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on Econometric Time Series |
| By: | Christophe Chorro (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Florian Ielpo (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, Pictet Asset Management - Pictet Asset Management) |
| Abstract: | This article discusses the finite distance properties of three likelihood-based estimation strategies for GARCH processes with non-Gaussian conditional distributions : (1) the maximum likelihood approach ; (2) the Quasi maximum Likelihood approach ; (3) a multi-steps recursive estimation approach (REC). We first run a Monte Carlo test which shows that the recursive method may be the most relevant approach for estimation purposes. We then turn to a sample of SP500 returns. We confirm that the REC estimates are statistically dominating the parameters estimated by the two other competing methods. Regardless of the selected model, REC estimates deliver the more stable results. |
| Keywords: | Maximum likelihood method, related-GARCH process, recursive estimation method, mixture of Gaussian distribution, Generalized Hyperbolic distributions, SP500. |
| Date: | 2010–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00523371_v1&r=ets |
| By: | Emmanuel Gobet (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS : UMR7641); Ali Suleiman (ENSIMAG - École nationale supérieure d'informatique et de mathématiques appliquées - Université Joseph Fourier - Grenoble I) |
| Abstract: | For general time-dependent local volatility models, we propose new approximation formulas for the price of call options. This extends previous results of [BGM10b] where stochastic expansions combined with Malliavin calculus were performed to obtain approximation formulas based on the local volatility At The Money. Here, we derive alternative expansions involving the local volatility at strike. Averaging both expansions give even more accurate results. Approximations of the implied volatility are provided as well. |
| Date: | 2010–10–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00523369_v1&r=ets |
| By: | Tschernig, Rolf; Weber, Enzo; Weigand, Roland |
| Abstract: | We propose an extension of structural fractionally integrated vector autoregressive models that avoids certain undesirable effects for impulse responses if long-run identification restrictions are imposed. We derive its Granger representation, investigate the effects of long-run restrictions and clarify their relation to finite-horizon schemes. It is illustrated by asymptotic analysis and simulations that enforcing integer integration orders can have severe consequences for impulse responses. In a system of US real output and aggregate prices effects of structural shocks strongly depend on integration order specification. In the statistically preferred fractional model the long-run restricted shock has only very short-lasting influence on GDP. |
| Keywords: | Long memory; structural VAR; misspecification; GDP; price level |
| JEL: | C32 E3 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:bay:rdwiwi:16901&r=ets |
| By: | Manabu Asai; Michael McAleer (University of Canterbury); Marcelo C. Medeiros |
| Abstract: | A wide variety of conditional and stochastic variance models has been used to estimate latent volatility (or risk). In this paper, we propose a new long memory asymmetric volatility model which captures more flexible asymmetric patterns as compared with existing models. We extend the new specification to realized volatility by taking account of measurement errors, and use the Efficient Importance Sampling technique to estimate the model. As an empirical example, we apply the new model to the realized volatility of Standard and Poor’s 500 Composite Index to show that the new specification of asymmetry significantly improves the goodness of fit, and that the out-of-sample forecasts and Value-at-Risk (VaR) thresholds are satisfactory. Overall, the results of the out-of-sample forecasts show the adequacy of the new asymmetric and long memory volatility model for the period including the global financial crisis. |
| Keywords: | Asymmetric volatility; long memory; realized volatility; measurement errors; efficient importance sampling |
| Date: | 2010–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:10/60&r=ets |
| By: | Andrew Harvey |
| Abstract: | The asymptotic distribution of maximum likelihood estimators is derived for a class of exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models. The result carries over to models for duration and realised volatility that use an exponential link function. A key feature of the model formulation is that the dynamics are driven by the score. |
| Keywords: | Duration models, Gamma distribution, General error distribution, Heteroskedasticity, Leverage, Score Student's t |
| JEL: | C22 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws103620&r=ets |
| By: | Croux, Christophe; Fried, R.; Gijbels, Irène; Mahieu, Koen |
| Abstract: | This paper proposes a robust forecasting method for non-stationary time series. The time series is modelled using non-parametric heteroscedastic regression, and fitted by a localized MM-estimator, combining high robustness and large efficiency. The proposed method is shown to produce reliable forecasts in the presence of outliers, non-linearity, and heteroscedasticity. In the absence of outliers, the forecasts are only slightly less precise than those based on a localized Least Squares estimator. An additional advantage of the MM-estimator is that it provides a robust estimate of the local variability of the time series. |
