Please cite the publication as :
Patilea,
V.,
"Adaptive Estimation of Vector Autoregressive Models with TimeVarying Variance: Application to Testing Linear Causality in Mean",
IRMARINSA and CREST ENSAI.
Please cite the companion website as :
Patilea, V., "Adaptive Estimation of Vector Autoregressive Models with TimeVarying Variance: Application to Testing Linear Causality in Mean", RunMyCode companion website, http://www.execandshare.org/CompanionSite/Site62
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 Grangercauses X1 linearly in mean.  
dimension of the subvector X2  The tests determine if X2 Grangercauses 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/ 
Computing Date  Status  Actions 

Hamdi Raïssi
IRMARINSA
France
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Consider an underdetermined system of linear equations y = Ax with known d*n matrix
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found by linear programming. In classical convex polytope theory, a polytope P is called kneighborly if every set of k
vertices of P span a face of P. Let aj denote the jth column of A, 1<=_j<=_n, let a0 = 0 and
let P denote the convex hull of the aj . We say P is outwardly kneighborly if every subset
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imply that, if A is a typical uniformlydistributed random orthoprojector with n = 2d
and n large, the sparsest nonnegative solution to y = Ax can be found by linear programming
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linear programming.
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Neighborliness of RandomlyProjected Simplices in High Dimensions
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The Phase Transition of Matrix Recovery from Gaussian Measurements Matches the Minimax MSE of Matrix Denoising
Abstract
Let X_0 be an unknown M by N matrix. In matrix recovery,
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= Trace(a_i' X_0) and each a_i is a M by N matrix. For measurement
matrices with Gaussian i.i.d entries, it known that if X_0 is of low rank,
it is recoverable from just a few measurements. A popular approach for matrix
recovery is Nuclear Norm Minimization (NNM): solving the convex optimization
problem min X_* subject to y_i=Trace(a_i' X) for all
1<= i<= n, where  . _* denotes the nuclear norm, namely, the
sum of singular values. Empirical work reveals a phase transition
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rank fraction \rho=r/N and aspect ratio \beta=M/N. Specifically, a curve
\delta^* = \delta^*(\rho;\beta) exists such that, if \delta >
\delta^*(\rho;\beta), NNM typically succeeds, while if \delta <
\delta^*(\rho;\beta), it typically fails.
An apparently quite different problem is matrix denoising in Gaussian noise,
where an unknown M by N matrix X_0 is to be estimated based on direct
noisy measurements Y = X_0 + Z, where the matrix Z has iid Gaussian
entries. It has been empirically observed that, if X_0 has low rank, it may
be recovered quite accurately from the noisy measurement Y. A popular
matrix denoising scheme solves the unconstrained optimization problem
min  Y  X _F^2/2 + \lambda X_*. When optimally tuned,
this scheme achieves the asymptotic minimax MSE, M( \rho ) = \lim_{N>
\infty} \inf_\lambda \sup_{\rank(X) <= \rho * N}
MSE(X,\hat{X}_\lambda).
We report extensive experiments showing that the phase transition
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Measurements) coincides with the minimax risk curve M(\rho) in the second
problem (Matrix Denoising in Gaussian Noise): \delta^*(\rho) = M(\rho),
for any rank fraction 0 < \rho < 1.
Our experiments considered matrices belonging to two constraint classes: real
M by N matrices, of various ranks and aspect ratios, and real symmetric
positive semidefinite N by N matrices, of various ranks. Different
predictions M(\rho) of the phase transition location were used in the two
different cases, and were validated by the experimental data.
Gavish,
M.,
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HighDimensional CentrallySymmetric Polytopes With Neighborliness Proportional to Dimension
Abstract
Let A be a d by n matrix, d < n. Let C be the regular cross polytope (octahedron) in
Rn. It has recently been shown that properties of the centrosymmetric polytope P = AC are
of interest for finding sparse solutions to the underdetermined system of equations y = Ax;
[9]. In particular, it is valuable to know that P is centrally kneighborly.
We study the face numbers of randomlyprojected crosspolytopes in the proportional dimensional
case where dn, where the projector A is chosen uniformly at random from
the Grassmann manifold of ddimensional orthoprojectors of Rn. We derive ?N(d) > 0 with
