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on Econometric Time Series |
| By: | Xiaohong Chen (Yale University); Roger Koenker (University of Illinois at Urbana-Champaign); Zhijie Xiao (Boston College) |
| Abstract: | Parametric copulas are shown to be attractive devices for specifying quantile autoregressive models for nonlinear time-series. Estimation of local, quantile-specific copula-based time series models offers some salient advantages over classical global parametric approaches. Consistency and asymptotic normality of the proposed quantile estimators are established under mild conditions, allowing for global misspecification of parametric copulas and marginals, and without assuming any mixing rate condition. These results lead to a general framework for inference and model specification testing of extreme conditional value-at-risk for financial time series data. |
| Keywords: | Quantile autoregression, Copula, Ergodic nonlinear Markov models |
| JEL: | C10 C13 C22 |
| Date: | 2008–10–08 |
| URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:691&r=ets |
| By: | Harvey, A. |
| Abstract: | A copula models the relationships between variables independently of their marginal distributions. When the variables are time series, the copula may change over time. A statistical framework is suggested for tracking these changes over time. When the marginal distribu- tions change, pre-filtering is necessary before constructing the indicator variables on which the tracking of the copula is based. This entails solving an even more basic problem, namely estimating time-varying quantiles. The methods are applied to the Hong Kong and Korean stock market indices. Some interesting movements are detected, particularly after the attack on the Hong Kong dollar in 1997. |
| Keywords: | Concordance, contagion, exponentially weighted moving average; quantiles; signal extraction, tail dependence. |
| JEL: | C14 C22 |
| Date: | 2008–09 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:0839&r=ets |
| By: | Harvey, A.; Chakravarty, T. |
| Abstract: | The GARCH-t model is widely used to predict volatilty. However, modeling the conditional variance as a linear combination of past squared observations may not be the best approach if the standardized observations are non-Gaussian. A simple modi.cation lets the conditional variance, or its logarithm, depend on past values of the score of a t-distribution. The fact that the transformed variable has a beta distribution makes it possible to derive the properties of the resulting models. A practical consequence is that the conditional variance is more resistant to extreme observations. Extensions to deal with leverage and more than one component are discussed, as are the implications of distributions other than Student's t. |
| Keywords: | Conditional heteroskedasticity; leverage; robustness; score; Student's t; volatility. |
| JEL: | C22 G10 |
| Date: | 2008–09 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:0840&r=ets |
| By: | Hugo Gerard; Kristoffer Nimark |
| Abstract: | This paper combines multivariate density forecasts of output growth, inflation and interest rates from a suite of models. An out-of-sample weighting scheme based on the predictive likelihood as proposed by Eklund and Karlsson (2005) and Andersson and Karlsson (2007) is used to combine the models. Three classes of models are considered: a Bayesian vector autoregression (BVAR), a factor-augmented vector autoregression (FAVAR) and a medium-scale dynamic stochastic general equilibrium (DSGE) model. Using Australian data, we find that, at short forecast horizons, the Bayesian VAR model is assigned the most weight, while at intermediate and longer horizons the factor model is preferred. The DSGE model is assigned little weight at all horizons, a result that can be attributed to the DSGE model producing density forecasts that are very wide when compared with the actual distribution of observations. While a density forecast evaluation exercise reveals little formal evidence that the optimally combined densities are superior to those from the best-performing individual model, or a simple equal-weighting scheme, this may be a result of the short sample available. |
| Keywords: | Density forecasts, combining forecasts, predictive criteria |
| Date: | 2008–08 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1117&r=ets |
| By: | Daisuke Nagakura (Institute for Monetary and Economic Studies, Bank of Japan (E-mail: daisuke.nagakura@boj.or.jp)) |
| Abstract: | In this paper, we propose a simple methodology for investigating how shocks to trend and cycle are correlated in unidentified unobserved components models, in which the correlation is not identified. The proposed methodology is applied to U.S. and U.K. real GDP data. We find that the correlation parameters are negative for both countries. We also investigate how changing the identification restriction results in different trend and cycle estimates. It is found that estimates of the trend and cycle can vary substantially depending on the identification restrictions imposed. |
| Keywords: | Business Cycle Analysis, Trend, Cycle, Permanent Component, Transitory Component, Unobserved Components Model |
| JEL: | C01 E32 |
| Date: | 2008–10 |
| URL: | http://d.repec.org/n?u=RePEc:ime:imedps:08-e-24&r=ets |
| By: | In Choi; Eiji Kurozumi |
