Journal of Data Science

In this article, we introduce a class of distributions that have heavy tails as compared to Pareto distribution of third kind, which we termed as Heavy Tailed Pareto (HP) distribution. Various structural properties of the new distribution are derived. It is shown that HP distribution is in the domain of attraction of minimum of Weibull distribution. A representation of HP distribution in terms of Weibull random variable is obtained. Two characterizations of HP distribution are obtained. The method of maximum likelihood is used for estimation of model parameters and simulation results are presented to assess the performance of new model. Marshall-Olkin Heavy Tailed Pareto (MOHP) distribution is also introduced and some of its properties are studied. It is shown that MOHP distribution is geometric extreme stable. An autoregressive time series model with the new model as marginal distribution is developed and its properties are studied.

Abstract: Price limits are applied to control risks in various futures mar kets. In this research, we proposed an adapted autoregressive model for the observed futures return by introducing dummy variables that represent limit moves. We also proposed a stochastic volatility model with dummy variables. These two models are used to investigate the existence of price de layed discovery effect and volatility spillover effect from price limits. We give an empirical study of the impact of price limits on copper and natural rubble futures in Shanghai Futures Exchange (SHFE) by using MCMC method. It is found that price limits are efficient in controlling copper futures price, but the rubber futures price is distorted significantly. This implies that the effects of price limits are significant for products with large fluctuation and frequent limits hit.