Forecasting the volatility of the Australian dollar using high‐frequency data: Does estimator accuracy improve forecast evaluation?

• Author: George Bailey,James M. Steeley
• DOI: http://doi.org/10.1002/ijfe.1723
• Published date: 01 July 2019
• Date: 01 July 2019

RESEARCH ARTICLE

Forecasting the volatility of the Australian dollar using

high‐frequency data: Does estimator accuracy improve

forecast evaluation?

George Bailey | James M. Steeley

School of Management, Keele University,

Keele ST5 5BG, UK

Correspondence

James M. Steeley, School of Management,

Keele University, Keele ST5 5BG, UK.

Email: j.steeley@keele.ac.uk

Abstract

We compare forecasts of the volatility of the Australian dollar exchange rate to

alternative measures of ex post volatility. We develop and apply a simple test

for the improvement in the ability of loss functions to distinguish between fore-

casts when the quality of a volatility estimator is increased. We find that both

realized variance and the daily high–low range provide a significant improve-

ment in loss function convergence relative to squared returns. We find that a

model of stochastic volatility provides the best forecasts for models that use

daily data, and the GARCH(1,1) model provides the best forecast using high‐

frequency data.

KEYWORDS

Australian dollar, exchange rate, high–low range, realized variance, stochastic volatility, volatility

forecasting

1|INTRODUCTION

A key purpose of volatility models is to produce forecasts

of volatility that are useful for the pricing of financial

assets that depend heavily on the evolution of volatility,

such as derivatives, and also for input into economic pol-

icy analysis and forecasting.

1

Because “true”volatility is

unobservable, volatility estimators are required when

one wishes to undertake a comparison of forecasted

values. However, the early studies of volatility forecast

evaluation

2

found that the forecasts performed poorly

when compared with the standard volatility estimator,

squared daily returns. Andersen and Bollerslev (1998)

demonstrated that more sophisticated estimators would

increase the explanatory power offered by the volatility

models and recommended the use of volatility measured

from high‐frequency (intraday) returns, which has

become known as realized variance.

A key consideration in the evaluation of forecasts,

more generally, is the selection of the loss function.

Hansen and Lunde (2005) examined 330 ARCH‐related

models to an exchange rate and a stock return series

and found that different loss functions selected different

models as providing the best volatility forecasts.

3

Combining the two issues, Hansen and Lunde (2006)

and Patton (2011) explore the theoretical and practical

interactions between the selected loss function and the

quality of the volatility estimator. Both papers identify

those loss functions that are less sensitive to the noise

in volatility proxies and show that more sophisticated

measures of volatility are better able to distinguish

between forecasts.

In this paper, we also focus on the interaction between

the choice of volatility estimator and the selection of loss

functions in the evaluation of volatility forecasts but seek

to answer the following specific question. Does the use of

more sophisticated volatility proxies generate greater con-

vergence amongst the forecast rankings across different

loss functions? This is useful knowledge in forecast eval-

uation because, if the answer is yes, it means that the

Received: 30 November 2017 Revised: 21 December 2018 Accepted: 30 December 2018

DOI: 10.1002/ijfe.1723

Int J Fin Econ. 2019;24:1355–1389. © 2019 John Wiley & Sons, Ltd.wileyonlinelibrary.com/journal/ijfe 1355

choice of loss function matters much less than would oth-

erwise be the case.

We contribute and innovate in number of important

ways. Both Hansen and Lunde (2006) and Patton (2011)

examine the volatility of IBM stock returns, over similar

time frames, ending in 2003. We examine an exchange

rate, specifically the Australian dollar/U.S. dollar (AUD/

USD) rate, and over recent years. Although Hansen and

Lunde (2005) did examine an exchange rate in their com-

parison of forecasts, they use only high‐frequency mea-

sures of volatility and, like many volatility forecasting

studies, used the German Mark (or Euro)/USD rate. The

AUD/USD is the fourth highest traded currency pair

(BIS, 2013) and has approximately double the trading

activity of the next two highest currency pairs.

4

The AUD

itself is the fifth highest traded currency, after the USD,

Euro, British Pound, and Japanese Yen. Using this cur-

rency pair, which is still highly traded, avoids the pitfalls

from overworking a dataset and has greater potential to

provide new empirical findings. However, we recognize

that such a narrow empirical application runs the risk that

our findings may be sample specific. So, as a control, we

additionally examine the AUD/USD at a different point

in time (2 years apart), the EUR/USD exchange rate (as a

different asset in the same asset class), and the S&P 500

index (as an asset in a different asset class).

