Variance: Application to Testing Linear Causality in Mean", RunMyCode companion website, http://www.execandshare.org/CompanionSite/Site62

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Variable/Parameters Description, constraint Comments
number of observations
    number of observations
    dimension of the process
      dimension of the process
      dimension of the first subvector X1
        The tests determine if X2 Granger-causes X1 linearly in mean.
        dimension of the subvector X2
          The tests determine if X2 Granger-causes X1 linearly in mean.
          autoregressive order
            The lag length of the VAR model. It have to be tested by using portmanteau tests developed in Patilea and Raïssi (2011).
            number of grid points
              The number of grid points corresponds to the number of candidate bandwidths for the non parametric estimation of the volatility structure.
              sup bound for the grid
                The input 'ma' serves to compute a sup bound of the grid in regard to the 'long run' variance of the ordinary least squares residuals and the sample size.
                min bound for the grid
                  The input 'mi' serves to compute a min bound of the grid in regard to the 'long run' variance of the ordinary least squares residuals and the sample size.
                  data
                    Data
                    Variable/Parameters Description Visualisation
                    number of observations
                    dimension of the process
                    dimension of the first subvector X1
                    dimension of the subvector X2
                    autoregressive order
                    number of grid points
                    sup bound for the grid
                    min bound for the grid
                    data The first column corresponds to the first differences of the U.S. balance on merchandise trade in billions dollars. The second column corresponds to the first differences of the U.S. balance on services in billions dollars. The linear Granger causality in mean from the from the balance on services to the balance on merchandise trade is tested. Data source: http://research.stlouisfed.org/
                    Adaptive Estimation of Vector Autoregressive Models with Time-Varying Variance: Application to Testing Linear Causality in Mean
                    H. Raïssi (2012)
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                    Forcasting Expected Shortfall with a Generalized Asymetric Student-t Distribution
                    Abstract
                    Financial returns typically display heavy tails and some skewness, and conditional variance models with these features often outperform more limited models. The difference in performance may be espe- cially important in estimating quantities that depend on tail features, including risk measures such as the expected shortfall. Here, using a recent generalization of the asymmetric Student-t distribution to allow separate parameters to control skewness and the thickness of each tail, we fit daily financial returns and forecast expected shortfall for the S&P 500 index and a number of individual company stocks; the generalized distribution is used for the standardized innovations in a nonlinear, asymmetric GARCH-type model. The results provide empirical evidence for the usefulness of the generalized distribution in improving prediction of downside market risk of financial assets.
                    Galbraith, W. J., and D. Zhu, "Forcasting Expected Shortfall with a Generalized Asymetric Student-t Distribution", Centre interuniversitaire de recherche en analyse des organisations.
                    Authors: Galbraith
                    Zhu
                    Coders: Galbraith
                    Zhu
                    Last update
                    07/27/2012
                    Ranking
                    41
                    Runs
                    9
                    Visits
                    143
                    Margin Backtesting
                    Abstract
                    This paper presents a validation framework for collateral requirements or margins on a derivatives exchange. It can be used by investors, risk managers, and regulators to check the accuracy of a margining system. The statistical tests presented in this study are based either on the number, frequency, magnitude, or timing of margin exceedances, which are de…ned as situations in which the trading loss of a market participant exceeds his or her margin. We also propose an original way to validate globally the margining system by aggregating individual backtesting statistics ob- tained for each market participant.
                    Hurlin, C., and C. Perignon, "Margin Backtesting", University of Orleans, HEC Paris.
                    Authors: Hurlin
                    Perignon
                    Coders: Hurlin
                    Perignon
                    Last update
                    07/23/2014
                    Ranking
                    36
                    Runs
                    377
                    Visits
                    433
                    Testing Interval Forecasts: A GMM-Based Approach
                    Abstract
                    This paper proposes a new evaluation framework of interval forecasts. Our model free test can be used to evaluate intervals forecasts and/or High Density Region, potentially discontinuous and/or asymmetric. Using simple J-statistic based on the moments defined by the orthonormal polynomials associated with the Binomial distribution, this new approach presents many advantages. First, its implementation is extremely easy. Second, it allows for a separate test for unconditional coverage, independence and conditional coverage hypothesis. Third, Monte-Carlo simulations show that for realistic sample sizes, our GMM test outperforms traditional LR test. These results are corroborated by an empirical application on SP500 and Nikkei stock market indexes. The empirical application for financial returns confirms that using a GMM test leads to major consequences for the ex-post evaluation of interval forecasts produced by linear versus non linear models.
                    Dumitrescu, E., C. Hurlin, "Testing Interval Forecasts: A GMM-Based Approach", Journal of Forecasting, -.
                    Authors: Dumitrescu
                    Hurlin
                    Madkour
                    Coders: Dumitrescu
                    Hurlin
                    Last update
                    06/05/2012
                    Ranking
                    10
                    Runs
                    29
                    Visits
                    340
                    A Theoretical and Empirical Comparison of Systemic Risk Measures: MES versus CoVaR
                    Abstract
                    In this paper, we propose a theoretical and empirical comparison of two popular systemic risk measures - Marginal Expected Shortfall (MES) and Delta Conditional Value at Risk (ΔCoVaR) - that can be estimated using publicly available data. First, we assume that the time-varying correlation completely captures the dependence between firm and market returns. Under this assumption, we derive three analytical results: (i) we show that the MES corresponds to the product of the conditional ES of market returns and the time-varying beta of this institution, (ii) we give an analytical expression of the ΔCoVaR and show that the CoVaR corresponds to the product of the VaR of the firm's returns and the time-varying linear projection coefficient of the market returns on the firm's returns and (iii) we derive the ratio of the MES to the ΔCoVaR. Second, we relax this assumption and propose an empirical comparison for a panel of 61 US financial institutions over the period from January 2000 to December 2010. For each measure, we propose a cross-sectional analysis, a time-series comparison and rankings analysis of these institutions based on the two measures.
