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on Econometric Time Series |
| By: | Busettti, F.; Harvey, A. |
| Abstract: | Quantiles provide a comprehensive description of the properties of a variable and tracking changes in quantiles over time using signal extraction methods can be informative. It is shown here how stationarity tests can be generalized to test the null hypothesis that a particular quantile is constant over time by using weighted indicators. Corresponding tests based on expectiles are also proposed; these might be expected to be more powerful for distributions that are not heavy-tailed. Tests for changing dispersion and asymmetry may be based on contrasts between particular quantiles or expectiles. We report Monte Carlo experiments investigating the e¤ectiveness of the proposed tests and then move on to consider how to test for relative time invariance, based on residuals from fitting a time-varying level or trend. Empirical examples, using stock returns and U.S. inflation, provide an indication of the practical importance of the tests. |
| Keywords: | Dispersion; expectiles; quantiles; skewness; stationarity tests; stochastic volatility, value at risk. |
| JEL: | C12 C22 |
| Date: | 2007–03 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:0657&r=ets |
| By: | DeRossi, G.; Harvey, A. |
| Abstract: | A time-varying quantile can be fitted to a sequence of observations by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modified state space signal extraction algorithm. It is shown that such time-varying quantiles satisfy the defining property of fixed quantiles in having the appropriate number of observations above and below. Expectiles are similar to quantiles except that they are defined by tail expectations. Like quantiles, time-varying expectiles can be estimated by a state space signal extraction algorithm and they satisfy properties that generalize the moment conditions associated with fixed expectiles. Time-varying quantiles and expectiles provide information on various aspects of a time series, such as dispersion and asymmetry, while estimates at the end of the series provide the basis for forecasting. Because the state space form can handle irregularly spaced observations, the proposed algorithms can be easily adapted to provide a viable means of computing spline-based non-parametric quantile and expectile regressions. |
| Keywords: | Asymmetric least squares; cubic splines; dispersion; non-parametric regression; quantile regression; signal extraction; state space smoother. |
| JEL: | C14 C22 |
| Date: | 2007–02 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:0660&r=ets |
| By: | Pagan, A.; Pesaran, M.H. |
| Abstract: | This paper considers the implications of the permanent/transitory decomposition of shocks for identification of structural models in the general case where the model might contain more than one permanent structural shock. It provides a simple and intuitive generalization of the in.uential work of Blanchard and Quah (1989), and shows that structural equations for which there are known permanent shocks must have no error correction terms present in them, thereby freeing up the latter to be used as instruments in estimating their parameters. The proposed approach is illustrated by a re-examination of the identification scheme used in a monetary model by Wickens and Motta (2001), and in a well known paper by Gali (1992) which deals with the construction of an IS-LM model with supply-side e¤ects. We show that the latter imposes more short-run restrictions than are needed because of a failure to fully utilize the cointegration information. |
| Keywords: | Permanent shocks, structural identification, error correction models, IS-LM models. |
| JEL: | C30 C32 E10 |
| Date: | 2007–01 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:0662&r=ets |
| By: | Badi H. Baltagi (Center for Policy Research, Maxwell School, Syracuse University, Syracuse, NY 13244-1020); Chihwa Kao (Center for Policy Research, Maxwell School, Syracuse University, Syracuse, NY 13244-1020); Long Liu (Department of Economics, Maxwell School, Syracuse University, Syracuse, NY 13244-1020) |
| Abstract: | This paper studies the asymptotic properties of standard panel data estimators in a simple panel regression model with error component disturbances. Both the regressor and the remainder disturbance term are assumed to be autoregressive and possibly non-stationary. Asymptotic distributions are derived for the standard panel data estimators including ordinary least squares, fixed effects, first-difference, and generalized least squares (GLS) estimators when both T and n are large. We show that all the estimators have asymptotic normal distributions and have different convergence rates dependent on the non-stationarity of the regressors and the remainder disturbances. We show using Monte Carlo experiments that the loss in efficiency of the OLS, FE and FD estimators relative to true GLS can be substantial. |
| Keywords: | Panel data, OLS, Fixed-effects, First-difference, GLS. |
| JEL: | C33 |
| Date: | 2007–05 |
