TITLE:
Optimal Threshold Determination for Securities Exchange Volumes Using Improved Maximum Product of Spacing Methodology
AUTHORS:
Peter Murage, Joseph Mung’atu, Everlyne Odero
KEYWORDS:
Extreme Value Theory (EVT), Maximum Product of Spacing (MPS), Generalized Pareto Distribution (GPD), Peaks over Threshold (POT), Nairobi Securities Exchange (NSE)
JOURNAL NAME:
Open Journal of Statistics,
Vol.9 No.3,
June
18,
2019
ABSTRACT: To
Statisticians, the structure of the extreme levels which exist in the tails of
the ordinary distributions is very important in analyzing, predicting and
forecasting the likelihood of an occurrence of extreme event. Extreme events
are defined as values of the event below or above a certain value called
threshold. A well chosen threshold helps to identify the extreme levels. Several methods
have been used to determine threshold so as to analyze and model extreme
events. One of the most successful methods is the
maximum product of spacing (MPS). However, there is a problem
encountered while modeling data through this method in that the method breaks
down when there is a tie in the exceedances. This study offers a solution to
model data even when it contains ties. In the study, a method that improved MPS
method for determining an optimal threshold for extreme values in a data set
containing ties was derived. The Generalized Pareto Distribution (GPD)
parameters for the optimal threshold were derived and compared to GPD
parameters determined through the standard MPS model. The study improved the
standard MPS methodology by introducing the concept of frequency and used Generalized
Pareto Distribution (GPD) and Peak over threshold (POT) methods as the basis of
identifying extreme values. The improved MPS models and the standard models
were applied to Nairobi Securities Exchange (NSE) trading volume data to
determine the GPD parameters for different sectors registered in NSE market and
their performance compared. It was realized that the improved MPS model
performed better than the standard models. This study will help the
Statisticians in different sectors of our economy to model extreme events
involving ties.