                    Benoit, S., G. Colletaz, C. Hurlin, and C. Perignon, "A Theoretical and Empirical Comparison of Systemic Risk Measures: MES versus CoVaR", SSRN.
                    Authors: Benoit
                    Colletaz
                    Hurlin
                    Perignon
                    Coders: Benoit
                    Colletaz
                    Hurlin
                    Perignon
                    Last update
                    10/25/2012
                    Ranking
                    53
                    Runs
                    181
                    Visits
                    398
                    Is Public Capital Really Productive? A Methodological Reappraisal
                    Abstract
                    We present an evaluation of the main empirical approaches used in the literature to estimate the contribution of public capital stock to growth and private factors' productivity. Based on a simple stochastic general equilibrium model, built as to reproduce the main long-run relations observed in US post-war historical data, we show that the production function approach may not be reliable to estimate this contribution. Our analysis reveals that this approach largely overestimates the public capital elasticity, given the presence of a common stochastic trend shared by all non-stationary inputs.
                    Minea, A., and C. Hurlin, "Is Public Capital Really Productive? A Methodological Reappraisal", University of Orleans.
                    Authors: Minea
                    Hurlin
                    Coders: Minea
                    Hurlin
                    Last update
                    09/10/2012
                    Ranking
                    43
                    Runs
                    3
                    Visits
                    42
                    Are Public Investment Efficient in Creating Capital Stocks in Developing Countries? Estimates of Government Net Capital Stocks for 26 Developing Countries, 1970-2002
                    Abstract
                    In many poor countries, the problem is not that governments do not invest, but that these investments do not create productive capital. So, the cost of public investments does not correspond to the value of the capital stocks. In this paper, we propose an original non parametric approach to evaluate the efficiency function that links variations (net of depreciation) of stocks to public investments. We consider four sectors (electricity, telecommunications, roads and railways) of two Latin American countries (Mexico and Colombia). We show that there is a large discrepancy between the amount of investments and the value of increases in stocks.
                    Arestoff, F., and C. Hurlin, "Are Public Investment Efficient in Creating Capital Stocks in Developing Countries? Estimates of Government Net Capital Stocks for 26 Developing Countries, 1970-2002 ", Economics Bulletin, 30, 1515-1531.
                    Authors: Arestoff
                    Hurlin
                    Coders: Arestoff
                    Hurlin
                    Last update
                    10/08/2012
                    Ranking
                    11
                    Runs
                    N.A.
                    Visits
                    26
                    The Optimal Hard Threshold for Singular Values is 4/sqrt(3)
                    Abstract
                    We consider recovery of low-rank matrices from noisy data by hard thresholding of singular values, where singular values below a prescribed threshold \lambda are set to 0. We study the asymptotic MSE in a framework where the matrix size is large compared to the rank of the matrix to be recovered, and the signal-to-noise ratio of the low-rank piece stays constant. The AMSE-optimal choice of hard threshold, in the case of n-by-n matrix in noise level \sigma, is simply (4/\sqrt{3}) \sqrt{n}\sigma \approx 2.309 \sqrt{n}\sigma when \sigma is known, or simply 2.858\cdot y_{med} when \sigma is unknown, where y_{med} is the median empirical singular value. For nonsquare m by n matrices with m \neq n, these thresholding coefficients are replaced with different provided constants. In our asymptotic framework, this thresholding rule adapts to unknown rank and to unknown noise level in an optimal manner: it is always better than hard thresholding at any other value, no matter what the matrix is that we are trying to recover, and is always better than ideal Truncated SVD (TSVD), which truncates at the true rank of the low-rank matrix we are trying to recover. Hard thresholding at the recommended value to recover an n-by-n matrix of rank r guarantees an AMSE at most 3nr\sigma^2. In comparison, the guarantee provided by TSVD is 5nr\sigma^2, the guarantee provided by optimally tuned singular value soft thresholding is 6nr\sigma^2, and the best guarantee achievable by any shrinkage of the data singular values is 2nr\sigma^2. Empirical evidence shows that these AMSE properties of the 4/\sqrt{3} thresholding rule remain valid even for relatively small n, and that performance improvement over TSVD and other shrinkage rules is substantial, turning it into the practical hard threshold of choice.
                    Gavish, M., and D. Donoho, "The Optimal Hard Threshold for Singular Values is 4/sqrt(3)", Stanford University.
                    Authors: Donoho
                    Gavish
                    Coders: Gavish
                    Donoho
                    Last update
                    05/30/2013
                    Ranking
                    9999
                    Runs
                    17
                    Visits
                    N.A.
                    Testing for Granger Non-causality in Heterogeneous Panels
                    Abstract
                    This paper proposes a very simple test of Granger (1969) non-causality for hetero- geneous panel data models. Our test statistic is based on the individual Wald statistics of Granger non causality averaged across the cross-section units. First, this statistic is shown to converge sequentially to a standard normal distribution. Second, the semi- asymptotic distribution of the average statistic is characterized for a fixed T sample. A standardized statistic based on an approximation of the moments of Wald statistics is hence proposed. Third, Monte Carlo experiments show that our standardized panel statistics have very good small sample properties, even in the presence of cross-sectional dependence.
                    Dumitrescu, E., and C. Hurlin, "Testing for Granger Non-causality in Heterogeneous Panels", Economic Modelling, Forthcoming.
                    Authors: Dumitrescu
                    Hurlin
                    Coders: Dumitrescu
                    Hurlin
                    Last update
                    07/12/2017
                    Ranking
                    40
                    Runs
                    451
                    Visits
                    502
                    Monotonicity in Asset Returns: New Tests with Applications to the Term Structure, the CAPM, and Portfolio Sorts
                    Abstract
                    Many theories in finance imply monotonic patterns in expected returns and other financial variables. The liquidity preference hypothesis predicts higher expected returns for bonds with longer times to maturity; the Capital Asset Pricing Model(CAPM)implies higher expected returns for stocks with higher betas; and standard asset pricing models imply that the pricing kernel is declining in market returns. The full set of implications of monotonicity is generally not exploited in empirical work, however. This paper proposes new and simple ways to test for monotonicity in financial variables and compares the proposed tests with extant alternatives such as t-tests, Bonferroni bounds, and multivariate inequality tests through empirical applications and simulations.
