Estimating and forecasting partially linear models with non stationary exogeneous variables

TL;DR

This paper introduces a backfitting method for estimating and forecasting periodically correlated partially linear models with exogenous variables, accommodating heteroskedastic noise and unknown periods, with proven convergence rates.

Contribution

It develops a novel backfitting approach for partially linear models with periodic correlation, extending applicability to unknown periods and heteroskedastic noise.

Findings

Estimator convergence rate established

Method effective with unknown periods

Handles heteroskedastic input noise

Abstract

This paper presents a backfitting-type method for estimating and forecasting a periodically correlated partially linear model with exogeneous variables and heteroskedastic input noise. A rate of convergence of the estimator is given. The results are valid even if the period is unknown.