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on Econometric Time Series |
| By: | Miguel A. Delgado; Carlos Velasco |
| Abstract: | We propose an asymptotically distribution-free transform of the sample autocorrelations of residuals in general parametric time series models, possibly non-linear in variables. The residuals autocorrelation function is the basic model checking tool in time series analysis, but it is useless when its distribution is incorrectly approximated because the effects of parameter estimation or of unnoticed higher order serial dependence have not been taken into account. The limiting distribution of residuals sample autocorrelations may be difficult to derive, particularly when the underlying innovations are not independent. However, the transformation we propose is easy to implement and the resulting transformed sample autocorrelations are asymptotically distributed as independent standard normals, providing an useful and intuitive device for model checking by taking over the role of the standard sample autocorrelations. We also discuss in detail alternatives to the classical Box-Pierce and Bartlett's Tp-process tests, showing that our transform entails no efficiency loss under Gaussianity. The finite sample performance of the procedures is examined in the context of a Monte Carlo experiment for the two goodness-of-fit tests discussed in the article. The proposed methodology is applied to modeling the autocovariance structure of the well known chemical process temperature reading data already used for the illustration of other statistical procedures. |
| Keywords: | Residuals autocorrelation function, Asymptotically pivotal statistics, Nonlinear in variables models, Long memory, Higher order serial dependence, Recursive residuals, Model checking, Local alternatives |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:cte:werepe:we101707&r=ets |
| By: | Ibrahim Ahamada (Centre d'Economie de la Sorbonne); Philippe Jolivaldt (Centre d'Economie de la Sorbonne) |
| Abstract: | In this article, we compare the performance of Hodrickk-Prescott and Baxter-King filters with a method of filtering based on the multi-resolution properties of wavelets. We show that overall the three methods remain comparable if the theoretical cyclical component is defined in the usual waveband, ranging between six and thirty two quarters. However the approach based on wavelets provides information about the business cycle, for example, its stability over time which the other two filters do not provide. Based on Monte Carlo simulation experiments, our method applied to the American GDP using growth rate data shows that the estimate of the business cycle component is richer in information than that deduced from the level of GDP and includes additional information about the post 1980 period of great moderation. |
| Keywords: | Filters HP, wavelets, Monte Carlo Simulation, break, business cycles. |
| JEL: | C15 C22 C65 E32 |
| Date: | 2010–03 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:10027&r=ets |
| By: | Ibrahim Ahamada (Centre d'Economie de la Sorbonne); Mohamed Boutahar (GREQAM - Université Aix-Marseille II) |
| Abstract: | Abrupt changes in the unconditional variance of returns have been recently revealed in many empirical studies. In this paper, we show that traditional KPSS-based tests have a low power against nonstationarities stemming from changes in the unconditional variance. More precisely, we show that even under very strong abrupt changes in the unconditional variance, the asymptotic moments of the statistics of these tests remain unchanged. To overcome this problem, we use some CUSUM-based tests adapted for small samples. These tests do not compete with KPSS-based tests and can be considered as complementary. CUSUM-based tests confirm the presence of strong abrupt changes in the unconditional variance of stock returns, whereas KPSS-based tests do not. Consequently, traditional stationary models are not always appropriate to describe stock returns. Finally, we show how a model allowing abrupt changes in the unconditional variance is well appropriate for CAC 40 stock returns. |
| Keywords: | KPSS test, panel stationarity test, unconditional variance, abrupt changes, stock returns, size-power curve. |
| JEL: | C12 C15 C23 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:10028&r=ets |
| By: | Helmut Luetkepohl |
| Abstract: | Despite the fact that many aggregates are nonlinear functions and the aggregation weights of many macroeconomic aggregates are timevarying, much of the literature on forecasting aggregates considers the case of linear aggregates with fixed, time-invariant aggregation weights. In this study a framework for nonlinear contemporaneous aggregation with possibly stochastic or time-varying weights is developed and different predictors for an aggregate are compared theoretically as well as with simulations. Two examples based on European unemployment and inflation series are used to illustrate the virtue of the theoretical setup and the forecasting results. |
| Keywords: | Forecasting, stochastic aggregation, autoregression, moving average,vector autoregressive process |
| JEL: | C32 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2010/11&r=ets |
| By: | Masaaki Fukasawa |
| Abstract: | Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are given; efficient delta hedging strategies with transaction costs and effective discretization schemes for the Euler-Maruyama approximation are constructed. |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1004.2107&r=ets |
| By: | Masaaki Fukasawa |
| Abstract: | The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes price and is uniform in bounded payoff func- tions. The result provides a validation of an existing singular perturbation expansion formula for the fast mean reverting stochastic volatility model. |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1004.2106&r=ets |
| By: | Francq, Christian; Zakoian, Jean-Michel |
| Abstract: | In conditionally heteroskedastic models, the optimal prediction of powers, or logarithms, of the absolute process has a simple expression in terms of the volatility process and an expectation involving the independent process. A standard procedure for estimating this prediction is to estimate the volatility by gaussian quasi-maximum likelihood (QML) in a first step, and to use empirical means based on rescaled innovations to estimate the expectation in a second step. This paper proposes an alternative one-step procedure, based on an appropriate non-gaussian QML estimation of the model, and establishes the asymptotic properties of the two approaches. Their performances are compared for finite-order GARCH models and for the infinite ARCH. For the standard GARCH(p, q) and the Asymmetric Power GARCH(p,q), it is shown that the ARE of the estimators only depends on the prediction problem and some moments of the independent process. An application to indexes of major stock exchanges is proposed. |
| Keywords: | APARCH; Infinite ARCH; Conditional Heteroskedasticity; Efficiency of estimators; GARCH; Prediction; Quasi Maximum Likelihood Estimation |
| JEL: | C13 C22 C01 |
| Date: | 2010–04–17 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:22155&r=ets |