                    Patton, J. A., and A. Timmermann, "Monotonicity in Asset Returns: New Tests with Applications to the Term Structure, the CAPM, and Portfolio Sorts", Journal of Financial Economics, 98, 605-625.
                    Authors: Patton
                    Timmermann
                    Coders: Patton
                    Timmermann
                    Last update
                    11/17/2012
                    Ranking
                    63
                    Runs
                    19
                    Visits
                    116
                    Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approximation Approach
                    Abstract
                    When a continuous-time diffusion is observed only at discrete dates, in most cases the transition distribution and hence the likelihood function of the observation is not explicitely computable. Using Hermite polynomials, I construct an explicit sequences of closed-form functions and show that it converges to the true (but unknown) likelihood function. I document that the approximation is very accurate and prove that maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and shares its asymptotic properties. Monte Carlo evidence reveals that this method outperforms other approximation schemes in situations relevant for financial models.
                    Aït-Sahalia, Y., "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approximation Approach", Econometrica, 70, 223-262.
                    Authors: Aït-Sahalia
                    Coders: Aït-Sahalia
                    Last update
                    10/29/2014
                    Ranking
                    2
                    Runs
                    119
                    Visits
                    621
                    Deterministic Matrices Matching the Compressed Sensing Phase Transitions of Gaussian Random Matrices
                    Abstract
                    In compressed sensing, one takes n < N samples of an N -dimensional vector x0 using an n × N matrix A, obtaining un-dersampled measurements y = Ax0 . For random matrices with Gaussian i.i.d entries, it is known that, when x0 is k-sparse, there is a precisely determined phase transition: for a certain region in the (k/n, n/N )-phase diagram, convex optimization min ||x||_1 subject to y = Ax, x ∈ X^N typically finds the sparsest solution, while outside that region, it typically fails. It has been shown empirically that the same property – with the same phase transition location – holds for a wide range of non-Gaussian random matrix ensembles. We consider specific deterministic matrices including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Extensive experiments show that for a typical k-sparse object, convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian matrices. In our experiments, we considered coefficients constrained to X^N for four different sets X ∈ {[0, 1], R_+ , R, C}. We establish this finding for each of the associated four phase transitions.
                    Monajemi, H., D. Donoho, "Deterministic Matrices Matching the Compressed Sensing Phase Transitions of Gaussian Random Matrices", Stanford University.
                    Authors: Monajemi
                    Jafarpour
                    Gavish
                    Donoho
                    Coders: Monajemi
                    Donoho
                    Last update
                    01/04/2013
                    Ranking
                    9999
                    Runs
                    13
                    Visits
                    86
                    Copula-Based Models for Financial Time Series
                    Abstract
                    This paper presents an overview of the literature on applications of copulas in the modelling of financial time series. Copulas have been used both in multivariate time series analysis, where they are used to charaterise the (conditional) cross-sectional dependence between individual time series, and in univariate time series analysis, where they are used to characterise the dependence between a sequence of observations of a scalar time series process. The paper includes a broad, brief, review of the many applications of copulas in finance and economics.
                    Patton, J. A., "Copula-Based Models for Financial Time Series", Handbook of Financial Time Series, Springer Verlag, -.
                    Authors: Patton
                    Coders: Patton
                    Last update
                    10/08/2012
                    Ranking
                    3
                    Runs
                    38
                    Visits
                    572
                    Mixed Logit with Repeated Choices: Households' Choices of Appliance Efficiency Level
                    Abstract
                    Mixed logit models, also called random-parameters or error-components logit, are a generalization of standard logit that do not exhibit the restrictive "independence from irrelevant alternatives" property and explicitly account for correlations in unobserved utility over repeated choices by each customer. Mixed logits are estimated for households’ choices of appliances under utility-sponsored programs that offer rebates or loans on high-efficiency appliances.
                    Train, K., "Mixed Logit with Repeated Choices: Households' Choices of Appliance Efficiency Level", The Review of Economics and Statistics, 80, 647-657.
                    Authors: Revelt
                    Train
                    Coders: Train
                    Last update
                    06/05/2012
                    Ranking
                    7
                    Runs
                    6
                    Visits
                    243
                    Network Effects and Infrastructure Productivity in Developing Countries
                    Abstract
                    This paper proposes to investigate the threshold effects of the productivity of infrastructure investment in developing countries within a panel data framework. Various speci.cations of an augmented production function that allow for endogenous thresholds are considered. The overwhelming outcome is the presence of strong threshold effects in the relationship between output and private and public inputs. Whatever the transition mechanism used, the testing procedures lead to strong rejection of the linearity of this relationship. In particular, the productivity of infrastructure investment generally exhibits some network effects. When the available stock of infrastructure is very low, investment in this sector has the same productivity as non-infrastructure investment. On the contrary, when a minimumnetwork is available, the marginal productivity of infrastructure investment is generally largely greater than the productivity of other investments. Finally, when the main network is achieved, its marginal productivity becomes similar to the productivity of other investment.
                    Candelon, B., G. Colletaz, and C. Hurlin, "Network Effects and Infrastructure Productivity in Developing Countries", Maastricht University.
