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on Econometrics |
| By: | Hafner, Christian |
| Abstract: | The maximum likelihood estimator applied to the dynamic conditional correlation model is severely biased in high dimensions. This is, in particular, the case where the cross-section dimension is close to the sample size. It is argued that one of the reasons for the bias lies in an ill-conditioned sample covariance matrix, which is used in the so-called variance targeting technique to match sample and theoretical unconditional covariances. A reduction of the bias is proposed by using shrinkage to target methods for the sample covariance matrix. Alternatively, the identity matrix, a single factor model, and equicorrelation are used as targets. Since the shrinkage intensity decreases towards zero with increasing sample size, the estimator is asymptotically equivalent to the maximum likelihood estimator. The finite sample performance of the proposed estimator over alternative estimators is demonstrated through a Monte Carlo study. Finally, an illustrative application to financial time series compares alternative estimation methods by means of commonly used statistical and economic criteria. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ner:louvai:info:hdl:2078.1/119718&r=ecm |
| By: | Dahlke, Mark |
| Abstract: | Post-stratification is used to improve the precision of survey estimators when categorical auxiliary information is available from external sources. In natural resource surveys, such information may be obtained from remote sensing data classified into categories and displayed as maps. These maps may be based on classification models fitted to the sample data. Such “endogenous post-stratification” violates the standard assumptions that observations are classified without error into post-strata, and post-stratum population counts are known. Properties of the endogenous post-stratification estimator (EPSE) are derived for the case of sample-fitted nonparametric models, with particular emphasis on monotone regression models. Asymptotic properties of the nonparametric EPSE are investigated under a superpopulation model framework. Simulation experiments illustrate the practical effects of first fitting a nonparametric model to survey data before poststratifying |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:ner:louvai:info:hdl:2078.1/127023&r=ecm |
| By: | Heuchenne, Cédric |
| Abstract: | Consider the random vector (X, Y ), where Y represents a response variable and X an explanatory variable. The response Y is subject to random right censoring, whereas X is completely observed. Let m(x) be a conditional location function of Y given X = x. In this paper we assume that m(⋅) belongs to some parametric class M={m_{θ}:θ ∈ Θ} and we propose a new method for estimating the true unknown value θ_{0}. The method is based on nonparametric imputation for the censored observations. The consistency and asymptotic normality of the proposed estimator are established. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ner:louvai:info:hdl:2078.1/127111&r=ecm |
| By: | Comte, Fabienne |
| Abstract: | We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395–408] have shown that a thresholded projection estimator can attain up to a constant minimax-rates of convergence in a general framework which allows us to cover the prediction problem with respect to the mean squared prediction error as well as the estimation of the slope function and its derivatives. This estimation procedure, however, requires an optimal choice of a tuning parameter with regard to certain characteristics of the slope function and the covariance operator associated with the functional regressor. As this information is usually inaccessible in practice, we investigate a fully data-driven choice of the tuning parameter which combines model selection and Lepski’s method. It is inspired by the recent work of Goldenshluger and Lepski [Ann. Statist. 39 (2011) 1608–1632]. The tuning parameter is selected as minimizer of a stochastic penalized contrast function imitating Lepski’s method among a random collection of admissible values. This choice of the tuning parameter depends only on the data and we show that within the general framework the resulting data-driven thresholded projection estimator can attain minimaxrates up to a constant over a variety of classes of slope functions and covariance operators. The results are illustrated considering different configurations which cover in particular the prediction problem as well as the estimation of the slope and its derivatives. A simulation study shows the reasonable performance of the fully data-driven estimation procedure. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ner:louvai:info:hdl:2078.1/127327&r=ecm |
| By: | Johannes, Jan |
| Abstract: | We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. The theory in this pa- per covers in particular point-wise estimation as well as the estimation of weighted averages of the slope parameter. We propose a plug-in estimator which is based on a dimension reduction technique and additional thresh- olding. It is shown that this estimator is consistent under mild assumptions. We derive a lower bound for the maximal mean squared error of any es- timator over a certain ellipsoid of slope parameters and a certain class of covariance operators associated with the regressor. It is shown that the proposed estimator attains this lower bound up to a constant and hence it is minimax optimal. Our results are appropriate to discuss a wide range of possible regressors, slope parameters and functionals. They are illus- trated by considering the point-wise estimation of the slope parameter or its derivatives and its average value over a given interval. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:ner:louvai:info:hdl:2078.1/127331&r=ecm |
| By: | Mutl, Jan (EBS Business School, Wiesbaden, Germany); Sögner, Leopold (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria) |
