Short time series modeling an application to Kenyan political opinion polls and the Nairobi stock exchange market data

Abstract

Modeling of time series with many observations has been a focus of considerable research both in theoretical and empirical applications over the last three decades. However, the problem of short time series modeling has not so far been adequately studied both in theory and practical applications, despite the fact that many real life situations involve fewer observations leading to short time series. This calls for making use of appropriate estimation techniques in order to come up with models that can capture the short time series properties and thus be adequately used for forecasting without losing the principle of parsimony. This study intended to determine efficient short time series models that would be able to capture the underlying characteristics of short time series (opinion polls and stock market data) so as to come up with good forecasts. Appropriate Autoregressive Moving Average (ARMA) and Autoregressive Fractionally Integrated Moving Average (ARFIMA) class of models were fitted to the short time series data. ARIMA-GARCH models were also fitted to the stock market data to model volatility. A model-selection strategy based on the corrected Akaike Information Criterion (AICC) was adopted to determine the correct model specification. Exact maximum likelihood estimation method was used to estimate the model parameters and the Root Mean Square Error (RMSE) used to evaluate the forecast performance of the models. The political opinion polls data used were obtained from the Infotrak Harris Research, Consumer Insight Research and Strategic Research for the period between September and December 2007. The stock market data were obtained from the Nairobi Stock Exchange. The weekly average company share prices for Access Kenya Group and Safaricom Limited were used. ARFIMA models are found to outperform ARMA models in forecasting the short time series polls data. ARIMA-GARCH model fitted better the Access Kenya data while for the Safaricom data, ARIMA model had the least RMSE values.