                    Authors: Candelon
                    Colletaz
                    Hurlin
                    Coders: Candelon
                    Colletaz
                    Hurlin
                    Last update
                    03/14/2013
                    Ranking
                    35
                    Runs
                    414
                    Visits
                    431
                    Threshold Effects of the Public Capital Productivity : An International Panel Smooth Transition Approach
                    Abstract
                    Using a non linear panel data model we examine the threshold effects in the productivity of the public capital stocks for a panel of 21 OECD countries observed over 1965-2001. Using the so-called "augmented production function" approach, we estimate various specifications of a Panel Smooth Threshold Regression (PSTR) model recently developed by Gonzalez, Teräsvirta and Van Dijk (2004). One of our main results is the existence of strong threshold effects in the relationship between output and private and public inputs : whatever the transition mechanism specified, tests strongly reject the linearity assumption. Moreover this model allows cross-country heterogeneity and time instability of the productivity without specification of an ex-ante classification over individuals. Consequently it is posible to give estimates of productivity coefficients for both private and public capital stocks at any time and for each countries in the sample. Finally we proposed estimates of individual time varying elasticities that are much more reasonable than those previously published.
                    Hurlin, C., "Threshold Effects of the Public Capital Productivity : An International Panel Smooth Transition Approach", University of Orléans.
                    Authors: Colletaz
                    Hurlin
                    Coders: Hurlin
                    Last update
                    07/22/2014
                    Ranking
                    31
                    Runs
                    2290
                    Visits
                    677
                    Evaluating Interval Forecasts
                    Abstract
                    A complete theory for evaluating interval forecasts has not been worked out to date. Most of the literature implicitly assumes homoskedastic errors even when this is clearly violated and proceed by merely testing for correct unconditional coverage. Consequently, the author sets out to build a consistent framework for conditional interval forecast evaluation, which is crucial when higher-order moment dynamics are present. The new methodology is demonstrated in an application to the exchange rate forecasting procedures advocated in risk management.
                    Hurlin, C., C. Perignon, "Evaluating Interval Forecasts", International Economic Review, 39, 841-862.
                    Authors: Christoffersen
                    Coders: Hurlin
                    Perignon
                    Last update
                    03/09/2012
                    Ranking
                    32
                    Runs
                    57
                    Visits
                    167
                    Backtesting Value-at-Risk: A Duration-Based Approach
                    Abstract
                    Financial risk model evaluation or backtesting is a key part of the internal model’s approach to market risk management as laid out by the Basle Committee on Banking Supervision. However, existing backtesting methods have relatively low power in realistic small sample settings. Our contribution is the exploration of new tools for backtesting based on the duration of days between the violations of the Value-at-Risk. Our Monte Carlo results show that in realistic situations, the new duration-based tests have considerably better power properties than the previously suggested tests.
                    Hurlin, C., and C. Perignon, "Backtesting Value-at-Risk: A Duration-Based Approach", Journal of Financial Econometrics, 2, 84-108.
                    Authors: Pelletier
                    Christoffersen
                    Coders: Hurlin
                    Perignon
                    Last update
                    07/23/2012
                    Ranking
                    26
                    Runs
                    17
                    Visits
                    207
                    Backtesting Value-at-Risk Accuracy: A Simple New Test
                    Abstract
                    This paper proposes a new test of value-at-risk (VAR) validation. Our test exploits the idea that the sequence of VAR violations (hit function) – taking value 1 - α if there is a violation, and -α otherwise – for a nominal coverage rate α verifies the properties of a martingale difference if the model used to quantify risk is adequate (Berkowitz et al., 2005). More precisely, we use the multivariate portmanteau statistic of Li and McLeod (1981), an extension to the multivariate framework of the test of Box and Pierce (1970), to jointly test the absence of autocorrelation in the vector of hit sequences for various coverage rates considered relevant for the management of extreme risks. We show that this shift to a multivariate dimension appreciably improves the power properties of the VAR validation test for reasonable sample sizes.
                    Hurlin, C., and S. Tokpavi, "Backtesting Value-at-Risk Accuracy: A Simple New Test", Journal of Risk, 9, 19-37.
                    Authors: Hurlin
                    Tokpavi
                    Coders: Hurlin
                    Tokpavi
                    Last update
                    03/13/2012
                    Ranking
                    49
                    Runs
                    2
                    Visits
                    240
                    How To Evaluate an Early Warning System? Towards a unified Statistical Framework for Assessing Financial Crises Forecasting Methods
                    Abstract
                    This paper proposes an original and unified toolbox to evaluate financial crisis Early Warning Systems (EWS). It presents four main advantages. First, it is a model-free method which can be used to asses the forecasts issued from different EWS (probit, logit, markov switching models, or combinations of models). Second, this toolbox can be applied to any type of crisis EWS (currency, banking, sovereign debt, etc.). Third, it does not only provide various criteria to evaluate the (absolute) validity of EWS forecasts but also proposes some tests to compare the relative performance of alternative EWS. Fourth, our toolbox can be used to evaluate both in-sample and out-of-sample forecasts. Applied to a logit model for twelve emerging countries we show that the yield spread is a key variable for predicting currency crises exclusively for South-Asian countries. Besides, the optimal cut-off correctly allows us to identify now on average more than 2/3 of the crisis and calm periods.
                    Candelon, B., E. Dumitrescu, and C. Hurlin, "How To Evaluate an Early Warning System? Towards a unified Statistical Framework for Assessing Financial Crises Forecasting Methods", IMF Economic Review, 60.
                    Authors: Candelon
                    Dumitrescu
                    Hurlin
                    Coders: Candelon
                    Dumitrescu
                    Hurlin
                    Last update
                    07/23/2012
                    Ranking
                    34
                    Runs
                    24
                    Visits
                    269
                    Forecasting Realized Volatility Using a Nonnegative Semiparametric Model
                    Abstract
                    This paper introduces a parsimonious and yet exible nonnegative semi-parametric model to forecast financial volatility. The new model extends the linear nonnegative autoregressive model of Barndor-Nielsen & Shephard (2001) and Nielsen & Shephard (2003) by way of a power transformation. It is semiparametric in the sense that the distributional form of its error component is left unspecified. The statistical properties of the model are discussed and a novel estimation method is proposed. Asymptotic properties are established for the new estimation method. Simulation studies validate the new estimation method. The out-of-sample performance of the proposed model is evaluated against a number of standard methods, using data on S&P 500 monthly realized volatilities. The competing models include the exponential smoothing method, a linear AR(1) model, a log-linear AR(1) model, and two long-memory ARFIMA models. Various loss functions are utilized to evaluate the predictive accuracy of the alternative methods. It is found that the new model generally produces highly competitive forecasts.
