Browsing by Author "Purchase, Michael Andrew"

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    Analysing GARCH models across different sample sizes
    (Stellenbosch : Stellenbosch University, 2023-03) Purchase, Michael Andrew; Conradie, Willie; Viljoen, Helena; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY: As initially constructed by Robert Engle and his student Tim Bollerslev, the GARCH model has the desired ability to model the changing variance (heteroskedasticity) of a time series. The primary goal of this study is to investigate changes in volatility, estimates of the parameters, forecasting error as well as excess kurtosis across different window lengths as this may indicate an appropriate sample size to use when fitting a GARCH model to a set of data. After examining the T = 6489 1-day logreturns on the FTSE/JSE-ALSI between 27 December 1995 and 15 December 2021, it was calculated that an average estimate for volatility of 0.193 670 should be expected. Given that a rolling window methodology was applied across 20 different window lengths under both the S-GARCH(1,1) and E-GARCH(1,1) models, a total of 180 000 GARCH models were fit with parameter and volatility estimates, information criteria and volatility forecasts being extracted. Given the construction of the asymmetric response function under the E-GARCH model, this model has greater ability to account for the `leverage effect' where negative market returns are greater drivers of higher volatility than positive returns of an equal magnitude. Among others, key results include volatility estimates across most window lengths taking longer to settle after the Global Financial Crisis (GFC) than after the COVID-19 pandemic. This was interesting because volatility reached higher levels during the latter, indicating that the South African market reacted more severely to the COVID-19 pandemic but also managed to adjust to new market conditions quicker than those after the Global Financial Crisis. In terms of parameter estimates under the S-GARCH(1,1) model, values for a and b under a window length of 100 trading days were often calculated infinitely close to zero and one respectively, indicating a strong possibility of the optimising algorithm arriving at local maxima of the likelihood function. With the exceptionally low p-values under the Jarque-Bera and Kolmogorov-Smirnov tests as well as all excess kurtosis values being greater than zero, substantial motivation was provided for the use of the Student's t-distribution when fitting GARCH models. Given the various results obtained around volatility, parameter estimates, RMSE and information criteria, it was concluded that a window length of 600 is perhaps the most appropriate when modelling GARCH volatility.