Although Patton (2011) examined forecasts from past

squared returns, using either a rolling window average

or a partial adjustment mechanism, and Hansen and

Lunde (2006) examine forecasts from a small number of

GARCH models, we consider a model of stochastic vola-

tility (Harvey, Ruiz, & Shephard, 1994) as well as a selec-

tion of GARCH models, also relaxing the distributional

assumptions in Hansen and Lunde (2006). Harvey et al.

(1994) showed that the stochastic volatility model fitted

well to four USD exchange rates, and comparisons to

GARCH models for exchange rate data have been con-

ducted by Heynen and Kat (1994), Dunis, Laws, and

Chauvin (2003), and Lopez (2001). However, all of these

studies focus on the cross rates of the USD with the Ger-

man Mark (or Euro), the Japanese Yen, the British

Pound, the Canadian Dollar, and the Swiss Franc, and

none use high‐frequency data. By contrast, Chortareas,

Jiang, and Nankervis (2011) do use high‐frequency data,

but only high‐frequency data, in their comparison of sto-

chastic volatility to (symmetric) GARCH models for

exchange rate data, and also for a subset of the aforemen-

tioned currencies. Moreover, the balance of evidence

from these studies is unable to clearly distinguish

between the forecasts from these two classes of model.

So our study will compare the stochastic volatility model

to a selection of GARCH models using a fresh data set, of

comparable trading activity levels, that includes both low‐

frequency and high‐frequency data. To our knowledge,

our study is the first to examine forecasts of the volatility

of the AUD/USD using the GARCH model applied

directly to high‐frequency data and the first to compare

this to forecasts derived from low‐frequency data.

We use the set of loss functions examined in Hansen

and Lunde (2005), which is broader than, but encom-

passes, those used by Patton (2011) and Hansen and

Lunde (2006). Our selection of volatility estimators is sim-

ilar to Patton (2011). As well as examining squared returns

and realized variance from high frequency returns, he also

considers the range‐based variance estimator of Parkinson

(1980). Although he calibrates the efficiency losses of this

volatility measure relative to those of squared returns and

realized variance measures, like Hansen and Lunde

(2006), he only uses realized variance and squared returns

in his empirical application. We believe our study to be

the first to include all the three measures in the empirical

application. Moreover, we focus on a different asset class

and a much more recent period of time.

The question of whether there is increased conver-

gence across loss functions of relative forecasting perfor-

mance when higher quality volatility estimators are

used is examined only indirectly by Hansen and Lunde

(2006) and Patton (2011). Hansen and Lunde (2006) pro-

vide comparative performance tables for the forecasts

from different models across different loss functions

using either squared returns or realized variance, whereas

Patton (2011) formally tests differences between such

forecasts using the tests proposed by Diebold and

Mariano (1995) and West (1996). In this study, we address

the question directly, by conducting paired ttests of the

mean (across forecasts/models) of the standard deviation

of the loss function rankings (across loss functions). A

smaller value of this mean indicates a greater conver-

gence of the rankings across loss functions, because con-

verged rankings would generate a zero standard deviation

across the loss functions for each model. We supplement

this, with a related procedure, similarly constructed, that

tests whether the ability of loss functions to distinguish

between the first and second best models is enhanced

by using more sophisticated variance estimators.

Our key findings are as follows. Using our test for

ranking convergence, we find that using either a range‐

based estimator (Parkinson, 1980) or a realized variance

estimator rather than squared returns as the measure of

ex post volatility results in a significant increase in the

convergence of loss function rankings. With better quality

measures of volatility, loss functions converge more

strongly on the preferred forecast. This is the case both

for loss functions classified as robust by Patton (2011)

and those not regarded as robust. Moreover, we also find

a significant increase in the ability of loss functions to

1356 BAILEY AND STEELEY

distinguish between the best and the second best models

when either the range measure or the realized variance

are used. Thus, the margin by which the best model is

chosen is significantly increased by using the higher qual-

ity volatility measures.

We find that there are significant differential gains in

terms of loss function ranking convergence by using the

realized variance measure, such that forecast comparison

tests are more able to facilitate the rejection of one or

more competing forecasts against a benchmark forecast.

