Comparison of forecasting performances: Does normalization and variance stabilization method beat GARCH(1,1)‐type models? Empirical evidence from the stock markets

• Author: Hamdi Emec,Emrah Gulay
• Published date: 01 March 2018
• Date: 01 March 2018
• DOI: http://doi.org/10.1002/for.2478

Received: 1 March 2015 Revised: 28 November 2016 Accepted: 20 April 2017

DOI: 10.1002/for.2478

RESEARCH ARTICLE

Comparison of forecasting performances: Does normalization

and variance stabilization method beat GARCH(1,1)-type

models? Empirical evidence from the stock markets

Emrah Gulay Hamdi Emec

Department of Econometrics, Dokuz Eylul

University,Buca, Izmir, Turkey

Correspondence

Emrah Gulay, Department of Econometrics,

Dokuz Eylul University IIBF,

Dokuzcesmeler Buca, Izmir 35160, Turkey.

Email: gulay.emrah@gmail.com

Abstract

In this paper, we present a comparison between the forecasting performances of

the normalization and variance stabilization method (NoVaS) and the GARCH(1,1),

EGARCH(1,1) and GJR-GARCH(1,1)models. Hence the aim of this study is to com-

pare the out-of-sample forecasting performances of the models used throughout the

study and to show that the NoVaS method is better than GARCH(1,1)-type models

in the context of out-of sample forecasting performance. Westudy the out-of-sample

forecasting performances of GARCH(1,1)-type models and NoVaS method based

on generalized error distribution, unlike normal and Student's t-distribution. Also,

what makes the study different is the use of the return series, calculated logarith-

mically and arithmetically in terms of forecasting performance. For comparing the

out-of-sample forecasting performances, we focused on different datasets, such as

S&P 500, logarithmic and arithmetic B˙

IST 100 return series. The key result of our

analysis is that the NoVaSmethod per formsbetter out-of-sample forecasting perfor-

mance than GARCH(1,1)-type models. The result can offeruseful guidance in model

building for out-of-sample forecasting purposes, aimed at improving forecasting

accuracy.

KEYWORDS

ARCH/GARCH models, financial time series, forecasting, forecasting performance measures, NoVaS,

volatility

1INTRODUCTION

It seems that many researchers who study modeling and fore-

casting volatility, which plays an important role in financial

markets, are becoming increasingly concerned over this field,

especially during the last few years. Portfoliomanagers, orga-

nizations dealing with buying of options, and market regula-

tors are interested in forecasting volatility with proper levels

of accuracy.This is one of t he main reasons whyforecasts that

have to be obtained bring into existence a basic component of

portfolio optimization, derivative pricing and value at risk.

The literature shows that various models have been used

to measure volatility in financial data. It is widely known

that the most successful of these models is the general-

ized autoregressive conditional heteroskedasticity (GARCH)

model, introduced by Bollerslev(1986). The basic idea, which

has an impact on the formation of the ARCH model sug-

gested by Engle (1982), has been shown to be the starting

point of GARCH models. Bollerslev developed the ARCH

models by adding features such as asymmetry, long mem-

ory or structural breaks to the structure of the ARCH model.

The major reason why GARCH models are important for

Journal of Forecasting.2018;37:133–150. wileyonlinelibrary.com/journal/for Copyright © 2017 John Wiley & Sons, Ltd. 133

134 GULAY AND EMEC

practitioners studying financial markets or other disciplines is

based on capturing facts about changing volatility,persistence

and volatility clustering.

Teräsvirta (1996) has shown that GARCH models show

poor forecasting performance. However, nonlinear time series

studies in the literature, such as Clements and Smith (1997),

have found that there are no statistical differences in terms

of forecasting performance when comparing simpler linear

models with nonlinear models, even if estimating under a true

model. At the same time, Andersen and Bollerslev (1998)

indicated in their studies that GARCH models actually show

good performance in forecasting volatility when selecting a

proxy variable, such as historical volatility, for unobservable

volatility. While Lundbergh and Teräsvirta (2002) and Van

Dijk et al. (2002) have reached similar results to Clements

and Smith, Malmsten and Teräsvirta (2004) haveachieved the

same results as Teräsvirta (1996).

