Modelling of non-stationarity in extreme share returns

Abstract

Financial risk control depends on the assumptions made about the distribution of share returns. A study on the behaviour of share market returns provides a practical solution for identifying the adequate statistical distribution assumption and accurate predictive interpretation. Most studies on modelling extreme returns only focus on traditional stationary sequences technique. In many cases, however, the interpretation of the extremes in return series clearly shows the existence of non-stationarity in the series. As an alternative, a non-stationarity algorithm is proposed to produce a more efficient model using a much simpler approach. In this study, a new statistical procedure based on the state of the time series namely a two-stage (TS) method are formed to classify the best extreme distribution fitting. In general, the extreme returns are illustrated by a parametric model which is driven by the asymptotic theory of extreme values of independent and identically distributed (i.i.d) random variables. The TS method is applied to several common distribution models typically used in modelling extreme share returns namely Generalized Lambda Distribution (GLD), Generalized Extreme Value Distribution (GEV), Generalized Pareto Distribution (GPA), Generalized Logistic Distribution (GLO) and Laplace Distribution (LAP). Monte Carlo simulations from known and unknown samples are carried out to appraise the performance of the non-stationary and the stationary techniques. The simulation results reveals that the TS method yields relatively more accurate parameter estimates than the stationary method, especially when estimating positive and monotonous cases trend sequences. The extreme quantile measures using the TS method are found to be more efficient than the conventional approach. This is because the TS method takes into consideration of the information in the time series when evaluating extreme quantile periods. The TS method also has the benefit of being computationally simpler since the transformed process is closer to the actual process. In this respect, the data appear to be more closely meet the assumptions of a statistical inference procedure that is to be applied. The overall results in this study conclude that the proposed TS method could improve the estimation of extreme returns and is a useful instrument for financial risk management.