Modelling the probability distribution of the time series stock price changes in the U.K. market
The thesis considers different aspects of the probability distribution of the time series of stock price changes in the UK market. It places particular emphasis on the character of the volatility of the series. Chapter 2 documents some preliminary findings about changes in the FT-ALL share price index. These findings are: (1) its distribution has fat tails; (2) the BDS test rejects the hypothesis of identically, and independently distributed price changes; (3) the BDS test applied to the GARCH(l, 1) residuals, adjusted according to de Lima (1995b), indicates that Autoregressive Conditional Heteroscedasticity explains most of the nonlinearity in the FT-ALL price changes. The hypothesis of constant variance is rejected for the FT-ALL series using the Loretan and Phillips test, reported in chapter 3. An intervention model along the lines of Box and Tiao (1975) is used to model possible shifts in the variance of the FT-ALL price changes during the 1973 oil crisis and the 1987 market crash. The model allows for slow decay in the shocks effects and a different level of volatility after both crises. The results suggest that the reaction of the UK market to both crises differs only with regard to the slow decay of the shocks. The null hypothesis of constant variance is "accepted" for the residuals from the intervention model. This "acceptance" is due to the filtering of the effects of the 1973 and 1987 crisis from the FT-ALL series. The hypothesis that GARCH volatility persistence becomes insignificant when the volume of trade is included is examined in chapter 4. In a test covering the price behaviour of 57 UK companies over the period from 4/1/1988 to 28/2/1994, it is found that although the parameter estimates of the GARCH model becomes insignificant when volume is used in the conditional variance of price changes, the autocorrelations of the squared residuals still exhibit a highly significant GARCH pattern. It is argued that the GARCH-volume model of Lamoureux and Lastrapes (1990b) suffers from a multicollinearity problem, apart from the possible simultaneity bias which could lead to an inconsistent estimate of the parameter for volume. It is found that unexpected volume reduces volatility persistence. This reduction can be attributed to the strong association in the timing of innovational outliers in the price changes and unexpected volume found in the study. The results are consistent with the market depth hypothesis of Bessembinder and Seguin (1993). The GARCH model with the conditional normal, Student's t and generalized error distributions is estimated for the UK FT-ALL price changes in chapter 5. The model also considers seasonal and leverage effects. The time period for the study is chosen so as to avoid including the 1987 crash. The results suggest:( 1) volatility persistence is low after the 1987 crash; (2) the ARMA and ARCH effects, along with the seasonal effects of Monday and holidays, explain a significant part of the departure from normality; (3) there is a need for leptokurtic distribution such as the Student's t; and (4) there is no evidence for a leverage effect in the FT-ALL series. That is, positive and negative surprises tend to affect volatility in the same way.