                    Preve, D., J. Yu, "Forecasting Realized Volatility Using a Nonnegative Semiparametric Model", Uppsala University.
                    Authors: Eriksson
                    Preve
                    Yu
                    Coders: Preve
                    Yu
                    Last update
                    06/06/2012
                    Ranking
                    64
                    Runs
                    19
                    Visits
                    114
                    Mixed Logit with Bounded Distributions of Correlated Partworths
                    Abstract
                    The use of a joint normal distribution for partworths is computationally attractive, particularly with Bayesian MCMC procedures, and yet is unrealistic for any attribute whose partworth is logically bounded (e.g., is necessarily positive or cannot be unboundedly large). A mixed logit is specified with partworths that are transformations of normally distributed terms, where the transformation induces bounds; examples include censored normals, log-normals, and SB distributions which are bounded on both sides. The model retains the computational advantages of joint normals while providing greater flexibility for the distributions of correlated partworths. The method is applied to data on customers’ choice among vehicles in stated choice experiments. The flexibility that the transformations allow is found to greatly improve the model, both in terms of fit and plausibility, without appreciably increasing the computational burden.
                    Train, K., "Mixed Logit with Bounded Distributions of Correlated Partworths ", Applications of Simulation Methods in Environmental Resource Economics , Chapter 7.
                    Authors: Sonnier
                    Train
                    Coders: Train
                    Last update
                    07/10/2012
                    Ranking
                    4
                    Runs
                    9
                    Visits
                    268
                    Value-at-Risk (Chapter 5: Computing VaR)
                    Abstract
                    Book description: To accommodate sweeping global economic changes, the risk management field has evolved substantially since the first edition of Value at Risk, making this revised edition a must. Updates include a new chapter on liquidity risk, information on the latest risk instruments and the expanded derivatives market, recent developments in Monte Carlo methods, and more. Value at Risk will help professional risk managers understand, and operate within, today’s dynamic new risk environment.
                    Hurlin, C., C. Perignon, "Value-at-Risk (Chapter 5: Computing VaR)", MacGraw-Hill, Third Edition.
                    Authors: Jorion
                    Coders: Hurlin
                    Perignon
                    Last update
                    03/19/2012
                    Ranking
                    44
                    Runs
                    63
                    Visits
                    328
                    The pernicious effects of contaminated data in risk management
                    Abstract
                    Banks hold capital to guard against unexpected surges in losses and long freezes in financial markets. The minimum level of capital is set by banking regulators as a function of the banks’ own estimates of their risk exposures. As a result, a great challenge for both banks and regulators is to validate internal risk models. We show that a large fraction of US and international banks uses contaminated data when testing their models. In particular, most banks validate their market risk model using profit-and-loss (P/L) data that include fees and commissions and intraday trading revenues. This practice is inconsistent with the definition of the employed market risk measure. Using both bank data and simulations, we find that data contamination has dramatic implications for model validation and can lead to the acceptance of misspecified risk models. Moreover, our estimates suggest that the use of contaminated data can significantly reduce (market-risk induced) regulatory capital.
                    Fresard, L., C. Perignon, and A. Wilhelmsson, "The pernicious effects of contaminated data in risk management", Journal of Banking and Finance, 35.
                    Authors: Fresard
                    Perignon
                    Wilhelmsson
                    Coders: Fresard
                    Perignon
                    Wilhelmsson
                    Last update
                    11/23/2012
                    Ranking
                    9999
                    Runs
                    N.A.
                    Visits
                    42
                    Techniques for Verifying the Accuracy of Risk Management Models
                    Abstract
                    Risk exposures are typically quantified in terms of a "Value at Risk" (VaR) estimate. A VaR estimate corresponds to a specific critical value of a portfolio's potential one-day profit and loss probability distribution. Given their function both as internal risk management tools and as potential regulatory measures of risk exposure, it is important to quantify the accuracy of an institution's VaR estimates. This study shows that the formal statistical procedures that would typically be used in performance-based VaR verification tests require large samples to produce a reliable assessment of a model's accuracy in predicting the size and likelihood of very low probability events. Verification test statistics based on historical trading profits and losses have very poor power in small samples, so it does not appear possible for a bank or its supervisor to verify the accuracy of a VaR estimate unless many years of performance data are available. Historical simulation-based verification test statistics also require long samples to generate accurate results: Estimates of 0.01 critical values exhibit substantial errors even in samples as large as ten years of daily data.
                    Hurlin, C., C. Perignon, "Techniques for Verifying the Accuracy of Risk Management Models", Journal of Derivatives, 3, 73-84.
                    Authors: Kupiec
                    Coders: Hurlin
                    Perignon
                    Last update
                    04/17/2012
                    Ranking
                    57
                    Runs
                    26
                    Visits
                    339
                    Outliers and GARCH Models in Financial Data
                    Abstract
                    We propose to extend the additive outlier (AO) identification procedure developed by Franses and Ghijsels(Franses, P.H., Ghijsels, H., 1999. Additive outliers, GARCH and forecasting volatility. International Journal of Forecasting, 15, 1–9) to take into account the innovative outliers (IOs) in a GARCH model. We apply it to three daily stock market indexes and examine the effects of outliers on the diagnostics of normality.
                    Charles, A., and O. Darné, D. Banulescu, E. Dumitrescu, "Outliers and GARCH Models in Financial Data", Economics Letters, 86, 347-352.
