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on Econometric Time Series |
| By: | Maurice J.G. Bun; Frank Windmeijer |
| Abstract: | The system GMM estimator for dynamic panel data models combines moment conditions for the model in first differences with moment conditions for the model in levels. It has been shown to improve on the GMM estimator in the first differenced model in terms of bias and root mean squared error. However, we show in this paper that in the covariance stationary panel data AR(1) model the expected values of the concentration parameters in the differenced and levels equations for the crosssection at time t are the same when the variances of the individual heterogeneity and idiosyncratic errors are the same. This indicates a weak instrument problem also for the equation in levels. We show that the 2SLS biases relative to that of the OLS biases are then similar for the equations in differences and levels, as are the size distortions of the Wald tests. These results are shown in a Monte Carlo study to extend to the panel data system GMM estimator. |
| Keywords: | Dynamic Panel Data, System GMM, Weak Instruments |
| JEL: | C12 C13 C23 |
| URL: | http://d.repec.org/n?u=RePEc:bri:uobdis:07/595&r=ets |
| By: | Luc, BAUWENS (UNIVERSITE CATHOLIQUE DE LOUVAIN, Department of Economics); G., STORTI |
| Abstract: | We present a novel GARCH model that accounts for time varying, state dependent, persistence in the volatility dynamics. The proposed model generalizes the component GARCH model of Ding and Granger (1996). The volatility is modelled as a convex combination of unobserved GARCH components where the combination weights are time varying as a function of appropriately chosen state variables. In order to make inference on the model parameters, we develop a Gibbs sampling algorithm. Adopting a fully Bayesian approach allows to easily obtain medium and long term predictions of relevant risk measures such as value at risk and expected shortfall. Finally we discuss the results of an application to a series of daily returns on the S&P500. |
| Keywords: | Persistence, Volatility components, Value-at-risk, Expected short-fall |
| JEL: | C11 C15 C22 |
| Date: | 2007–03–28 |
| URL: | http://d.repec.org/n?u=RePEc:ctl:louvec:2007012&r=ets |
| By: | Pierre Perron (Department of Economics, Boston University); Zhongjun Qu (Department of Economics, Boston University) |
| Abstract: | Recently, there has been an upsurge of interest on the possibility of confusing long memory and structural changes in level. Many studies have documented the fact that when a stationary short memory process is contaminated by level shifts the estimate of the fractional differencing parameter is biased away from zero and the autocovariance function exhibits a slow rate of decay, akin to a long memory process. Yet, no theoretical results are available pertaining to the distributions of the estimates. We fill this gap by analyzing the properties of the log periodogram estimate when the jump component is specified by a simple mixture model. Our theoretical results explain many findings reported and uncover new features. Simulations are presented to highlight the properties of the distributions and to assess the adequacy of our limit results as approximations to the finite sample distributions. Also, we explain how the limit distribution changes as the number of frequencies used varies, a feature that is different from the case with a pure fractionally integrated model. We confront this practical implication to daily SP500 absolute returns and their square roots over the period 1928-2002. Our findings are remarkable, the path of the log periodogram estimates clearly follows a pattern that would obtain if the true underlying process was one of short-memory contaminated by level shifts instead of a pure fractionally integrated process. A simple testing procedure is also proposed, which reinforces this conclusion. |
| Keywords: | structural change, jumps, long memory processes, fractional integration, Poisson process, frequency domain estimates. |
| JEL: | C22 |
| Date: | 2006–12 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2006-016&r=ets |
| By: | Ai Deng (Bates White, LLC); Pierre Perron (Department of Economics, Boston University) |
| Abstract: | We consider the power properties of the CUSUM and CUSUM of squares tests in the presence of a one-time change in the parameters of a linear regression model. A result due to Ploberger and Krämer (1990) is that the CUSUM of squares test has only trivial asymptotic local power in this case, while the CUSUM test has non-trivial local asymptotic power unless the change is orthogonal to the mean regressor. The main theme of the paper is that such conclusions obtained from a local asymptotic framework are not reliable guides to what happens in finite samples. The approach we take is to derive expansions of the test statistics that retain terms related to the magnitude of the change under the alternative hypothesis. This enables us to analyze what happens for non-local to zero breaks. Our theoretical results are able to explain how the power function of the tests can be drastically different depending on whether one deals with a static regression with uncorrelated errors, a static regression with correlated errors, a dynamic regression with lagged dependent variables, or whether a correction for non-Normality is applied in the case of the CUSUM of squares. We discuss in which cases the tests are subject to a non-monotonic power function that goes to zero as the magnitude of the change increases, and uncover some curious properties. All theoretical results are verified to yield good guides to the finite sample power through simulation experiments. We finally highlight the practical importance of our results. |
| Keywords: | Change-point, Mean shift, Local asymptotic power, Recursive residuals, Dynamic models. |
| Date: | 2007–03 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2007-020&r=ets |
| By: | Pierre Perron (Department of Economics, Boston University); Tomoyoshi Yabu (Department of Economics, Boston University) |
| Abstract: | This paper considers the problem of testing for structural changes in the trend function of a univariate time series without any prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. We propose a new approach that builds on the work of Perron and Yabu (2005), based on a Feasible Quasi Generalized Least Squares procedure that uses a superefficient estimate of the sum of autoregressive parameters á when á = 1. In the case of a known break date, the resulting Wald test has a chi- square limit distribution in both the I(0) and I(1) cases. When the break date is unknown, the Exp function of Andrews and Ploberger (1994) yields a test with identical limit distributions in the two cases so that a testing procedure with nearly the same size in the I(0) and I(1) cases can be obtained. To improve the finite sample properties of the tests, we used the bias corrected version of the OLS estimate of á proposed by Roy and Fuller (2001). We show our procedure to be substantially more powerful then currently available alternatives and also to have a power function that is close to that attainable if we knew the true value of á in many cases. The extension to the case of multiple breaks is also discussed. |
| Keywords: | structural change, unit root, median-unbiased estimates, GLS procedure, super efficient estimates. |
| JEL: | C22 |
| Date: | 2007–03 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2007-025&r=ets |