EVALUATION OF FORECASTING PERFORMANCE OF DIFFERENT SAMPLING INTERVALS OF SHARE PRICES OF NAIROBI SECURITIES EXCHANGE USING GARCH MODELS

Abstract

Prediction of the stock market has been of enormous interest for the past decades, as having an accurate idea of its future performance can help traders invest more appropriately and timely to maximize profits; Better forecasts translate to better risk management and better option pricing for the stock market products. This thesis examined and evaluated the forecasting ability of Nairobi Securities Exchange (NSE) share prices at different time points using Generalized Autoregressive Conditional Heteroskedasticity (GARCH) Time series models. Daily, weekly and monthly share prices of specific companies listed in the Nairobi Securities Exchange were utilized in the research study. The study covered the period from 3 rd January 2006 to 31st January 2012. In order to obtain the most favorable forecasts, appropriate models were first determined for each time point for the companies chosen from amongst the lower order GARCH models that is GARCH (1, 1), GARCH (1, 2), GARCH (2, 1) and GARCH (2, 2). Lower order GARCH models were utilized because of their simplicity and their ability to capture the stylized features exhibited by financial time series. In each case, the best fitting GARCH models were chosen based on Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Models with the least AIC and BIC values were preferred. Parameter estimation and model fitting were done using the chosen models. Adequacy of the chosen models was done using Ljung Box and Lagrange Multiplier Autoregressive Conditional Heteroskedasticity (ARCH LM) tests. The selected models were then utilized in forecasting. One month ahead prices and forecasting performance of daily, weekly and monthly returns were compared using statistical forecasting accuracy measures such as Mean Absolute Errors (MAE), Root Mean squared Errors (RMSE) and MAPE for each company so as to determine intervals with best forecasting ability. The intervals with the least mean errors were considered to have the best predictive ability as compared to the other time points. Three companies namely; National Bank of Kenya (NBK), East African Portland cement and the Kenya Airways (KQ) were selected purposively because of their consistency in the NSE for the period of study and were also representative of three sectors namely; Finance and Investment, Industrial and Allied and Commercial and services as categorized in the NSE. The data was obtained from NSE and analyzed using the R software version 3.1.0 and results presented in tables and graphs. The results revealed that GARCH (1, 1) models performed well in modeling most return series for companies investigated especially for daily and monthly returns. GARCH (2, 1) seemed better for KQ weekly data while GARCH (2, 2) performed poorly for all the data sets. While comparing the forecasting performance of each time point based on the selected models, daily data gave better prediction, followed by weekly and lastly monthly returns. This suggests that the models generally perform well when modeled with higher frequency data.