Modelling the distribution of the extreme share returns in Singapore

Tolikas, Konstantinos; Gettinby, G.

doi:10.1016/j.jempfin.2008.06.006

Cited by 29 publications

(23 citation statements)

References 24 publications

(29 reference statements)

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“…[13] Studied the distribution of extreme stock market index on both tails and discovered that the GL distribution characterized the extremes better than the GEV and GP for daily, weekly and monthly financial returns as there is persisting evidence of autocorrelation and heteroskedasticty in the financial data. This owes to the fact that the GL distribution has a fatter tail than the other aforementioned distributions.…”

Section: Methodology Distributionsmentioning

confidence: 99%

“…Therefore, a method of estimating parameters that minimize these errors must be chosen. Parameter estimates for the limiting distributions are calculated using the probability weighted moments (PWM) technique outlined in [9] and [13] instead of the conventional MLE as used in [8] and other researchers. This technique was chosen as it generates more unbiased parameter estimates than popular MLE method for small sample sizes, which is the norm for EVT data sets.…”

Section: Parameter Estimationmentioning

confidence: 99%

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The Distribution Analysis for Extreme Returns of Nikkei 225 Index: Based on the Extreme Value Distribution of GEV and GL

An¹,

Duah²

2017

ABR

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This paper focuses on the problem of modelling extreme events in the financial market. The choice of the distribution that adequately models the extreme behavior of the financial time series. Extreme Value Theory outlines the framework for determining the best fit distribution for the data. The generalized extreme value distribution and the generalized Pareto distribution are the traditional distributions that most analysts resort to using. However, recent works have shown that the generalized logistic distribution can also capture the effect of the extreme due to its fat tailed characteristic. In this paper, we determine appropriate distribution for extreme returns of Nikkei225 Index and analyze the importance of the generalized logistic distribution in modelling extreme events in the financial market in order to accurately conduct risk measure analysis.

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Section: Methodology Distributionsmentioning

confidence: 99%

Section: Parameter Estimationmentioning

confidence: 99%

The Distribution Analysis for Extreme Returns of Nikkei 225 Index: Based on the Extreme Value Distribution of GEV and GL

An¹,

Duah²

2017

ABR

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“…See for eg. [1, 23,24] etc. Also [25] empirically showed that GL is better than GEV to model extreme movements in the stock, commodities and bond markets.…”

Section: Definition 14 a Random Variable X Is Said To Follow The Genmentioning

confidence: 99%

“…Among the various generalization of logistic distribution, the one given by Hosking (see [30]) is called the 5th generalized logistic distribution ( [29]). This form of generalized logistic distribution is used for many real life applications, see for example [1,23,24,30,31]. Motivated by this we introduce the 5th generalized logistic distribution and call this generalization of logistic distribution as generalized logistic distribution.…”

Section: Is Symmetric Distribution Which Belongs To the Domain Of Attmentioning

confidence: 99%

Importance of Generalized Logistic Distribution in Extreme Value Modeling

Nidhin¹,

Chandran²

2013

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We consider a problem from stock market modeling, precisely, choice of adequate distribution of modeling extremal behavior of stock market data. Generalized extreme value (GEV) distribution and generalized Pareto (GP) distribution are the classical distributions for this problem. However, from 2004, [1] and many other researchers have been empirically showing that generalized logistic (GL) distribution is a better model than GEV and GP distributions in modeling extreme movement of stock market data. In this paper, we show that these results are not accidental. We prove the theoretical importance of GL distribution in extreme value modeling. For proving this, we introduce a general multivariate limit theorem and deduce some important multivariate theorems in probability as special cases. By using the theorem, we derive a limit theorem in extreme value theory, where GL distribution plays central role instead of GEV distribution. The proof of this result is parallel to the proof of classical extremal types theorem, in the sense that, it possess important characteristic in classical extreme value theory, for e.g. distributional property, stability, convergence and multivariate extension etc.

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“…The method of L-moments provides nearly unbiased estimates relative to the other estimation methods (less sample variances), and provides a better identifi cation of the parent distribution for a given data sample and more robust results in the presence of outliers, especially in small sample studies [13,23]. Since 1990, L-moments has been widely used by many researchers across the world in a variety of fi elds [24][25][26][27]. In order to avoid undue favor due to outliers in data, a more robust estimation method (i.e., TL-moments as introduced by Elamir and Seheult [11]) can be used.…”

Section: Introductionmentioning

confidence: 99%

Finding Probability Distributions for Annual Daily Maximum Rainfall in Pakistan Using Linear Moments and Variants

Ahmad

Abbass²,

Saghir

et al. 2016

Pol. J. Environ. Stud.

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In this study, at-site frequency analysis (AFA) of an annual daily maximum rainfall (ADMR) series was carried out using the method of linear moments (L-moments) and their variants such as trimmed linear moments (TL-moments) and higher order linear moments (LH-moments). The ADMR series we investigated was observed at 28 meteorological observatories across Pakistan as retrieved from the Pakistan Meteorological Department (PMD). The basic aim of the study was to fi nd best-fi t (i.e., the most suitable) probability distribution among the class of various probability distributions. Initially different goodness-offi t (GOF) measures such as the Kolmogorov-Smirnov test (KST), Anderson-Darling test (ADT), root mean square error (RMSE) and L-moments ratio diagram (LRD) were applied to determine not only the best-fi t distributions but also the best linear estimation method for AFA. We observed that no single probability distribution could be declared as the best-fi t distribution for all the stations. Five distributions were found to be the most appropriate: generalized extreme value (GEV), three parameter lognormal (LN3), Pearson type III (P3), generalized logistic (GLO), and generalized pareto (GPA). The TL-moments method was also applied for parameter estimation to mitigate the effect of outliers on fi nal estimates. LH-moments were used for estimating the upper part of probability distributions and larger events in the data samples. LH moments alleviate the unwanted affects due to small sample values that may be obvious during estimation of events related to larger return periods. Using different GOF tests, we observed that the L-moments method was best for eight stations, TL-moments with trimming (1, 0), and LH-moments with level η =2, 3, 4 were best for six and 14 stations, respectively. A theoretical relationship between TL-moments and LH-moments was also revisited, which revealed that LH-moments are special cases of TL-moments when we are motivated to make trimming only from the lower side.

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Modelling the distribution of the extreme share returns in Singapore

Cited by 29 publications

References 24 publications

The Distribution Analysis for Extreme Returns of Nikkei 225 Index: Based on the Extreme Value Distribution of GEV and GL

The Distribution Analysis for Extreme Returns of Nikkei 225 Index: Based on the Extreme Value Distribution of GEV and GL

Importance of Generalized Logistic Distribution in Extreme Value Modeling

Finding Probability Distributions for Annual Daily Maximum Rainfall in Pakistan Using Linear Moments and Variants

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