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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/4114

Title: GARCH Volatility Modeling and Forecasting of Continuously Compounded Returns; Case Study: Ghana Stock Exchange
Authors: Nyarkoh, Peter Kofi Jnr.
Issue Date: 20-Jun-2011
Abstract: This research presents a rudimentary description of the procedures and applica- tions of ARMA specification in financial time series modeling of the Guinness Ghana Limited and further replicates those concepts on 21 listed companies in the Ghana Stock Exchange Databank Stock Index. The data is from the first financial week in January of 2004 to the last financial week in December of 2008 excluding non-trading days and public holidays. Several tests of the statistical sig- nificance and accuracy of the most appropriate SARIMA(p, d, q)(P,D,Q)S and ARIMA(p, d, q) specifications are performed through checks on the asymptotic standard errors, adoption and implementation of the principle of parsimony, ex- amining correlogram plots among other several tests before final selection is made. Analysis is performed to test for ARCH effect presence and a final confirmation is thus achieved by using Engle’s Lagrange multiplier test with a null hypothesis of ’no ARCH effects’. All shares except ABL show no presence of ARCH effects. Conditional volatility is thus modeled from the GARCH specification model fit- ted to ABL which is an ARCH(1) model. The volatility is forecasted for 3 years ahead. These tests are replicated at the sector level (i.e.one level higher than the share level), it is discovered that the ARMA specification for all sectors captures all the ARCH effects. Which implies that the volatility of ABL vanishes at the sector level. A further replication of concepts is performed at the industry level(i.e one level higher than the sector level), it is also discovered that, the ARMA spec- ification for all industries captures all the ARCH effects. However at the over all DSI returns level, it is discovered that after a SARIMA(2, 1, 3)(2, 0, 1)1 model specification a GARCH(1, 1) model is fit to capture the uncaptured non-linear ARCH effects present. The ARCH coefficient of the GARCH(1, 1), α was found to be positive and statistically significant which indicates significant short run volatility persistence (i.e. there is significant ARCH effects in the series). The es- timate of β, the GARCH coefficient, which represents the contribution of shocks to long run volatility persistence, has a positive and statistically significant value. This means that there is significant long run persistence in volatility. It is con- cluded that since the sum of the ARCH and GARCH coefficients, α + β > 1, volatility shock is strongly persistent and under the GARCH model, there is no covariance stationarity.
Description: A thesis submitted to the School of Graduate Studies, Kwame Nkrumah University of Science and Technology, Kumasi, in partial fulfilment of the requirements for the award of the Degree of Master of Philosophy in Mathematics, 2011
URI: http://hdl.handle.net/123456789/4114
Appears in Collections:College of Science

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