Estimating long memory in panel random-coefficient AR(1) data

TL;DR

This paper develops a method to estimate the tail index of random-coefficient AR(1) processes in panel data, enabling detection of long memory behavior through asymptotic analysis and simulation validation.

Contribution

It introduces a novel estimator for the tail index in panel RCA(1) data and a testing procedure for long memory detection, with proven asymptotic properties.

Findings

Estimator shows good finite-sample performance.

Testing procedure effectively detects long memory.

Asymptotic normality established under specific conditions.

Abstract

It is well-known that random-coefficient AR(1) process can have long memory depending on the index $\beta$ of the tail distribution function of the random coefficient, if it is a regularly varying function at unity. We discuss estimation of $\beta$ from panel data comprising N random-coefficient AR(1) series, each of length T. The estimator of $\beta$ is constructed as a version of the tail index estimator of Goldie and Smith (1987) applied to sample lag 1 autocorrelations of individual time series. Its asymptotic normality is derived under certain conditions on N, T and some parameters of our statistical model. Based on this result, we construct a statistical procedure to test if the panel random-coefficient AR(1) data exhibit long memory. A simulation study illustrates finite-sample performance of the introduced estimator and testing procedure.