Influence of deterministic trend on the estimated parameters of GARCH(1,1) model

TL;DR

This study investigates how deterministic trends influence the estimation of GARCH(1,1) model parameters in financial time series, revealing that longer series are less affected, but certain parameter conditions cause dependency on trend features.

Contribution

The paper provides a Monte Carlo simulation analysis showing the impact of deterministic trends on GARCH(1,1) parameter estimation, highlighting conditions where estimates are sensitive to trend characteristics.

Findings

Longer time series are less affected by detrending errors.

Estimated parameters depend on trend amplitude and structure when ARCH > GARCH coefficients.

Parameter estimates are influenced by the number of trend segments and their ratio to noise.

Abstract

The log returns of financial time series are usually modeled by means of the stationary GARCH(1,1) stochastic process or its generalizations which can not properly describe the nonstationary deterministic components of the original series. We analyze the influence of deterministic trends on the GARCH(1,1) parameters using Monte Carlo simulations. The statistical ensembles contain numerically generated time series composed by GARCH(1,1) noise superposed on deterministic trends. The GARCH(1,1) parameters characteristic for financial time series longer than one year are not affected by the detrending errors. We also show that if the ARCH coefficient is greater than the GARCH coefficient, then the estimated GARCH(1,1) parameters depend on the number of monotonic parts of the trend and on the ratio between the trend and the noise amplitudes.