Asymptotic Normality of Estimates in Flexible Seasonal Time Series Model with Weak Dependent Error Terms

TL;DR

This paper establishes the asymptotic normality of local linear estimators in flexible seasonal time series models with weak dependent errors, broadening the understanding of estimator behavior under minimal assumptions.

Contribution

It extends existing results by proving consistency and asymptotic normality of estimators under weak dependence conditions without requiring specific error distributions.

Findings

Asymptotic normality holds under $eta$-mixing conditions.

Results apply to $k$-weak and $eta$-weak dependent error terms.

Estimates are consistent without specifying error distribution.

Abstract

In this article, we consider flexible seasonal time series models which consist of a common trend function over periods and additive individual trend (seasonal effect) functions. The consistency and asymptotic normality of the local linear estimators were obtained under the $\alpha$-mixing conditions and without specifying the error distribution. We develop these results to consistency and asymptotic normality of local linear estimates by using central limit theorems for flexible seasonal time series model, which error terms are $k$-weak dependent and $\lambda$-weak dependent random variables.