Outlier Detection in the Lognormal Logarithmic Conditional Autoregressive Range Model
| DOI | http://doi.org/10.1111/obes.12081 |
| Date | 01 February 2016 |
| Published date | 01 February 2016 |
126
©2014 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 78, 1 (2016) 0305–9049
doi: 10.1111/obes.12081
Outlier Detection in the Lognormal Logarithmic
Conditional Autoregressive Range Model
Min-Hsien Chiang†, Ray Yeutien Chou‡ and Li-Min Wang§
†Institute of International Business, National Cheng Kung University, No.1, University
Road, Tainan City, 701, Taiwan (email: mchiang@mail.ncku.edu.tw)
‡Institute of Economics, Academia Sinica, 128 Academia Road, Section 2,Nankang, Taipei
115, Taiwan (e-mail: rchou@econ.sinica.edu.tw)
§Risk Management Division, Bank SinoPac, 9F., No. 306, Sec. 2, Bade Rd., Zhongshan
Dist.Taipei City 104, Taiwan (e-mail: wanglm06@gmail.com)
Abstract
An outlier detection procedure in the lognormal logarithmic conditional autoregressive
range (lognormal Log-CARR) model is proposed. The proposed test statistic is demon-
strated to be well-sized and to have good power using Monte Carlo simulations.
Furthermore, the outlier detection procedure suffers less from the masking effect caused by
multiple outliers. The results of an empirical investigation show that the proposed method
can effectively detect volatility outliers and improve forecasting accuracy.
I. Introduction
Forecasting return volatility is a major concern in financial analysis with regard to asset
pricing, asset allocation and risk management. In addition to suitable volatility model and
volatility measure, quality data are also essential to obtain good volatility forecasts. In
practice, the observed data could present abnormal observations due to impacts of unusual
events, such as financial crises or critical announcements. Consequently, the accuracy of
parameter estimates and volatility forecasting cannot be guaranteed in the presence of these
extreme observations, i.e. volatility outliers.1
The aim of this paper is thus to develop a volatility outlier detection procedure and to
investigate whether the accuracy of volatility forecasts is influenced by the presence of
outliers. Specifically, influences of additive outliers (AO) and innovative outliers (IO) will
be examined in this paper.
The volatility proxy used in this paper is the price range, which is defined as the
differences between the highest and lowest logarithmic security prices during a predefined
JEL Classification numbers: C22, C53.
1The outliers are an important issue in time series models, such as ARMA models (Fox, 1972; Pe˜na,1990; Chen
and Liu, 1993) and the GARCH-family models (Franses and Ghijsels, 1999; van Dijk, Franses and Lucas, 1999;
Park, 2002; Charles and Darne, 2005, 2006; Charles, 2008; Muler and Yohai, 2002, 2008).
Outlier detection in the lognormal Log-CARR 127
time interval (e.g. an hourly, daily, weekly or monthly frequency). It has been shown in the
literature to be a more effective volatility estimator than return-based ones (e.g. Parkinson,
1980; Andersen and Bollerslev, 1998; Alizadeh, Brandt and Diebold, 2002; Brandt and
Jones, 2006).
We then adopt a specific price range model, the lognormal logarithmic conditional
autoregressive range model2(hereafter, lognormal Log-CARR), for examining possible
volatility outliers.The conditional autoregressive range (CARR) model introduced by Chou
(2005) aims to incorporate the volatility clustering property and to provide more effective
volatilityestimation compared with the retur n-based volatilitymodels, such as the GARCH-
type ones. On the other hand, the ARMA-form of the lognormal Log-CARR model enables
us to achieve volatility outlier detection by modifying the detection procedures used in the
ARMA model of Chen and Liu (1993) to avoid the possible masking effect that can arise
in volatility outlier detection. The proposed test statistics are demonstrated to perform very
well both in size and powersimulations. Further more, weapply the proposed outlier detec-
tion procedure to three stock price range series and demonstrate its effectiveness.
The remainder of this paper is organized as follows: section II introduces the lognor-
mal Log-CARR model. Section III presents the proposed outlier detection method in the
lognormal Log-CARR model, whilesection IV examines the sampling proper ties of the test
statistic and the performance of the outlier detection method.An empirical application of the
proposed method to three stock price range series is given in section V, and finally, section
VI presents the conclusions of this paper.
II. The lognormal Log-CARR model and statistical properties
The CARR model was first proposed by Chou (2005) to examine the dynamic structure of
range series. Similar to the Logarithmic Autoregressive Conditional Duration (Log-ACD)
model of Bauwens and Giot (2000) which is an extension of theACD model of Engle and
Russell (1998), the Log-CARR model proposed also relaxes the positivity restrictions on
parameters of the conditional mean function.
The Log-ACD model
The Log-ACD model of Bauwens and Giot (2000) is defined as follows:3
xi=exp(i)vi,(1)
i=+
p
j=1
jln(xi−j)+
q
l=1
li−l,(2)
where xidenotes the duration, which can be the time elapsed between two consecutive
trades, two consecutive bid-ask quotes, etc. viis usually assumed to follow the distribu-
tions with positive supports, such as exponential and Weibull distributions. iis the func-
2The lognormal Log-CARR model was adopted in Chiang and Wang (2011) as a basic framework to examine the
volatility contagion across stock markets.
3This model is named the Log-ACD1model in Bauwens and Giot (2000). Readers can also see the survey paper
of Pacurar (2008) for details.
©2014 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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