Consistent Estimates for the Near(2) and Nlar(2) Time Series Models

Abstract

Consistent and asymptotically normal estimates for all four parameters of the NEAR(2) and NLAR(2) time series models are obtained. The estimates are given in explicit form and are easy to compute, but with simulation experiments the standard errors are large, especially for small values of the parameters, so very substantial sample sizes may be needed. Hence, from this point of view, the NEAR(2) and NLAR(2) models are of limited practical value. The simulations indicate, however, that reasonably good estimates can be obtained for sample sizes in the range used by Lawrance and Lewis in their investigation of a series of wind data.

Estimation of Parameters in the NLAR(p) Model

“…The results of Karlsen and Tjstheim (1988) are quite similar to the first set of estimates in Tables I and II. As the sample size increases, three sets of estimates seem to converge to the true parameter values, indicating consistency.…”

Zero‐Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros

“…This follows from Slutsky's theorem. We estimate the asymptotic variances and by replacing ( π , α , μ ) by the consistent estimators proposed here in this section. Remark A small simulation study is presented in the Supporting Information in order to observe the finite‐sample performance of the proposed estimators. Remark As suggested by one of the referees, another way to estimate the parameters of our process is the two‐step CLS estimation methods introduced by Karlsen & Tjostheim ().…”

Poisson–geometric INAR(1) process for modeling count time series with overdispersion

“…In simulated samples, cases like these usually happen when μ is very small compared with λ . Remark As suggested by the referees, another way to estimate the parameters of the PGINAR(1) process is the two‐step CLS estimation methods proposed by KARLSEN and TJOSTHEIM (). For more details, see RISTIć et al ().…”