the property that, for any ? < ?N(d), with overwhelming probability for large d, the number
of kdimensional faces of P = AC is the same as for C, for 0 k d. This implies that
P is centrally bdcneighborly, and its skeleton Skel[? d](P) is combinatorially equivalent to
Skel[? d]©. We display graphs of ?N.
Two weaker notions of neighborliness are also important for understanding sparse solutions
of linear equations: facial neighborliness and sectional neighborliness [9]; we study
both. The weakest, (k, e)facial neighborliness, asks if the kfaces are all simplicial and if
the numbers of kdimensional faces fk(P) >= fk(C)(1  e). We characterize and compute
the critical proportion ?F (d) > 0 at which phase transition occurs in k/d. The other, (k, e)
sectional neighborliness, asks whether all, except for a small fraction epsilon, of the kdimensional
intrinsic sections of P are kdimensional crosspolytopes. (Intrinsic sections intersect P with
kdimensional subspaces spanned by vertices of P.) We characterize and compute a proportion
?S(d) > 0 guaranteeing this property for k/d ~ ? < ?S(d). We display graphs of ?S and
?F.
Donoho,
D.,
"HighDimensional CentrallySymmetric Polytopes With Neighborliness Proportional to Dimension",
Discrete & Computational Geometry, 35, 617652.
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Donoho
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Structural Sign Patterns and Reduced Form Restrictions
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This paper reconsiders the degree to which the signpatterns of hypothesized structural arrays limit the possible outcomes for the signpattern of the corresponding estimated reducedform. The conditions under which any structuralrestrictions would apply were believed to be very narrow, rarely found to apply, and virtually never investigated. As a result, current practice does not test the structural hypothesis in terms of the comparison of the estimated reducedform and the permissible reducedformsignpatterns. This paper shows that such tests are always possible. Namely, that the signpatterns of the hypothesized structural arrays always limit the signpatterns that can be taken on by the estimated reducedform. Given this, it is always possible to falsify a structural hypothesis based only upon the signpattern proposed. Necessary conditions, algorithmic principles, and examples are provided to illustrate the analytic principle and the means of its application.
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G.,
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Testing for Unit Roots in the Presence of Uncertainty Over Both the Trend and Initial Condition
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In this paper we provide a joint treatment of two major problems that surround testing for a unit root in practice: uncertainty as to whether or not a linear deterministic trend is present in the data, and uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not. We suggest decision rules based on the union of rejections of four standard unit root tests (OLS and quasidifferenced demeaned and detrended ADF unit root tests), along with information regarding the magnitude of the trend and initial condition, to allow simultaneously for both trend and initial condition uncertainty.
Colletaz,
G.,
"Testing for Unit Roots in the Presence of Uncertainty Over Both the Trend and Initial Condition",
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How to Forecast LongRun Volatility: Regime Switching and the Estimation of Multifractal Processes
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We propose a discretetime stochastic volatility model in which regime switching serves three purposes. First, changes in regimes capture lowfrequency variations. Second, they specify intermediatefrequency dynamics usually assigned to smooth autoregressive transitions. Finally, highfrequency switches generate substantial outliers. Thus a single mechanism captures three features that are typically viewed as distinct in the literature. Maximumlikelihood estimation is developed and performs well in finite samples. Using exchange rates, we estimate a version of the process with four parameters and more than a thousand states. The multifractal outperforms GARCH, MSGARCH, and FIGARCH in and outofsample. Considerable gains in forecasting accuracy are obtained at horizons of 10 to 50 days.
Calvet,
E.
L.,
and
A.
J.
Fisher,
"How to Forecast LongRun Volatility: Regime Switching and the Estimation of Multifractal Processes",
Journal of Financial Econometrics, 2, 4983.
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Calvet
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Bartlett's Formula for a General Class of Non Linear Processes
Abstract