| Abstract: | We study dynamic panel data models where the long run outcome for a particular crosssection is affected by a weighted average of the outcomes in the other cross-sections. We show that imposing such a structure implies several cointegrating relationships that are nonlinear in the coefficients to be estimated. Assuming that the weights are exogenously given, we extend the dynamic ordinary least squares methodology and provide a dynamic two-stage least squares estimator. We derive the large sample properties of our proposed estimator and investigate its small sample distribution in a simulation study. Then our methodology is applied to US financial market data, which consist of credit default swap spreads, firm specific and industry data. A "closeness" measure for firms is based on inputoutput matrices. Our estimates show that this particular form of spatial correlation of credit default spreads is substantial and highly significant. |
| Keywords: | Dynamic ordinary least squares, cointegration, credit risk, spatial autocorrelation |
| JEL: | C31 C32 |
| Date: | 2013–05 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihsesp:296&r=ecm |
| By: | Segers, Johan |
| Abstract: | The choice for parametric techniques in the discussion article is motivated by the claim that for multivariate extreme-value distributions, “owing to the curse of dimensionality, nonparametric estimation has essentially been confined to the bivariate case” (Section 2.3). Thanks to recent developments, this is no longer true if data take the form of multivariate maxima, as is the case in the article. A wide range of nonparametric, rank-based estimators and tests are nowadays available for extreme-value copulas. Since max-stable processes have extreme-value copulas, these methods are applicable for inference on max-stable processes too. The aim of this note is to make the link between extreme-value copulas and max-stable processes explicit and to review the existing nonparametric inference methods. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ner:louvai:info:hdl:2078.1/127118&r=ecm |
| By: | Mateusz Pipień (National Bank of Poland, Economic Institute) |
| Abstract: | We check the empirical importance of some generalisations of the conditional distribution in M-GARCH case. A copula M-GARCH model with coordinate free conditional distribution is considered, as a continuation of research concerning specification of the conditional distribution in multivariate volatility models, see Pipień (2007) and (2010). The main advantage of the proposed family of probability distributions is that the coordinate axes, along which heavy tails and symmetry can be modelled, are subject to statistical inference. Along a set of specified coordinates both, linear and nonlinear dependence can be expressed in a decomposed form. In the empirical part of the paper we considered a problem of modelling the dynamics of the returns on the spot and future quotations of the WIG20 index from the Warsaw Stock Exchange. On the basis of the posterior odds ratio we checked the data support of considered generalisation, comparing it with BEKK model with the conditional distribution simply constructed as a product of the univariate skewed components. Our example clearly showed the empirical importance of the proposed class of the coordinate free conditional distributions. |
| Keywords: | Bayes factors, multivariate GARCH models, coordinate free distributions, Householder matrices |
| JEL: | C11 C32 C52 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:nbp:nbpmis:151&r=ecm |
| By: | Barbara Rossi; Tatevik Sehkposyan |
| Abstract: | We propose new methods for evaluating predictive densities. The methods include Kolmogorov-Smirnov and Cramer-von Mises-type tests for the correct specification of predictive densities robust to dynamic mis-specification. The novelty is that the tests can detect mis-specification in the predictive densities even if it appears only over a fraction of the sample, due to the presence of instabilities. Our results indicate that our tests are well sized and have good power in detecting mis-specification in predictive densities, even when it is time-varying. An application to density forecasts of the Survey of Professional Forecasters demonstrates the usefulness of the proposed methodologies. |
| Keywords: | predictive density, dynamic mis-specification, instability, structural change, forecast evaluation |
| JEL: | C22 C52 C53 |
| Date: | 2013–02 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:688&r=ecm |
| By: | Wolfgang Polasek (Institute of Advanced Studies, Austria) |
| Abstract: | The mean square error (MSE) compares point forecasts or a location parameter of the forecasting distribution with actual observations by the quadratic loss criterion. This paper shows how the Theil decomposition of the MSE error into a bias, variance and noise component which was proposed for univariate time series can be used to evaluate and compare multiple time series forecasts. Thus, for multivariate time series the ordinary and the alternative Theil decomposition is applied to decompose the MSE matrix. As an alternative we propose the average predictive ordinate criterion (APOC) which evaluates the ordinates of the predictive distribution for comparing forecasts of volatile time series. The multivariate Theil decomposition for the MSE and APOC criterion is used to compare and evaluate 3-dimensional VAR-GARCH-M time series forecasts for stock indices and exchange rates. |
| Keywords: | Forecast comparisons, average predictive ordinate criterion APOC, MSE matrix and multivariate predictions, multivariate and alternative Theil decomposition |
| Date: | 2013–05 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:23_13&r=ecm |
| By: | Songnian Chen (Department of Economics, Hong Kong University of Science and Technology); Shakeeb Khan (Department of Economics, Duke University); Xun Tang (Department of Economics, University of Pennsylvania) |
| Abstract: | We quantify the identifying power of special regressors in heteroskedastic binary regressions with median-independent or conditionally symmetric errors. We measure the identifying power using two criteria: the set of regressor values that help point identify coefficients in latent payoffs as in (Manski 1988); and the Fisher information of coefficients as in (Chamberlain 1986). We find for median-independent errors, requiring one of the regressors to be “special" (in a sense similar to (Lewbel 2000)) does not add to the identifying power or the information for coefficients. Nonetheless it does help identify the error distribution and the average structural function. For conditionally symmetric errors, the presence of a special regressor improves the identifying power by the criterion in (Manski 1988), and the Fisher information for coefficients is strictly positive under mild conditions. We propose a new estimator for coefficients that converges at the parametric rate under symmetric errors and a special regressor, and report its decent performance in small samples through simulations. |