| URL: | http://d.repec.org/n?u=RePEc:max:cprwps:93&r=ets |
| By: | Ashton de Silva; Rob J. Hyndman; Ralph D. Snyder |
| Abstract: | The vector innovation structural time series framework is proposed as a way of modelling a set of related time series. Like all multi-series approaches, the aim is to exploit potential inter-series dependencies to improve the fit and forecasts. A key feature of the framework is that the series are decomposed into common components such as trend and seasonal effects. Equations that describe the evolution of these components through time are used as the sole way of representing the inter-temporal dependencies. The approach is illustrated on a bivariate data set comprising Australian exchange rates of the UK pound and US dollar. Its forecasting capacity is compared to other common single- and multi-series approaches in an experiment using time series from a large macroeconomic database. |
| Keywords: | Vector innovation structural time series, state space model, multivariate time series, exponential smoothing, forecast comparison, vector autoregression. |
| JEL: | C32 C51 C53 |
| Date: | 2007–05 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2007-3&r=ets |
| By: | Ana Beatriz Galvão (Queen Mary, University of London) |
| Abstract: | This paper proposes a new regression model – a smooth transition mixed data sampling (STMIDAS) approach – that captures recurrent changes in the ability of a high frequency variable in predicting a low frequency variable. The STMIDAS regression is employed for testing changes in the ability of financial variables in forecasting US output growth. The estimation of the optimal weights for aggregating weekly data inside the quarter improves the measurement of the predictive ability of the yield curve slope for output growth. Allowing for changes in the impact of the short-rate and the stock returns in future growth is decisive for finding in-sample and out-of-sample evidence of their predictive ability at horizons longer than one year. |
| Keywords: | Smooth transition, MIDAS, Predictive ability, Asset prices, Output growth |
| JEL: | C22 C53 E44 |
| Date: | 2007–05 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp595&r=ets |
| By: | W. Robert Reed (University of Canterbury); Haichun Ye |
| Abstract: | This study employs Monte Carlo experiments to evaluate the performances of a number of common panel data estimators when serial correlation and cross-sectional dependence are both present. It focuses on fixed effects models with less than 100 cross-sectional units and between 10 and 25 time periods (such as are commonly employed in empirical growth studies). Estimator performance is compared on two dimensions: (i) root mean square error and (ii) accuracy of estimated confidence intervals. An innovation of our study is that our simulated panel data sets are designed to look like “real-world” panel data. We find large differences in the performances of the respective estimators. Further, estimators that perform well on efficiency grounds may perform poorly when estimating confidence intervals, and vice versa. Our experimental results form the basis for a set of estimator recommendations. These are applied to “out of sample” simulated panel data sets and found to perform well. |
| Keywords: | Panel Data estimation; Monte Carlo analysis; FGLS; PCSE; Groupwise Heteroscedasticity; Serial Correlation; Cross-sectional Dependence; Stata; EViews |
| JEL: | C23 C15 |
| Date: | 2007–04–30 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:07/01&r=ets |
| By: | Wagner, Martin (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria); Hlouskova, Jaroslava (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria) |
| Abstract: | This paper presents results concerning the performance of both single equation and system panel cointegration tests and estimators. The study considers the tests developed in Pedroni (1999, 2004), Westerlund (2005), Larsson, Lyhagen, and Löthgren (2001) and Breitung (2005); and the estimators developed in Phillips and Moon (1999), Pedroni (2000), Kao and Chiang (2000), Mark and Sul (2003), Pedroni (2001) and Breitung (2005). We study the impact of stable autoregressive roots approaching the unit circle, of I(2) components, of short-run cross-sectional correlation and of cross-unit cointegration on the performance of the tests and estimators. The data are simulated from three-dimensional individual specific VAR systems with cointegrating ranks varying from zero to two for fourteen different panel dimensions. The usual specifications of deterministic components are considered. |
| Keywords: | Cross-sectional dependence, estimator, panel cointegration, simulation study, test |
| JEL: | C12 C15 C23 |
| Date: | 2007–05 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihsesp:210&r=ets |
| By: | Mika Meitz; Pentti Saikkonen |