A Bartletttype formula is proposed for the asymptotic distribution of the sample autocorrelations of nonlinear processes. The asymptotic covariances between sample autocorrelations are expressed as the sum of two terms. The first term corresponds to the standard Bartlett's formula for linear processes, involving only the autocorrelation function of the observed process. The second term, which is specific to nonlinear processes, involves the autocorrelation function of the observed process, the kurtosis of the linear innovation process and the autocorrelation function of its square. This formula is obtained under a symmetry assumption on the linear innovation process. It is illustrated on ARMA–GARCH models and compared to the standard formula. An empirical application on financial time series is proposed.
Francq,
C.,
and
J.
Zakoian,
"Bartlett's Formula for a General Class of Non Linear Processes",
Journal of Time Series Analysis, 30, 449465.
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Francq
Zakoian
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Forcasting Expected Shortfall with a Generalized Asymetric Studentt 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 Studentt 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 GARCHtype 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 Studentt Distribution",
Centre interuniversitaire de recherche en analyse des organisations.
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Galbraith
Zhu
Coders:
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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.
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Hurlin
Perignon
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Testing Interval Forecasts: A GMMBased 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 Jstatistic 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, MonteCarlo 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 expost evaluation of interval forecasts produced by linear versus non linear models.
Dumitrescu,
E.,
C.
Hurlin,
"Testing Interval Forecasts: A GMMBased Approach",
Journal of Forecasting, .
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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 timevarying 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 timevarying 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 timevarying 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 crosssectional analysis, a timeseries 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 longrun relations observed in US postwar 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 nonstationary 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, 19702002
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, 19702002 ",
Economics Bulletin, 30, 15151531.
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 lowrank 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 signaltonoise ratio of the lowrank piece stays constant. The AMSEoptimal choice of hard threshold, in the case of nbyn 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 lowrank matrix we are trying to recover. Hard thresholding at the recommended value to recover an nbyn 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 Noncausality in Heterogeneous Panels
Abstract
This paper proposes a very simple test of Granger (1969) noncausality for hetero
geneous panel data models. Our test statistic is based on the individual Wald statistics
of Granger non causality averaged across the crosssection 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 crosssectional
dependence.
Dumitrescu,
E.,
and
C.
Hurlin,
"Testing for Granger Noncausality 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 ttests, 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, 605625.
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 ClosedForm Approximation Approach
Abstract
When a continuoustime 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 closedform 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.
AïtSahalia,
Y.,
"Maximum Likelihood Estimation of Discretely Sampled Diffusions: A ClosedForm Approximation Approach",
Econometrica, 70, 223262.
Authors:
AïtSahalia
Coders:
AïtSahalia
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 undersampled measurements y = Ax0 . For random matrices with Gaussian i.i.d entries, it is known that, when x0 is ksparse, 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 nonGaussian random matrix ensembles. We consider speciﬁc deterministic matrices including Spikes and Sines, Spikes and Noiselets, Paley Frames, DelsarteGoethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Extensive experiments show that for a typical ksparse 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

