Nonparametric estimation of the distribution of the autoregressive coefficient from panel random-coefficient AR(1) data

TL;DR

This paper develops nonparametric methods to estimate the distribution of autoregressive coefficients in panel AR(1) data, establishing consistency, asymptotic properties, and goodness-of-fit tests, with simulation comparisons to parametric methods.

Contribution

It introduces a nonparametric approach for estimating the distribution of AR(1) coefficients from panel data, including asymptotic theory and goodness-of-fit testing.

Findings

The empirical distribution function is consistent and asymptotically normal.

Kernel density estimators are effective under regularity conditions.

Simulation shows competitive performance with parametric methods.

Abstract

We discuss nonparametric estimation of the distribution function $G(x)$ of the autoregressive coefficient $a \in (-1,1)$ from a panel of $N$ random-coefficient AR(1) data, each of length $n$, by the empirical distribution function of lag 1 sample autocorrelations of individual AR(1) processes. Consistency and asymptotic normality of the empirical distribution function and a class of kernel density estimators is established under some regularity conditions on $G(x)$ as $N$ and $n$ increase to infinity. The Kolmogorov-Smirnov goodness-of-fit test for simple and composite hypotheses of Beta distributed $a$ is discussed. A simulation study for goodness-of-fit testing compares the finite-sample performance of our nonparametric estimator to the performance of its parametric analogue discussed in Beran et al. (2010).