| Abstract: | In this paper, Mallows'(1973) Cp criterion, Akaike's (1973) AIC, Hurvich and Tsai's (1989) corrected AIC and the BIC of Akaike (1978) and Schwarz (1978) are derived for the leads-and-lags cointegrating regression. Deriving model selection criteria for the leads-and-lags regression is a nontrivial task since the true model is of infinite dimension. This paper justifies using the conventional formulas of those model selection criteria for the leads-and-lags cointegrating regression. The numbers of leads and lags can be selected in scientific ways using the model selection criteria. Simulation results regarding the bias and mean squared error of the long-run coefficient estimates are reported. It is found that the model selection criteria are successful in reducing bias and mean squared error relative to the conventional, fixed selection rules. Among the model selection criteria, the BIC appears to be most successful in reducing MSE, and Cp in reducing bias. We also observe that, in most cases, the selection rules without the restriction that the numbers of the leads and lags be the same have an advantage over those with it. |
| Keywords: | Cointegration, Leads-and-lags regression, AIC, Cor-rected AIC, BIC, Cp |
| Date: | 2008–10 |
| URL: | http://d.repec.org/n?u=RePEc:hst:ghsdps:gd08-006&r=ets |
| By: | Francis X. Diebold (Department of Economics, University of Pennsylvania); Georg H. Strasser (Department of Economics, Boston College) |
| Abstract: | We argue for incorporating the financial economics of market microstructure into the financial econometrics of asset return volatility estimation. In particular, we use market microstructure theory to derive the cross-correlation function between latent returns and market microstructure noise, which feature prominently in the recent volatility literature. The cross-correlation at zero displacement is typically negative, and cross-correlations at nonzero displacements are positive and decay geometrically. If market makers are sufficiently risk averse, however, the cross-correlation pattern is inverted. Our results are useful for assessing the validity of the frequently-assumed independence of latent price and microstructure noise, for explaining observed crosscorrelation patterns, for predicting as-yet undiscovered patterns, and for making informed conjectures as to improved volatility estimation methods. |
| Keywords: | Realized volatility, Market microstructure theory, High-frequency data, Financial econometrics |
| JEL: | G14 G20 D82 D83 C51 |
| Date: | 2008–10–09 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:08-038&r=ets |
| By: | V. V. Chari; Patrick J. Kehoe; Ellen R. McGrattan |
| Abstract: | The central finding of the recent structural vector autoregression (SVAR) literature with a differenced specification of hours is that technology shocks lead to a fall in hours. Researchers have used this finding to argue that real business cycle models are unpromising. We subject this SVAR specification to a natural economic test by showing that when applied to data generated from a multiple-shock business cycle model, the procedure incorrectly concludes that the model could not have generated the data as long as demand shocks play a nontrivial role. We also test another popular specification, which uses the level of hours, and show that with nontrivial demand shocks, it cannot distinguish between real business cycle models and sticky price models. The crux of the problem for both SVAR specifications is that available data necessitate a VAR with a small number of lags and, when demand shocks play a nontrivial role, such a VAR is a poor approximation to the model's infinite order VAR. |
| JEL: | C32 C51 E13 E2 E3 E32 E37 |
| Date: | 2008–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:14430&r=ets |
| By: | Anthony W. Lynch; Jessica A. Wachter |
| Abstract: | Many applications in financial economics use data series with different starting or ending dates. This paper describes estimation methods, based on the generalized method of moments (GMM), which make use of all available data for each moment condition. We introduce two asymptotically equivalent estimators that are consistent, asymptotically normal, and more efficient asymptotically than standard GMM. We apply these methods to estimating predictive regressions in international data and show that the use of the full sample affects point estimates and standard errors for both assets with data available for the full period and assets with data available for a subset of the period. Monte Carlo experiments demonstrate that reductions hold for small-sample standard errors as well as asymptotic ones. These methods are extended to more general patterns of missing data, and are shown to be more efficient than estimators that ignore intervals of the data, and thus more efficient than standard GMM. |
| JEL: | C32 G12 |
| Date: | 2008–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:14411&r=ets |
| By: | Mustapha Belkhouja (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales - CNRS : UMR6579); Imene Mootamri (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales - CNRS : UMR6579); Mohamed Boutahar (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales - CNRS : UMR6579) |
| Abstract: | The aim of this paper is to study the dynamic evolution of inflation rate. The model is constructed by extending the ARFIMA-GARCH to ARFIMA with a time varying GARCH model where the transition from one regime to another is evolving smoothly over time. We show by Monte Carlo experiments that the constancy parameter tests perform well. We apply then this new model on eight countries from Europe, Japan and Canada and find that this model is appropriate for six among these countries. |
| Keywords: | ARFIMA model, Generalised autoregressive conditional heteroscedasticity model, Inflation rate, Long memory process, Nonlinear time series, Time-varying parameter mode |
| Date: | 2008–10–20 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-00331986_v1&r=ets |