Time series forecasting using functional partial least square regression with stochastic volatility, GARCH, and exponential smoothing

• Date: 01 April 2018
• Author: Jong‐Min Kim,Hojin Jung
• Published date: 01 April 2018
• DOI: http://doi.org/10.1002/for.2498

Received: 25 January 2017 Revised: 8 June 2017 Accepted: 27 August 2017

DOI: 10.1002/for.2498

RESEARCH ARTICLE

Time series forecasting using functional partial least square

regression with stochastic volatility, GARCH, and

exponential smoothing

Jong-Min Kim1Hojin Jung2

1Statistics Discipline, Division of Science

and Mathematics, University of

Minnesota–Morris, Morris, MN, USA

2School of Economics, Henan University,

Kaifeng, Henan, China

Correspondence

Hojin Jung, School of Economics, Henan

University, Ming Lun Street,Kaifeng,

Henan, 475001, China.

Email: 2hojin.jung@gmail.com

Abstract

We propose a method for improving the predictive ability of standard fore-

casting models used in financial economics. Our approach is based on the

functional partial least squares (FPLS) model, which is capable of avoiding

multicollinearity in regression by efficiently extracting information from the

high-dimensional market data. By using its well-known ability, we can incor-

porate auxiliary variables that improve the predictive accuracy. We provide an

empirical application of our proposed methodology in terms of its ability to pre-

dict the conditional average log return and the volatility of crude oil prices via

exponential smoothing, Bayesian stochastic volatility,and GARCH (generalized

autoregressive conditional heteroskedasticity) models, respectively. In particu-

lar,what we call functional data analysis (FDA) traces in this article are obtained

via the FPLS regression from both the crude oil returns and auxiliary variables of

the exchange rates of major currencies. Forforecast performance evaluation, we

compare out-of-sample forecasting accuracy of the standard models with FDA

traces to the accuracy of the same forecasting models with the observed crude

oil returns, principal component regression (PCR), and least absolute shrink-

age and selection operator (LASSO) models. We find evidence that the standard

models with FDAtraces significantly outperform our competing models. Finally,

they are also compared with the test for superior predictive ability and the reality

check for data snooping. Our empirical results show that our new methodology

significantly improves predictive ability of standard models in forecasting the

latent average log return and the volatility of financial time series.

KEYWORDS

Bayesian stochastic volatility,exponential smoothing method, functional partial least square regres-

sion, forecasting, GARCH

1INTRODUCTION

Recent empirical investigation has been challenged by

high-dimensional datasets in financial economics. Many

financial data are also characterized by high frequency,

so that functional representations naturally arise from

repeated observations. This feature substantially com-

plicates econometric modeling and statistical analysis.

Functional data analysis (FDA) has recently gained

considerable importance in the literature (see Ramsay

Journal of Forecasting. 2018;37:269–280. wileyonlinelibrary.com/journal/for Copyright © 2017 John Wiley & Sons, Ltd. 269