CopulaBased 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) crosssectional 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.,
"CopulaBased 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 randomparameters or errorcomponents 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 utilitysponsored programs that offer rebates or loans on highefficiency appliances.
Train,
K.,
"Mixed Logit with Repeated Choices: Households' Choices of Appliance Efficiency Level",
The Review of Economics and Statistics, 80, 647657.
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 noninfrastructure 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 19652001. Using the socalled "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 crosscountry heterogeneity and time instability of the productivity without specification of an exante 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 higherorder 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, 841862.
Authors:
Christoffersen
Coders:
Hurlin
Perignon Last update
03/09/2012
Ranking
32
Runs
57
Visits
167

Backtesting ValueatRisk: A DurationBased 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 ValueatRisk. Our Monte Carlo results show that in realistic situations, the
new durationbased tests have considerably better power properties than the
previously suggested tests.
Hurlin,
C.,
and
C.
Perignon,
"Backtesting ValueatRisk: A DurationBased Approach",
Journal of Financial Econometrics, 2, 84108.
Authors:
Pelletier
Christoffersen
Coders:
Hurlin
Perignon Last update
07/23/2012
Ranking
26
Runs
17
Visits
207

Backtesting ValueatRisk Accuracy: A Simple New Test
Abstract
This paper proposes a new test of valueatrisk (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 ValueatRisk Accuracy: A Simple New Test",
Journal of Risk, 9, 1937.
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 modelfree 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 insample and outofsample 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 SouthAsian countries. Besides, the optimal cutoff 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 semiparametric model to forecast financial volatility. The new model extends the linear nonnegative autoregressive model of BarndorNielsen & 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 outofsample 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 loglinear AR(1) model, and two longmemory 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, lognormals, 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

ValueatRisk (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,
"ValueatRisk (Chapter 5: Computing VaR)",
MacGrawHill, Third Edition.
Authors:
Jorion
Coders:
Hurlin
Perignon Last update
03/19/2012
Ranking
44
Runs
63
Visits
328

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 oneday 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 performancebased 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 simulationbased 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, 7384.
Authors:
Kupiec
Coders:
Hurlin
Perignon Last update
04/17/2012
Ranking
57
Runs
26
Visits
339

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 profitandloss (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 (marketrisk 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

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, 347352.
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 valueweighted index, while the factor extracted allowing heteroskedasticity
explains 57.3%. Accounting for heteroskedasticity is also important for tests of
the APT, with pvalues sometimes depending strongly on the factor extraction method
used.
Jones,
S.
C.,
"Extracting Factors from Heteroskedastic Asset Returns",
Journal of Financial Economics, 62, 293325.
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 opensource budgetsimulation 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 ValueatRisk 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 datadriven 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, 22332244.
Authors:
Escanciano
Pei
Coders:
Escanciano
Pei Last update
02/22/2013
Ranking
9999
Runs
N.A.
Visits
32

A Generalized Asymmetric Studentt Distribution with Application to Financial Econometrics
Abstract
This paper proposes a new class of asymmetric Studentt (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 finitesample conformity with these asymptotic properties.
Colletaz,
G.,
"A Generalized Asymmetric Studentt Distribution with Application to Financial Econometrics",
Journal of Econometrics, 157, 297305.
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 crosssections (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, 191221.
Authors:
Bai
Ng
Coders:
Hurlin
Last update
01/29/2013
Ranking
39
Runs
66
Visits
230

Unit Root Tests in Panel Data: Asymptotic and FiniteSample Properties
Abstract
We consider pooling crosssection 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 crosssection and time series dimensions of the panel grow large, the pooled tstatistic 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 panelbased 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 FiniteSample Properties",
Journal of Econometrics, 108, 124.
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
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 bootstrapbased 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, 631652.
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 pvalues from a unit root test applied to each group in the panel data. Combining pvalues to formulate tests is a common practice in metaanalysis. This paper also reports the finite sample performance of our combination unit root tests and Im et al.'s [Mimeo (1995)] tbar test. The results show that most of the combination tests are more powerful than the tbar test in finite samples. Application of the combination unit root tests to the postBretton 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, 249272.
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 tbar 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 nonnegative 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 tbar 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 tbar 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, 5374.
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 crosssectional units are correlated. To model this crosssectional 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, 81126.
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 optimalsparsity
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 outofsample 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 finetune the forecast
selection to current economic conditions. To this end, we propose a twostep 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
parameterreduction methods for macroeconomic forecasting using a large number of
predictors.
Giacomini,
R.,
"Tests of Conditional Predictive Ability ",
Econometrica, 74, 15451578.
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 fullrank matrix D ( R^NL with N<L, we define the signal’s overcomplete representation as a ( R^L satisfying S=Da. Among the infinitely many solutions of this underdetermined linear system of equations, we have special interest in the sparsest representation, i.e., the one minimizing a0. 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 , 511532.
Authors:
Donoho
Elad
Coders:
Donoho
Elad Last update
10/08/2012
Ranking
29
Runs
N.A.
Visits
63

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