arXiv subjects

Vytaute Pilipauskaite

Publications and source records attributed to Vytaute Pilipauskaite.

3 recordsLinked to original sources

arXiv2019

Sample covariances of random-coefficient AR(1) panel model

The present paper obtains a complete description of the limit distributions of sample covariances in N x n panel data when N and n jointly increase, possibly at different rate. The panel is formed by N independent samples of length n from random-coefficient AR(1) process with the tail distribution function of the random coefficient regularly varying at the unit root with exponent $β$ > 0. We show that for $β$ $\in$ (0, 2) the sample covariances may display a variety of stable and non-stable limit behaviors with stability parameter depending on $β$ and the mutual increase rate of N and n.

math.ST↗

arXiv2019

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

It is well-known that random-coefficient AR(1) process can have long memory depending on the index $β$ of the tail distribution function of the random coefficient, if it is a regularly varying function at unity. We discuss estimation of $β$ from panel data comprising N random-coefficient AR(1) series, each of length T. The estimator of $β$ 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.

math.ST↗

arXiv2013

Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes

We discuss joint temporal and contemporaneous aggregation of $N$ independent copies of AR(1) process with random-coefficient $a \in [0,1)$ when $N$ and time scale $n$ increase at different rate. Assuming that $a$ has a density, regularly varying at $a = 1$ with exponent $-1 < β< 1$, different joint limits of normalized aggregated partial sums are shown to exist when $N^{1/(1+β)}/n$ tends to (i) $\infty$, (ii) 0, (iii) $0 < μ< \infty$. The limit process arising under (iii) admits a Poisson integral representation on $(0,\infty) \times C(\mathbb{R})$ and enjoys "intermediate" properties between fractional Brownian motion limit in (i) and sub-Gaussian limit in (ii).

math.ST↗