                    Authors: Charles
                    Darné
                    Coders: Charles
                    Darné
                    Banulescu
                    Dumitrescu
                    Last update
                    06/22/2012
                    Ranking
                    15
                    Runs
                    61
                    Visits
                    238
                    Extracting Factors from Heteroskedastic Asset Returns
                    Abstract
                    This paper proposes an alternative to the asymptotic principal components procedure of Connor and Korajczyk (Journal of Financial Economics, 1986) that is robust to time series heteroskedasticity in the factor model residuals. The new method is simple to use and requires no assumptions stronger than those made by Connor and Korajczyk. It is demonstrated through simulations and analysis of actual stock market data that allowing heteroskedasticity sometimes improves the quality of the extracted factors quite dramatically. Over the period from 1989 to 1993, for example, a single factor extracted using the Connor and Korajczyk method explains only 8.2% of the variation of the CRSP value-weighted index, while the factor extracted allowing heteroskedasticity explains 57.3%. Accounting for heteroskedasticity is also important for tests of the APT, with p-values sometimes depending strongly on the factor extraction method used.
                    Jones, S. C., "Extracting Factors from Heteroskedastic Asset Returns", Journal of Financial Economics, 62, 293-325.
                    Authors: Jones
                    Coders: Jones
                    Last update
                    11/17/2012
                    Ranking
                    30
                    Runs
                    17
                    Visits
                    81
                    Currency Crises Early Warning Systems: why they should be Dynamic
                    Abstract
                    This paper introduces a new generation of Early Warning Systems (EWS) which takes into account the dynamics, i.e. the persistence in the binary crisis indicator. We elaborate on Kauppi and Saikonnen (2008), which allows to consider several dynamic specifications by re- lying on an exact maximum likelihood estimation method. Applied so as to predict currency crises for fifteen countries, this new EWS turns out to exhibit significantly better predic- tive abilities than the existing models both within and out of the sample, thus vindicating dynamic models in the quest for optimal EWS.
                    Candelon, B., E. Dumitrescu, and C. Hurlin, "Currency Crises Early Warning Systems: why they should be Dynamic", Maastricht University.
                    Authors: Candelon
                    Dumitrescu
                    Hurlin
                    Coders: Candelon
                    Dumitrescu
                    Hurlin
                    Last update
                    06/04/2012
                    Ranking
                    45
                    Runs
                    64
                    Visits
                    112
                    Modeling State Credit Risks in Illinois and Indiana
                    Abstract
                    I use an open-source budget-simulation model to evaluate Illinois’s credit risk and to compare it to that of Indiana, a neighboring state generally believed to have better fiscal management. Based on a review of the history and theory of state credit performance, I assume that a state will default if the aggregate of its interest and pension costs reaches 30 percent of total revenues. In Illinois, this ratio is currently 10 percent, compared to 4 percent in Indiana. My analysis finds that neither state will reach the critical threshold in the next few years under any reasonable economic scenario, suggesting no material default risk. Over the longer term, Illinois has some chance of reaching the default threshold, but it would likely be able to take policy actions to lower the ratio before then. If market participants accept my finding that Illinois does not have material default risk, Illinois’s bond yields willfall, yielding cost savings for taxpayers as the state rolls over its debt.
                    Joffe, D. M., "Modeling State Credit Risks in Illinois and Indiana", Mercatus Center.
                    Authors: Joffe
                    Coders: Joffe
                    Last update
                    08/01/2013
                    Ranking
                    9999
                    Runs
                    N.A.
                    Visits
                    N.A.
                    Pitfalls in backtesting Historical Simulation VaR models
                    Abstract
                    Abstract Historical Simulation (HS) and its variant, the Filtered Historical Simulation (FHS), are the most popular Value-at-Risk forecast methods at commercial banks. These forecast methods are traditionally evaluated by means of the unconditional backtest. This paper formally shows that the unconditional backtest is always inconsistent for backtesting HS and FHS models, with a power function that can be even smaller than the nominal level in large samples. Our findings have fundamental implications in the determination of market risk capital requirements, and also explain Monte Carlo and empirical findings in previous studies. We also propose a data-driven weighted backtest with good power properties to evaluate HS and FHS forecasts. A Monte Carlo study and an empirical application with three US stocks confirm our theoretical findings. The empirical application shows that multiplication factors computed under the current regulatory framework are downward biased, as they inherit the inconsistency of the unconditional backtest.
                    Escanciano, J., and P. Pei, "Pitfalls in backtesting Historical Simulation VaR models", Journal of Banking and Finance, 36, 2233-2244.
                    Authors: Escanciano
                    Pei
                    Coders: Escanciano
                    Pei
                    Last update
                    02/22/2013
                    Ranking
                    9999
                    Runs
                    N.A.
                    Visits
                    32
                    A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics
                    Abstract
                    This paper proposes a new class of asymmetric Student-t (AST) distributions, and investigates its properties, gives procedures for estimation, and indicates applications in financial econometrics. We derive analytical expressions for the cdf, quantile function, moments, and quantities useful in financial econometric applications such as the Expected Shortfall. A stochastic representation of the distribution is also given. Although the AST density does not satisfy the usual regularity conditions for maximum likelihood estimation, we establish consistency, asymptotic normality and efficiency of ML estimators and derive an explicit analytical expression for the asymptotic covariance matrix. A Monte Carlo study indicates generally good finite-sample conformity with these asymptotic properties.
                    Colletaz, G., "A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics", Journal of Econometrics, 157, 297-305.
                    Authors: Zhu
                    Galbraith
                    Coders: Colletaz
                    Last update
                    05/05/2012
                    Ranking
                    38
                    Runs
                    6
                    Visits
                    95
                    Determining the Number of Factors in Approximate Factors Models
                    Abstract
                    In this paper we develop some econometric theory for factor models of large dimensions. The focus is the determination of the number of factors (r), which is an unresolved issue in the rapidly growing literature on multifactor models. We first establish the convergence rate for the factor estimates that will allow for consistent estimation of r. We then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria. The theory is developed under the framework of large cross-sections (N) and large time dimensions (T). No restriction is imposed on the relation between N and T. Simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice.