The studies that concentrate on improving forecasting

performances of the models have been centered on the

assumption that the errors arise from distinct distributions.

Models estimated under the assumption that the errors fol-

low a normal distribution (ND) have been studied in the

literature for a long time. However, it seems that the mod-

els made their estimates under the assumption that the

errors follow Student's t(ST) or generalized error distribu-

tion (GED), which can be compared with each other with

respect to forecasting performance. The findings of the stud-

ies in the literature emphasize that forecasting performances

out-of-sample and in-sample are very different from each

other (Brzeszczynski & Welfe,2004; Loudon, Watt, & Yadav,

2000). For example, Franses and Ghijsels (1999) showed

that the GARCH(1,1) model, with ST, has the worst fore-

casting performance. In another study (Lopez, 2001) the

authors focused on exchange rates. They compared forecast-

ing performances of the GARCH(1,1) model under different

distributions. As a result of their study, they founddifferences

in forecasting performances. Accuracies in model specifi-

cations or assumptions related to varied distributions are

not sufficient in themselves for modeling volatility. Also, it

is quite clear that numerous forecasting performance mea-

surements have been used in many studies on modeling

volatility. The most common forecasting performance mea-

surements are mean square error (MSE) and mean absolute

error (MAE).

This paper aims to show that the GARCH(1,1) model has

good forecasting performance for squared returns, providing

accurate forecasting performance measurement; good predic-

tors are selected for the model. Also, this paper points out

that the NoVaS method is better than the GARCH(1,1)-type

models in terms of out-of-sample forecasting performance,

and there is no difference in using logarithmic return series

and arithmetic return series with respect to forecasting

volatility.

This paper is organized as follows. Section 2 explains

the concept of volatility; we discuss the reasons affecting

volatility and determinants of changes in volatility. Section 3

contains the literature review.In Section 4, we discuss NoVaS

methodology and present datasets. In Section 5 the empiri-

cal results are discussed. Finally,in Section 6, conclusions are

listed.

2CONCEPT OF VOLATILITY

Volatility, which has an important place in the discipline of

finance, has become a crucial topic for practitioners deal-

ing with financial markets or even the general audience

(Daly, 2011). To illustrate the importance of understanding

volatility, the stock market crash of 1987 in the USA may be

cited as an example.

On October 19, 1987, the Dow Jones Industrial Index

dropped by over508 points from 2246.7 to 1738.4 points. This

decline was the biggest 1-day drop in the Dow's history from

1885 until then. At the same time, this slump was the largest

percentage decline. Despite this, all attention was focused on

the absolute magnitude of the decline. Even though the Dow

Jones Industrial Index fell 190 points or 6.9% on October 13,

1989, this decline elicited reactions among people interested

in the financial markets. A majority of academicians work-

ing in the field of finance asserted that volatility needs to be

calculated as a percentage of change in price or return series

(Schwert, 1990).

One way to examine whether there are any influences on

volatility is to calculate volatility over various frequencies.

Observations based on history indicate that some volatility

clusters are long lived, lasting over 10-year periods, whereas

others are short lived, lasting only a few hours. The main

source of price changes in the market is news about the real

values of an asset. If such news comes out one after the

other, and the data have high frequency, including the news

source, return series show volatility clustering. The causes of

volatility are likely to be pressures and irregularities at higher

frequencies. These pressures and irregularities are mostly

named noises. Macroeconomic and institutional changes are

very likely to be causes of volatility at lower frequencies.

For instance, excess volatility is associated with macroeco-

nomic events in the 1930s. In general, the frequency tells us

about the kind of volatility clustering that will be seen in a

dataset. While low-frequency data allow only low-frequency

or macroeconomic fluctuations, high-frequency data reflect

characteristics of volatility much better (Demetrescu, 2007).

3LITERATURE REVIEW

Predicting and forecasting volatility has become one of the

most interesting topics in financial markets. It follows from