If squared returns are used as the measure of ex post vol-

atility, the forecast comparison tests are less able to dis-

tinguish between any of the competing forecasts. Taken

together, these results also suggest that although the

range measure may provide an improvement upon the

use of squared returns, and so be a valuable substitute

for realized variance when high‐frequency data is

unavailable or too costly to collect, it is still not going to

be as reliable as using realized variance.

We find that the regression‐based tests are not

enhanced by the use of realized variance for forecasts

derived from daily data, which is in contrast to early stud-

ies, such as Andersen and Bollerslev (1998) but is in line

with more recent studies, such as McMillan and Speight

(2012) and Chortareas et al. (2011). This is the case both

in regard to the regression R

2

and tests of forecast

unbiasedness.

Regarding the specific characteristics of the AUD/USD

exchange rate, we find among the models applied to daily

data that the stochastic volatility model is ranked the

highest by the loss functions and is significantly better

than the next best model when realized variance is used

as the ex post volatility measure. The best performing

GARCH model out of sample is the GJR‐GARCH model,

which reflects significant asymmetries in the volatility in

sample, but that this result is not stable, as in the earlier

sample of the AUD/USD the base‐line GARCH(1,1)

model is preferred, despite also there being asymmetries

in the volatility in sample. These asymmetries imply that

an unanticipated depreciation of the AUD will have a

greater impact of the volatility of the exchange rate than

an unanticipated appreciation, relative to the USD. In

contrast to earlier studies, we find little evidence that

power ARCH models add value to the modelling or fore-

casting of the exchange rate, although again this result

appears to have some sample specificity. We also find

no differences between forecasts generated assuming nor-

mally distributed errors as opposed to those from

t‐distributed errors, although the latter provides a signifi-

cantly better fit in sample.

We find that a GARCH model of daily volatility that is

generated from intraday data provides forecasts that are

superior to the stochastic volatility model from daily data

for most, but not all, loss functions and variance estima-

tors. This is not only the case for the AUD/USD, in both

sample periods, but also for our two control samples. This

result indicates that, as has been found in studies of other

exchange rates and for other asset classes, intraday data

are the most valuable for both evaluating forecasts and

also generating forecasts of daily volatility.

The remainder of the paper proceeds as follows.

Section 2 reviews related literature to provide some con-

text for our work and enable comparisons to our findings

to be drawn. Section 3 describes the stochastic volatility

model and the GARCH models that will be used to fore-

cast the exchange rate, describes the computation of the

ex post volatility measures, and explains the forecast eval-

uation testing procedures. In Section 4, we describe the

data and report the results of the model estimation in

sample and the out of sample forecast evaluations.

Section 5 summarizes and concludes.

2|RELATED LITERATURE

The literature on volatility forecasting and the evalua-

tion of these forecasts are extensive and have grown

alongside the development of models of volatility.

5

However, the literature on evaluating forecasts of

exchange rate volatility is relatively small and so pre-

sents further opportunities for discovery.

6

Our work con-

tributes to a number of literatures including, but not

limited to, the literature on forecasting exchange rates,

both with low‐frequency and high‐frequency data, fore-

cast comparisons using high‐frequency data, and to stud-

ies of specific financial markets, in this case the

AUD/USD exchange rate.

Evaluating forecasts of the volatility of exchange rates

was first undertaken by Taylor (1986) who compared fore-

casts from his AMARCH model with the exponentially

weighted moving average model in Taylor and Kingsman

(1979), using daily data for the £/$ between 1974 and

1982, and marginally favouring the exponentially

weighted moving average model. Forecast comparison

has thereafter broadened out to evaluate forecasts from a

variety of models in the GARCH class, stochastic volatility

models, autoregressive models of squared and absolute

returns, and models including implied volatility from

options. Bera and Higgins (1997), who examined the

weekly $/£ rate between 1985 and 1991, favoured a

GARCH model over a bilinear model, whereas Cumby

et al. (1993), who examine the weekly Yen/$ between

1977 and 1990, favoured an EGARCH model over histori-

cal measures of volatility. By contrast, Figlewski (1997),

who examine the daily DM/$ rate over the period 1971 to

1995, favoured a historical measure over a GARCH model.

Jorion (1995), who examined both the DM/$ and the Yen/$

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