Diagnostic Tests for Non-causal Time Series with Infinite Variance

TL;DR

This paper develops goodness-of-fit tests for non-causal autoregressive time series with infinite variance stable noise, enabling model assessment in data with extreme outliers or bursts.

Contribution

It introduces asymptotic normality results for residual autocorrelations and rank-based tests in non-Gaussian stable noise settings, expanding model diagnostic tools.

Findings

Sample autocorrelation functions of trimmed residuals are asymptotically normal.

Rank correlations of residuals and squared residuals are asymptotically normal.

A variety of portmanteau statistics are applicable for model assessment.

Abstract

We study goodness-of-fit testing for non-causal autoregressive time series with non-Gaussian stable noise. To model time series exhibiting sharp spikes or occasional bursts of outlying observations, the exponent of the non-Gaussian stable variables is assumed to be less than two. Under such conditions, the innovation variables have no finite second moment. We proved that the sample autocorrelation functions of the trimmed residuals are asymptotically normal. Nonparametric tests are also investigated. The rank correlations of the residuals or the squared residuals are shown to be asymptotically normal. Thus, an assortment of portmanteau statistics are available for model assessment.