| Abstract: | This paper studies a class of Markov models which consist of two components. Typically, one of the components is observable and the other is unobservable or `hidden`. Conditions under which geometric ergodicity of the unobservable component is inherited by the joint process formed of the two components are given. This implies existence of initial values such that the joint process is strictly stationary and ?-mixing. In addition to this, conditions for the existence of moments are also obtained and extensions to the case of nonstationary initial values are provided. All these results are applied to a general model which includes as special cases various first order generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive conditional duration (ACD) models with possibly complicated non-linear structures. The results only require mild moment assumptions and in some cases provide necessary and sufficient conditions for geometric ergodicity. |
| Keywords: | Generalized Autoregressive Conditional Heteroskedasticity, Autoregressive Conditional Duration, GARCH-in-mean, Nonlinear Time Series Models, Geometric Erogidicity, Mixing, Strict Stationarity, Existence of Moments, Markov Models |
| JEL: | C10 C22 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:327&r=ets |
| By: | Mika Meitz; Pentti Saikkonen |
| Abstract: | This paper studies the stability of nonlinear autoregressive models with conditionality heteroskedastic errors. We consider a nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a nonlinear first order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. Conditions under which the model is stable in the sense that its Markov chain representation is geometrically ergodic are provided. This implies the existence of an initial distribution such that the process is strictly stationary and ?-mixing. Conditions under which the stationary distribution has finite moments are also given. The results cover several nonlinear specifications recently proposed for both the conditional mean and conditional variance, and only require mild moment conditions. |
| Keywords: | Nonlinear Autoregression, Generalized Autoregressive Conditional Heteroskedasticity, Nonlinear Time Series Models, Geometric Ergodicity, Mixing, Strict Stationarity, Existence of Moments, Markov Models |
| JEL: | C10 C22 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:328&r=ets |
| By: | Silvestro Di Sanzo (Department of Economics, University Of Alicante) |
| Abstract: | Recent studies have showed that it is troublesome, in practice, to distinguish between long memory and nonlinear processes. Therefore, it is of obvious interest to try to capture both features of long memory and non-linearity into a single time series model to be able to assess their relative importance. In this paper we put forward such a model, where we combine the features of long memory and Markov nonlinearity. A Markov Chain Monte Carlo algorithm is proposed to estimate the model and evaluate its forecasting performance using Bayesian predictive densities. The resulting forecasts are a significant improvement over those obtained by the linear long memory and Markov switching models. |
| Keywords: | Markov-Switching models, Bootstrap, Gibbs Sampling |
| JEL: | C11 C15 C22 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:03_07&r=ets |
| By: | Chen, Pu; Chihying, Hsiao |
| Abstract: | Applying a probabilistic causal approach, we define a class of time series causal models (TSCM) based on stationary Bayesian networks. A TSCM can be seen as a structural VAR identified by the causal relations among the variables. We classify TSCMs into observationally equivalent classes by providing a necessary and sufficient condition for the observational equivalence. Applying an automated learning algorithm, we are able to consistently identify the data-generating causal structure up to the class of observational equivalence. In this way we can characterize the empirical testable causal orders among variables based on their observed time series data. It is shown that while an unconstrained VAR model does not imply any causal orders in the variables, a TSCM that contains some empirically testable causal orders implies a restricted SVAR model. We also discuss the relation between the probabilistic causal concept presented in TSCMs and the concept of Granger causality. It is demonstrated in an application example that this methodology can be used to construct structural equations with causal interpretations. |
| Keywords: | Automated Learning, Bayesian Network, Inferred Causation, VAR, Wage-Price Spiral |
| JEL: | C1 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:ifwedp:5529&r=ets |
| By: | Westerlund, Joakim; Basher, Syed A. |
| Abstract: | In this paper, we study the effect that different serial correlation adjustment methods can have on panel cointegration testing. As an example, we consider the very popular tests developed by Pedroni (1999, 2004). Results based on both simulated and real data suggest that different adjustment methods can lead to significant variations in test outcome, and thus also in the conclusions. |
| Keywords: | Panel Data; Cointegration Testing; Parametric and Semiparametric Methods. |
| JEL: | C32 C33 C14 C15 |
| Date: | 2007–05–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:3261&r=ets |