                    Hurlin, C., "Determining the Number of Factors in Approximate Factors Models", Econometrica, 70, 191-221.
                    Authors: Bai
                    Ng
                    Coders: Hurlin
                    Last update
                    01/29/2013
                    Ranking
                    39
                    Runs
                    66
                    Visits
                    230
                    Unit Root Tests in Panel Data: Asymptotic and Finite-Sample Properties
                    Abstract
                    We consider pooling cross-section time series data for testing the unit root hypothesis. The degree of persistence in individual regression error, the intercept and trend coefficient are allowed to vary freely across individuals. As both the cross-section and time series dimensions of the panel grow large, the pooled t-statistic has a limiting normal distribution that depends on the regression specification but is free from nuisance parameters. Monte Carlo simulations indicate that the asymptotic results provide a good approximation to the test statistics in panels of moderate size, and that the power of the panel-based unit root test is dramatically higher, compared to performing a separate unitroottest for each individual time series.
                    Hurlin, C., "Unit Root Tests in Panel Data: Asymptotic and Finite-Sample Properties", Journal of Econometrics, 108, 1-24.
                    Authors: Levin
                    Lin
                    Chu
                    Coders: Hurlin
                    Last update
                    06/28/2012
                    Ranking
                    37
                    Runs
                    220
                    Visits
                    322
                    Maximum Likelihood Methods for Models of Markets in Disequilibrium
                    Abstract
                    For the abstract, please click on: http://www.jstor.org/discover/10.2307/1914215?uid=3738016&uid=2&uid=4&sid=56146953873
                    Hurlin, C., "Maximum Likelihood Methods for Models of Markets in Disequilibrium", Econometrica, 42, 1013-1030.
                    Authors: Maddala
                    Nelson
                    Coders: Hurlin
                    Last update
                    02/15/2013
                    Ranking
                    50
                    Runs
                    85
                    Visits
                    391
                    A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test
                    Abstract
                    The panel data unit root test suggested by Levin and Lin (LL) has been widely used in several applications, notably in papers on tests of the purchasing power parity hypothesis. This test is based on a very restrictive hypothesis which is rarely ever of interest in practice. The Im–Pesaran–Shin (IPS) test relaxes the restrictive assumption of the LL test. This paper argues that although the IPS test has been offered as a generalization of the LL test, it is best viewed as a test for summarizing the evidence from a number of independent tests of the sample hypothesis. This problem has a long statistical history going back to R. A. Fisher. This paper suggests the Fisher test as a panel data unit root test, compares it with the LL and IPS tests, and the Bonferroni bounds test which is valid for correlated tests. Overall, the evidence points to the Fisher test with bootstrap-based critical values as the preferred choice. We also suggest the use of the Fisher test for testing stationarity as the null and also in testing for cointegration in panel data.
                    Hurlin, C., "A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test", Oxford Bulletin of Economics and Statistics, 61, 631-652.
                    Authors: Maddala
                    Wu
                    Coders: Hurlin
                    Last update
                    10/08/2012
                    Ranking
                    59
                    Runs
                    217
                    Visits
                    129
                    Unit Root Tests for Panel Data
                    Abstract
                    This paper develops unit root tests for panel data. These tests are devised under more general assumptions than the tests previously proposed. First, the number of groups in the panel data is assumed to be either finite or infinite. Second, each group is assumed to have different types of nonstochastic and stochastic components. Third, the time series spans for the groups are assumed to be all different. Fourth, the alternative where some groups have a unit root and others do not can be dealt with by the tests. The tests can also be used for the null of stationarity and for cointegration, once relevant changes are made in the model, hypotheses, assumptions and underlying tests. The main idea for our unit root tests is to combine p-values from a unit root test applied to each group in the panel data. Combining p-values to formulate tests is a common practice in meta-analysis. This paper also reports the finite sample performance of our combination unit root tests and Im et al.'s [Mimeo (1995)] t-bar test. The results show that most of the combination tests are more powerful than the t-bar test in finite samples. Application of the combination unit root tests to the post-Bretton Woods US real exchange rate data provides some evidence in favor of the PPP hypothesis.
                    Hurlin, C., "Unit Root Tests for Panel Data", Journal of International Money and Finance, 20, 249-272.
                    Authors: Choi
                    Coders: Hurlin
                    Last update
                    10/08/2012
                    Ranking
                    60
                    Runs
                    62
                    Visits
                    261
                    Testing for Unit Roots in Heterogeneous Panels
                    Abstract
                    This paper proposes unit root tests for dynamic heterogeneous panels based on the mean of individual unit root statistics. In particular it proposes a standardized t-bar test statistic based on the (augmented) Dickey–Fuller statistics averaged across the groups. Under a general setting this statistic is shown to converge in probability to a standard normal variate sequentially with T (the time series dimension) →∞, followed by N (the cross sectional dimension) →∞. A diagonal convergence result with T and N→∞ while N/T→k,k being a finite non-negative constant, is also conjectured. In the special case where errors in individual Dickey–Fuller (DF) regressions are serially uncorrelated a modified version of the standardized t-bar statistic is shown to be distributed as standard normal as N→∞ for a fixed T, so long as T>5 in the case of DF regressions with intercepts and T>6 in the case of DF regressions with intercepts and linear time trends. An exact fixed N and T test is also developed using the simple average of the DF statistics. Monte Carlo results show that if a large enough lag order is selected for the underlying ADF regressions, then the small sample performances of the t-bar test is reasonably satisfactory and generally better than the test proposed by Levin and Lin (Unpublished manuscript, University of California, San Diego, 1993).
                    Hurlin, C., "Testing for Unit Roots in Heterogeneous Panels ", Journal of Econometrics, 115, 53-74.
