Low and high prices can improve covariance forecasts: The evidence based on currency rates

• Date: 01 September 2018
• DOI: http://doi.org/10.1002/for.2525
• Author: Piotr Fiszeder
• Published date: 01 September 2018

RESEARCH ARTICLE

Low and high prices can improve covariance forecasts: The

evidence based on currency rates

Piotr Fiszeder

Department of Econometrics and

Statistics, Faculty of Economics Sciences

and Management, Nicolaus Copernicus

University in Torun, Toruń, Poland

Correspondence

Piotr Fiszeder, Department of

Econometrics and Statistics, Faculty of

Economics Sciences and Management,

Nicolaus Copernicus University in Torun,

ul. Gagarina 13a, 87‐100 Toruń, Poland

Email: piotr.fiszeder@umk.pl

Funding information

Narodowe Centrum Nauki, Grant/Award

Number: 2016/21/B/HS4/00662

[Correction added on 27 April 2018, after

first online publication: At the bottom of

page 5, the text “fixed size of 250”was

revised to “fixed size of 500”].

Abstract

In this paper we introduce a new specification of the BEKK model, where its

parameters are estimated with the use of closing and additionally low and high

prices. In an empirical application, we show that the use of additional informa-

tion related to low and high prices in the formulation of the BEKK model

improved the estimation of the covariance matrix of returns and increased

the accuracy of covariance and variance forecasts based on this model, com-

pared with using closing prices only. This analysis was performed for the fol-

lowing three most heavily traded currency pairs in the Forex market: EUR/

USD, USD/JPY, and GBP/USD. The main result obtained in this study is robust

to the applied forecast evaluation criterion. This issue is important from a prac-

tical viewpoint, because daily low and high prices are available with closing

prices for most financial series.

KEYWORDS

covariance of returns, currencies, forecasting, low and highprices, volatility models

1|INTRODUCTION

Volatility plays a key role in many financial and macro-

economic issues. Volatility models of financial instru-

ments that are commonly used in practice are largely

based solely on closing prices. However, the application

of information about low and high prices may lead to

much more accurate estimates of volatility. The outcomes

of empirical and simulation studies show that variance

estimators constructed based on low, high, and addition-

ally open and closing prices are from more than five up

to even more than seven times more efficient than

estimators constructed exclusively on closing prices (see,

e.g., Fiszeder & Perczak, 2013; Garman & Klass, 1980;

Parkinson, 1980; Rogers & Satchell, 1991; Yang & Zhang,

2000). Despite good statistical properties, these estimators

have not found widespread use in empirical studies, due

to the fact of omission of the time dependence of variance.

In recent years, however, numerous dynamic models have

been constructed based on the price range, or its

transformations, which is the difference between high

and low prices (see, e.g., Alizadeh, Brandt, & Diebold,

2002; Brandt & Jones, 2006; Chou, 2005; Mapa, 2003;

Molnar, 2011). Low and high prices were also applied to

construct the likelihood function used for the estimation

of parameters of generalized autoregressive conditional

heteroskedasticity (GARCH) models (see Fiszeder &

Perczak, 2016; Lildholdt, 2002; Venter, de Jongh, &

Griebenow, 2005).

The models in all of the above‐cited studies are for

univariate processes. In financial applications, however,

the use of univariate models rarely turns out to be suffi-

cient. Investment portfolios consist of many assets whose

returns are often related (in the mean or variance) and

additionally have time‐varying conditional variances.

Analysis of the multivariate processes is therefore neces-

sary for the construction and valuation of portfolios of

financial instruments and the management of its risk.

Analyses of multivariate models based on low and high

prices are still at the initial stage of research. The idea of

Received: 16 November 2017 Accepted: 10 February 2018

DOI: 10.1002/for.2525

Journal of Forecasting. 2018;37:641–649. Copyright © 2018 John Wiley & Sons, Ltd.wileyonlinelibrary.com/journal/for 641