| Keywords: | Heteroscedasticity; Non-parametric regression; Prediction; Outliers; Robustness; |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:ner:leuven:urn:hdl:123456789/277099&r=ets |
| By: | Todd E. Clark; Michael W. McCracken |
| Abstract: | This chapter provides an overview of pseudo-out-of-sample tests of unconditional predictive ability. We begin by providing an overview of the literature, including both empirical applications and theoretical contributions. We then delineate two distinct methodologies for conducting inference: one based on the analytics in West (1996) and the other based on those in Giacomini and White (2006). These two approaches are then carefully described in the context of pairwise tests of equal forecast accuracy between two models. We consider both non-nested and nested comparisons. Monte Carlo evidence provides some guidance as to when the two forms of analytics are most appropriate, in a nested model context. |
| Keywords: | Economic forecasting |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedlwp:2010-031&r=ets |
| By: | Michael J. Dueker; Michael T. Owyang; Martin Sola |
| Abstract: | Smooth-transition autoregressive (STAR) models have proven to be worthy competitors of Markov-switching models of regime shifts, but the assumption of a time-invariant threshold level does not seem realistic and it holds back this class of models from reaching their potential usefulness. Indeed, an estimate of a time-varying threshold level of unemployment, for example, might serve as a meaningful estimate of the natural rate of unemployment. More precisely, within a STAR framework, one might call the time-varying threshold the “tipping level” rate of unemployment, at which the mean and dynamics of the unemployment rate shift. In addition, once the threshold level is allowed to be time-varying, one can add an error-correction term—between the lagged level of unemployment and the lagged threshold level—to the autoregressive terms in the STAR model. In this way, the time-varying latent threshold level serves dual roles: as a demarcation between regimes and as part of an error-correction term.free rate puzzles, and the occurrence of trading break-downs. |
| Keywords: | Time-series analysis ; Capital assets pricing model ; Unemployment |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedlwp:2010-029&r=ets |
| By: | Todd E. Clark; Michael W. McCracken |
| Abstract: | This paper develops a novel and effective bootstrap method for simulating asymptotic critical values for tests of equal forecast accuracy and encompassing among many nested models. The bootstrap, which combines elements of fixed regressor and wild bootstrap methods, is simple to use. We first derive the asymptotic distributions of tests of equal forecast accuracy and encompassing applied to forecasts from multiple models that nest the benchmark model – that is, reality check tests applied to nested models. We then prove the validity of the bootstrap for these tests. Monte Carlo experiments indicate that our proposed bootstrap has better finite-sample size and power than other methods designed for comparison of non-nested models. We conclude with empirical applications to multiple-model forecasts of commodity prices and GDP growth. |
| Keywords: | Economic forecasting |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedlwp:2010-032&r=ets |
| By: | Leão, Dorival; Ohashi, Alberto |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:ibm:ibmecp:wpe_212&r=ets |
| By: | Buchen, Teresa; Wohlrabe, Klaus |
| Abstract: | This paper evaluates the forecast performance of boosting, a variable selection device, and compares it with the forecast combination schemes and dynamic factor models presented in Stock and Watson (2006). Using the same data set and comparison methodology, we find that boosting is a serious competitor for forecasting US industrial production growth in the short run and that it performs best in the longer run. |
| Keywords: | Forecasting; Boosting; Cross-validation |
| JEL: | C53 E27 |
| Date: | 2010–09–06 |
| URL: | http://d.repec.org/n?u=RePEc:lmu:muenec:11788&r=ets |
| By: | Wolfgang Putschoegl |
| Abstract: | We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on how to further improve the calibration procedure. |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1010.1212&r=ets |
| By: | Boubacar Mainassara, Yacouba |
| Abstract: | This article considers the problem of order selection of the vector autoregressive moving-average models and of the sub-class of the vector autoregressive models under the assumption that the errors are uncorrelated but not necessarily independent. We propose a modified version of the AIC (Akaike information criterion). This criterion requires the estimation of the matrice involved in the asymptotic variance of the quasi-maximum likelihood estimator of these models. Monte carlo experiments show that the proposed modified criterion estimates the model orders more accurately than the standard AIC and AICc (corrected AIC) in large samples and often in small samples. |
| Keywords: | AIC, discrepancy, identification, Kullback-Leibler information, model selection, QMLE, order selection, weak VARMA models. |
| JEL: | C52 C22 C01 |
| Date: | 2010–06–21 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:24981&r=ets |