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on Econometric Time Series |
| By: | Demetrescu, Matei; Sibbertsen, Philipp |
| Abstract: | Many time series exhibit unconditional heteroskedasticity, often in addition to conditional one. But such time-varying volatility of the data generating process can have rather adverse effects when inferring about its persistence; e.g. unit root and stationarity tests possess null distributions depending on the so-called variance profile. On the contrary, this is guaranteed if taking protective actions as simple as using White standard errors (which are employed anyway to deal with conditional heteroskedasticity). The paper explores the influence of time-varying volatility on fractionally integrated processes. Concretely, we discuss how to model long memory in the presence of time-varying volatility, and analyze the effects of such nonstationarity on several existing inferential procedures for the fractional integration parameter. Based on asymptotic arguments and Monte Carlo simulations, we show that periodogram-based estimators, such as the local Whittle or the log-periodogram regression estimator, remain consistent, but have asymptotic distributions whose variance depends on the variance profile. Time-domain, regression-based tests for fractional integration retain their validity if White standard errors are used. Finally, the modified range-scale statistic is only affected if the series require adjustment for deterministic components. |
| Keywords: | Time-varying variance, Heteroskedasticity, Persistence, Fractional integration, Modulated process |
| JEL: | C12 C22 |
| Date: | 2014–07 |
| URL: | http://d.repec.org/n?u=RePEc:han:dpaper:dp-531&r=ets |
| By: | K. Nadarajah; Gael M. Martin; D.S. Poskitt |
| Abstract: | In this paper we quantify the impact of model mis-specification on the properties of parameter estimators applied to fractionally integrated processes. We demonstrate the asymptotic equivalence of four alternative parametric methods: frequency domain maximum likelihood, Whittle estimation, time domain maximum likelihood and conditional sum of squares. We show that all four estimators converge to the same pseudo-true value and provide an analytical representation of their (common) asymptotic distribution. As well as providing theoretical insights, we explore the finite sample properties of the alternative estimators when used to fit mis-specified models. In particular we demonstrate that when the difference between the true and pseudo-true values of the long memory parameter is sufficiently large, a clear distinction between the frequency domain and time domain estimators can be observed - in terms of the accuracy with which the finite sample distributions replicate the common asymptotic distribution - with the time domain estimators exhibiting a closer match overall. Simulation experiments also demonstrate that the two time-domain estimators have the smallest bias and mean squared error as estimators of the pseudo-true value of the long memory parameter, with conditional sum of squares being the most accurate estimator overall and having a relative efficiency that is approximately double that of frequency domain maximum likelihood, across a range of mis-specification designs. |
| Keywords: | nd phrases: bias, conditional sum of squares, frequency domain, long memory models, maximum likelihood, mean squared error, pseudo true parameter, time domain, Whittle. |
| JEL: | C18 C22 C52 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2014-18&r=ets |
| By: | Norman Swanson (Rutgers University); Richard Urbach (Conning Germany Gmbh) |
| Abstract: | In this paper, we provide new evidence on the empirical usefulness of various simple seasonal models, and underscore the importance of carefully designing criteria by which one judges alternative models. In particular, we underscore the importance of both choice of forecast or simulation horizon and choice between minimizing point or distribution based loss measures. Our empirical analysis centers around the implementation of a series of simulation and prediction experiments, as well as a discussion of the stochastic properties of seasonal unit root models. Our prediction experiments are based on analysis of a group of 14 variables have been chosen to closely mimic the set of indicators used by the Federal Reserve to help in setting U.S. monetary policy, and our simulation experiments are based on a comparison of simulated and historical distributions of said variables using the testing approach of Corradi and Swanson (2007a). |
| Keywords: | seasonal unit root, periodic autoregression, difference stationary |
| JEL: | C13 C22 C52 |
| Date: | 2013–08–10 |
| URL: | http://d.repec.org/n?u=RePEc:rut:rutres:201323&r=ets |