| Keywords: | Binary regression, heteroskedasticity., identification, information, median independence, conditional symmetry |
| JEL: | A12 |
| Date: | 2013–04–16 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:13-021&r=ecm |
| By: | Wojciech Charemza; Carlos Diaz Vela; Svetlana Makarova |
| Abstract: | Issues related to classification, interpretation and estimation of inflationary uncertainties are addressed in the context of their application for constructing probability forecasts of inflation. It is shown that confusions in defining uncertainties lead to potential misunderstandings of such forecasts. The principal source of such confusion is in ignoring the effect of feedback from the policy action undertaken on the basis of forecasts of inflation onto uncertainties. In order to resolve this problem a new class of skew normal distributions (weighted skew normal, WSN) have been proposed and its properties derived. It is shown that parameters of WSN distribution can be interpreted in relation to the monetary policy strength and symmetry. It has been fitted to empirical distributions of inflation multi-step forecast errors of inflation for 34 countries, alongside others distributions already existing in the literature. The estimation method applied is using the minimum distance criteria between the empirical and theoretical distributions. Results lead to some constructive conclusions regarding the strength and asymmetry of monetary policy and confirm the applicability of WSN to producing probabilistic forecasts of inflation. |
| Keywords: | inflation forecasting; uncertainty; monetary policy; non-normality |
| JEL: | C54 E37 E52 |
| Date: | 2013–05 |
| URL: | http://d.repec.org/n?u=RePEc:lec:leecon:13/06&r=ecm |
| By: | Noh, Hohsuk |
| Abstract: | Varying coefficient models are useful extensions of classical lin- ear models. In practice, some of the coefficients may be just constant, while other coefficients are varying. Several methods have been developed to uti- lize the information that some coefficient functions are constant to improve estimation efficiency. However, in order for such methods to really work, the information about which coefficient functions are constant should be given in advance. In this paper, we propose a computationally efficient method to discriminate in a consistent way the constant coefficient functions from the varying ones. Additionally, we compare the performance of our proposal with that of previous methods developed for the same purpose in terms of model selection accuracy and computing time. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ner:louvai:info:hdl:2078.1/127044&r=ecm |
| By: | Timmermans, Catherine |
| Abstract: | Our goal is to predict a scalar value or a group membership from the discretized observation of curves with sharp local features that might vary both vertically and horizontally. To this aim, we propose to combine the use of the nonparametric functional regression estimator developed by Ferraty and Vieu (2006) [18] with the Bagidis semimetric developed by Timmermans and von Sachs (submitted for publication) [36] with a view of efficiently measuring dissimilarities between curves with sharp patterns. This association is revealed as powerful. Under quite general conditions, we first obtain an asymptotic expansion for the small ball probability indicating that Bagidis induces a fractal topology on the functional space. We then provide the rate of convergence of the nonparametric regression estimator in this case, as a function of the parameters of the Bagidis semimetric. We propose to optimize those parameters using a cross-validation procedure, and show the optimality of the selected vector. This last result has a larger scope and concerns the optimization of any vector parameter characterizing a semimetric used in this context. The performances of our methodology are assessed on simulated and real data examples. Results are shown to be superior to those obtained using competing semimetrics as soon as the variations of the significant sharp patterns in the curves have a horizontal component. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:ner:louvai:info:hdl:2078.1/118369&r=ecm |
| By: | Noh, Hohsuk |
| Abstract: | Varying coefficient (VC) models are commonly used to study dynamic patterns in many scientific areas. In particular, VC models in quantile regression are known to provide a more complete description of the response distribution than in mean regression. In this paper, we develop a variable selection method for VC models in quantile regression using a shrinkage idea. The proposed method is based on the basis expansion of each varying coefficient and the regularization penalty on the Euclidean norm of the corresponding coefficient vector. We show that our estimator is obtained as an optimal solution to the second order cone programming (SOCP) problem and that the proposed procedure has consistency in vari- able selection under suitable conditions. Further, we show that the esti- mated relevant coefficients converge to the true functions at the univariate optimal rate. Finally, the method is illustrated with numerical simulations including the analysis of forced expiratory volume (FEV) data. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ner:louvai:info:hdl:2078.1/127117&r=ecm |
| By: | Segers, Johan |
| Abstract: | Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is non-restrictive in the sense that it is needed anyway to ensure that the candidate limiting process exists and has continuous trajectories. In addition, resampling methods based on the multiplier central limit theorem, which require consistent estimation of the first-order derivatives, continue to be valid. Under certain growth conditions on the second-order partial derivatives that allow for explosive behavior near the boundaries, the almost sure rate in Stute’s representation of the empirical copula process can be recovered. The conditions are verified, for instance, in the case of the Gaussian copula with full-rank correlation matrix, many Archimedean copulas, and many extreme-value copulas. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ner:louvai:info:hdl:2078.1/127116&r=ecm |