Model Identification for Infinite Variance Autoregressive Processes
نویسندگان
چکیده
We consider model identification for infinite variance autoregressive time series processes. It is shown that a consistent estimate of autoregressive model order can be obtained by minimizing Akaike’s information criterion, and we use all-pass models to identify noncausal autoregressive processes and estimate the order of noncausality (the number of roots of the autoregressive polynomial inside the unit circle in the complex plane). We examine the performance of the order selection procedures for finite samples via simulation, and use the techniques to fit a noncausal autoregressive model to stock market trading volume data. ∗Corresponding author. Department of Statistics, Northwestern University, 2006 Sheridan Road, Evanston, IL 60208, USA. Telephone: 1 847 467 4533. E-mail: [email protected]. JEL classification codes. C13, C22.
منابع مشابه
Title : Empirical processes for infinite variance autoregressive models
Univariate and multivariate empirical processes based on residuals of Infinite variance autoregressive processes are investigated. The results are used to develop tests of independence and Goodness of fit.
متن کاملMoving Average Processes with Infinite Variance
The sample autocorrelation function (acf) of a stationary process has played a central statistical role in traditional time series analysis, where the assumption is made that the marginal distribution has a second moment. Now, the classical methods based on acf are not applicable in heavy tailed modeling. Using the codifference function as dependence measure for such processes be shown it be as...
متن کاملConsistent estimation and order selection for non-stationary autoregressive processes with stable innovations
A possibly non-stationary autoregressive process, of unknown finite order, with possibly infinite-variance innovations is studied. The Ordinary Least Squares autoregressive parameter estimates are shown to be consistent, and their rate of convergence, which depends on the index of stability, α, is established. We also establish consistency of lag-order selection criteria in the non-stationary c...
متن کاملWeighted Least Absolute Deviations Estimation for Arma Models with Infinite Variance
For autoregressive and moving-average (ARMA) models with infinite variance innovations, quasi-likelihood based estimators (such as Whittle’s estimators ) suffer from complex asymptotic distributions depending on unknown tail indices. This makes the statistical inference for such models difficult. In contrast, the least absolute deviations estimators (LADE) are more appealing in dealing with hea...
متن کاملQuantile Inference for Near-integrated Autoregressive Time Series with Infinite Variance
The limiting distribution of the quantile estimate for the autoregressive coefficient of a near-integrated first order autoregressive model with infinite variance errors is derived. Since the limiting distribution depends on the unknown density function of the errors, an empirical likelihood ratio statistic is proposed from which confidence intervals can be constructed for the near unit root mo...
متن کامل