EXPLOITING INFINITE VARIANCE THROUGH DUMMY VARIABLES IN NONSTATIONARY AUTOREGRESSIONS

Exploiting Infinite Variance through Dummy Variables in an AR model

In this paper we consider estimation and unit root testing in AR(1) models with infinite variance innovations. Specifically, we study the asymptotic properties of estimators obtained by dummying out ”large” innovations, i.e. exceeding a given threshold. These estimators reflect the common practice of dealing with large residuals by including impulse dummies in the estimated regression. Iterativ...

Prediction Errors in Nonstationary Autoregressions of Infinite Order

Abstract Assume that observations are generated from a nonstationary autoregressive (AR) processes of infinite order. We adopt a finite-order approximation model to predict future observations and obtain an asymptotic expression for the mean-squared prediction error (MSPE) of the least squares predictor. This expression provides the first exact assessment of the impacts of nonstationarity, mode...

Toward optimal multistep forecasts in nonstationary autoregressions (Running title: Forecasting nonstationary autoregressions)

Choice of Variables in Vector Autoregressions∗

Suppose that a dataset with N time series is available. N1 < N of those are the variables of interest. You want to estimate a vector autoregression (VAR) with the variables of interest. Which of the remaining N−N1 variables, if any, should you include in the VAR with the variables of interest? We develop a Bayesian methodology to answer this question. This question arises in most applications o...

Moving 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...