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on Econometric Time Series |
| By: | Peter R. Hansen (Stanford University, Department of Economics, 579 Serra Mall, Stanford, CA 94305-6072, USA & CREATES); Asger Lunde (Aarhus University, School of Economics and Management, Bartholins Allé 10, Aarhus, Denmark & CREATES) |
| Abstract: | An economic time series can often be viewed as a noisy proxy for an underlying economic variable. Measurement errors will influence the dynamic properties of the observed process and may conceal the persistence of the underlying time series. In this paper we develop instrumental variable (IV) methods for extracting information about the latent process. Our framework can be used to estimate the autocorrelation function of the latent volatility process and a key persistence parameter. Our analysis is motivated by the recent literature on realized (volatility) measures, such as the realized variance, that are imperfect estimates of actual volatility. In an empirical analysis using realized measures for the DJIA stocks we find the underlying volatility to be near unit root in all cases. Although standard unit root tests are asymptotically justified, we find them to be misleading in our application despite the large sample. Unit root tests based on the IV estimator have better finite sample properties in this context. |
| Keywords: | Persistence, Autocorrelation Function, Measurement Error, Instrumental Variables, Realized Variance, Realized Kernel, Volatility |
| JEL: | C10 C22 C80 |
| Date: | 2010–02–04 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-08&r=ets |
| By: | George Athanasopoulos; Ashton de Silva |
| Abstract: | In this paper we propose a new set of multivariate stochastic models that capture time varying seasonality within the vector innovations structural time series (VISTS) framework. These models encapsulate exponential smoothing methods in a multivariate setting. The models considered are the local level, local trend and damped trend VISTS models with an additive multivariate seasonal component. We evaluate their performances for forecasting international tourist arrivals from eleven source countries to Australia and New Zealand. |
| Keywords: | Holt-Winters’ method, Stochastic seasonality, Vector innovations state space models. |
| JEL: | C32 C53 |
| Date: | 2010–02–22 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2009-11&r=ets |
| By: | Makram El-Shagi |
| Abstract: | We develop an evolutionary algorithm to estimate Threshold Vector Error Correction models (TVECM) with more than two cointegrated variables. Since disregarding a threshold in cointegration models renders standard approaches to the estimation of the cointegration vectors inefficient, TVECM necessitate a simultaneous estimation of the cointegration vector(s) and the threshold. As far as two cointegrated variables are considered this is commonly achieved by a grid search. However, grid search quickly becomes computationally unfeasible if more than two variables are cointegrated. Therefore, the likelihood function has to be maximized using heuristic approaches. Depending on the precise problem structure the evolutionary approach developed in the present paper for this purpose saves 90 to 99 per cent of the computation time of a grid search. |
| Keywords: | EvolutionaryStrategy,GeneticAlgorithm,TVECM |
| JEL: | C61 C32 |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:iwh:dispap:1-10&r=ets |
| By: | Marcus J Chambers |
| Abstract: | This paper reports the results of an extensive investigation into the use of the jackknife as a method of estimation in stationary autoregressive models. In addition to providing some general theoretical results concerning jackknife methods it is shown that a method based on the use of non-overlapping sub-intervals is found to work particularly well and is capable of reducing bias and root mean squared error (RMSE) compared to ordinary least squares (OLS), subject to a suitable choice of the number of sub-samples, rules-of-thumb for which are provided. The jackknife estimators also outperform OLS when the distribution of the disturbances departs from normality and when it is subject to autoregressive conditional heteroskedasticity. Furthermore the jackknife estimators are much closer to being median-unbiased than their OLS counterparts. |
| Date: | 2010–02–04 |
| URL: | http://d.repec.org/n?u=RePEc:esx:essedp:684&r=ets |
| By: | Marcus J Chambers; Maria Kyriacou |
| Abstract: | This paper analyses the properties of jackknife estimators of the first-order autoregressive coefficient when the time series of interest contains a unit root. It is shown that, when the sub-samples do not overlap, the sub-sample estimators have different limiting distributions from the full-sample estimator and, hence, the jackknife estimator in its usual form does not eliminate fully the first-order bias as intended. The joint moment generating function of the numerator and denominator of these limiting distributions is derived and used to calculate the expectations that determine the optimal jackknife weights. Two methods of avoiding this procedure are proposed and investigated, one based on inclusion of an intercept in the regressions, the other based on adjusting the observations in the sub-samples. Extensions to more general augmented Dickey-Fuller (ADF) regressions are also considered. In addition to the theoretical results extensive simulations reveal the impressive bias reductions that can be obtained with these computationally simple jackknife estimators and they also highlight the importance of correct lag-length selection in ADF regressions. |
| Date: | 2010–02–04 |
| URL: | http://d.repec.org/n?u=RePEc:esx:essedp:685&r=ets |
| By: | Francq, Christian; Zakoian, Jean-Michel |
| Abstract: | We establish the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of a class of multivariate GARCH processes. The conditions are mild and coincide with the minimal ones in the univariate case. In particular, contrary to the current literature on the estimation of multivariate GARCH models, no moment assumption is made on the observed process. Instead, we require strict stationarity, for which a necessary and sufficient condition is established. |
| Keywords: | Asymptotic Normality; Conditional Heteroskedasticity; Consistency; Constant Conditional Correlation; Multivariate GARCH; Quasi Maximum Likelihood Estimation; Strict Stationarity Condition |
| JEL: | C13 C32 C01 |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:20779&r=ets |