Abstract
In this paper, we propose parametric and nonparametric locally andasymptotically optimal tests for regression models with superdiagonal bilinear time series errors in short panel data (large n, small T). We establish a local asymptotic normality property– with respect to intercept μ, regression coefficient β, the scale parameter σ of the error, and the parameter b of panel superdiagonal bilinear model (which is the parameter of interest)– for a given density f1 of the error terms. Rank-based versions of optimal parametric tests are provided. This result, which allows, by Hájek’s representation theorem, the construction of locally asymptotically optimal rank-based tests for the null hypothesis b = 0 (absence of panel superdiagonal bilinear model). These tests –at specified innovation densities f1– are optimal (most stringent), but remain valid under any actual underlying density. From contiguity, we obtain the limiting distribution of our test statistics under the null and local sequences of alternatives. The asymptotic relative efficiencies, with respect to the pseudo-Gaussian parametric tests, are derived. A Monte Carlo study confirms the good performance of the proposed tests.
Highlights
Recent evolution in theory and applications has provided very powerful convenient tools for the modelling of time series data, and in the last decades, we have seen a growing interest in nonlinear models
To derive optimal tests, the uniform local asymptotic normality (ULAN) property is established for a class of panel regression models with superdiagonal bilinear time series errors via the quadratic mean differentiability of f 1/2, where f is the density of εi,t
We shall state the uniform local asymptotic normality property for the model (1), with respect to intercept μ, regression coefficient β, scale parameter σ2 and the parameter of interest b, for fixed density f1 ∈ FA, the reader is referred to Le Cam & Yang (2000)
Summary
Recent evolution in theory and applications has provided very powerful convenient tools for the modelling of time series data, and in the last decades, we have seen a growing interest in nonlinear models. To derive optimal tests, the uniform local asymptotic normality (ULAN) property is established for a class of panel regression models with superdiagonal bilinear time series errors via the quadratic mean differentiability of f 1/2, where f is the density of εi,t. This last property (see, Le Cam & Yang, 2000), has recognized success in a variety of testing problems: see, Swensen (1985), Akharif & Hallin (2003), Cassart, Hallin & Paindaveine (2011), Bennala, Hallin & Paindaveine (2012) and Fihri, Akharif, Mellouk & Hallin (2020).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have