                    Authors: Im
                    Pesaran
                    Shin
                    Coders: Hurlin
                    Last update
                    10/08/2012
                    Ranking
                    61
                    Runs
                    57
                    Visits
                    106
                    Testing for a Unit Root in Panels with Dynamic Factors
                    Abstract
                    This paper studies testing for a unit root for large n and T panels in which the cross-sectional units are correlated. To model this cross-sectional correlation, we assume that the data are generated by an unknown number of unobservable common factors. We propose unit root tests in this environment and derive their (Gaussian) asymptotic distribution under the null hypothesis of a unit root and local alternatives. We show that these tests have significant asymptotic power when the model has no incidental trends. However, when there are incidental trends in the model and it is necessary to remove heterogeneous deterministic components, we show that these tests have no power against the same local alternatives. Through Monte Carlo simulations, we provide evidence on the finite sample properties of these new tests.
                    Hurlin, C., "Testing for a Unit Root in Panels with Dynamic Factors", Journal of Econometrics, 122, 81-126.
                    Authors: Moon
                    Perron
                    Coders: Hurlin
                    Last update
                    10/08/2012
                    Ranking
                    62
                    Runs
                    399
                    Visits
                    124
                    Stable Recovery of Sparse Overcomplete Representations in the Presence of Noise
                    Abstract
                    Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in general, the problem of finding sparse representations must be unstable in the presence of noise. This paper establishes the possibility of stable recovery under a combination of sufficient sparsity and favorable structure of the overcomplete system. Considering an ideal underlying signal that has a sufficiently sparse representation, it is assumed that only a noisy version of it can be observed. Assuming further that the overcomplete system is incoherent, it is shown that the optimally sparse approximation to the noisy data differs from the optimally sparse decomposition of the ideal noiseless signal by at most a constant multiple of the noise level. As this optimal-sparsity method requires heavy (combinatorial) computational effort, approximation algorithms are considered. It is shown that similar stability is also available using the basis and the matching pursuit algorithms. Furthermore, it is shown that these methods result in sparse approximation of the noisy data that contains only terms also appearing in the unique sparsest representation of the ideal noiseless sparse signal.
                    Donoho, D., M. Elad, and V. Temlyakov, "Stable Recovery of Sparse Overcomplete Representations in the Presence of Noise", Transactions on Information Theory, 52.
                    Authors: Donoho
                    Elad
                    Temlyakov
                    Coders: Donoho
                    Elad
                    Temlyakov
                    Last update
                    10/08/2012
                    Ranking
                    14
                    Runs
                    10
                    Visits
                    89
                    Tests of Conditional Predictive Ability
                    Abstract
                    We propose a framework for out-of-sample predictive ability testing and forecast selection designed for use in the realistic situation in which the forecasting model is possibly misspecified, due to unmodeled dynamics, unmodeled heterogeneity, incorrect functional form, or any combination of these. Relative to the existing literature (Diebold and Mariano (1995) and West (1996)), we introduce two main innovations: (i) We derive our tests in an environment where the finite sample properties of the estimators on which the forecasts may depend are preserved asymptotically. (ii) We accommodate conditional evaluation objectives (can we predict which forecast will be more accurate at a future date?), which nest unconditional objectives (which forecast was more accurate on average?), that have been the sole focus of previous literature. As a result of (i), our tests have several advantages: they capture the effect of estimation uncertainty on relative forecast performance, they can handle forecasts based on both nested and nonnested models, they allow the forecasts to be produced by general estimation methods, and they are easy to compute. Although both unconditional and conditional approaches are informative, conditioning can help fine-tune the forecast selection to current economic conditions. To this end, we propose a two-step decision rule that uses current information to select the best forecast for the future date of interest. We illustrate the usefulness of our approach by comparing forecasts from leading parameter-reduction methods for macroeconomic forecasting using a large number of predictors.
                    Giacomini, R., "Tests of Conditional Predictive Ability ", Econometrica, 74, 1545-1578.
                    Authors: White
                    Giacomini
                    Coders: Giacomini
                    Last update
                    07/04/2012
                    Ranking
                    25
                    Runs
                    17
                    Visits
                    67
                    On the Stability of the Basis Pursuit in the Presence of Noise
                    Abstract
                    Given a signal S ( R^N and a full-rank matrix D ( R^NL with N<L, we define the signal’s over-complete representation as a ( R^L satisfying S=Da. Among the infinitely many solutions of this under-determined linear system of equations, we have special interest in the sparsest representation, i.e., the one minimizing ||a||0. This problem has a combinatorial flavor to it, and its direct solution is impossible even for moderate L. Approximation algorithms are thus required, and one such appealing technique is the basis pursuit (BP) algorithm. This algorithm has been the focus of recent theoretical research effort. It was found that if indeed the representation is sparse enough, BP finds it accurately. When an error is permitted in the composition of the signal, we no longer require exact equality S=Da. The BP has been extended to treat this case, leading to a denoizing algorithm. The natural question to pose is how the abovementioned theoretical results generalize to this more practical mode of operation. In this paper we propose such a generalization. The behavior of the basis pursuit in the presence of noise has been the subject of two independent very wide contributions released for publication very recently. This paper is another contribution in this direction, but as opposed to the others mentioned, this paper aims to present a somewhat simplified picture of the topic, and thus could be referred to as a primer to this field. Specifically, we establish here the stability of the BP in the presence of noise for sparse enough representations. We study both the case of a general dictionary D, and a special case where D is built as a union of orthonormal bases. This work is a direct generalization of noiseless BP study, and indeed, when the noise power is reduced to zero, we obtain the known results of the noiseless BP.
                    Donoho, D., and M. Elad, "On the Stability of the Basis Pursuit in the Presence of Noise ", Signal Processing , 86 , 511-532.
                    Authors: Donoho
                    Elad
                    Coders: Donoho
                    Elad
                    Last update
                    10/08/2012
                    Ranking
                    29
                    Runs
                    N.A.
                    Visits
                    63
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