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

Remigijus Leipus, Anne Philippe, Vytautė Pilipauskaitė and Donatas Surgailis

Journal of Multivariate Analysis, 2017, vol. 153, issue C, 121-135

Abstract: 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).

Keywords: Random-coefficient autoregression; Empirical process; Kolmogorov–Smirnov statistic; Goodness-of-fit testing; Kernel density estimator; Panel data (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2016.09.007

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