Prediction Future Asset Price which is Non-concordant with the Historical Distribution

摘要

This paper attempts to predict the major characteristics of the future asset price which is non-concordant with the distribution estimated from the price today and the prices on a large number of previous days. The three major characteristics of the i-th non-concordant asset price are the length of the interval between the occurrence time of the previous non-concordant asset price and that of the present non-concordant asset price, the indicator which denotes that the non-concordant price is extremely small or large by its values -1 and 1 respectively, and the degree of non-concordance given by the negative logarithm of the probability of the left tail or right tail of which one of the end points is given by the observed future price. The vector of three major characteristics of the next non-concordant price is modelled to be dependent on the vectors corresponding to the present and 1-1 previous non-concordant prices via a 3-dimensional conditional distribution which is derived from a 3(1 + 1)-dimensional power-normal mixture distribution. The marginal distribution for each of the three major characteristics can then be derived from the conditional distribution. The mean of the j-th marginal distribution is an estimate of the value of the j-th characteristics of the next non-concordant price. Meanwhile, the 100(α/2) % and 100(1 - α/2) % points of the j-th marginal distribution can be used to form a prediction interval for the j-th characteristic of the next non-concordant price. The performance measures of the above estimates and prediction intervals indicate that the fitted conditional distribution is satisfactory. Thus the incorporation of the distribution of the characteristics of the next non-concordant price in the model for asset price has a good potential of yielding a more realistic model.