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

We discuss nonparametric estimation of the distribution function G(x) of the autoregressive coefficient a∈(−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).