Efficiency Evaluation In Modelling Stock Data Using Arch And Bilinear Models

ABSTRACT

Modelling of stock market data has witnessed a significant increase in literature over the past

two decades. Focus has been mainly on the use of the ARCH model with its various extensions

due to its ability to capture heteroscedasticity prevalent in the financial and monetary variables.

However, other suitable models like the bilinear models have not been exploited to model stock

market data so as to determine the most efficient model between the ARCH and bilinear models.

The underlying problem is that of identifying the most efficient model that can be applied to

stock exchange data for forecasting and prediction. The purpose of this study was to determine

the most efficient model between the two models namely, ARCH and bilinear models when

applied to stock market data. The data was obtained from the Nairobi Stock Exchange (NSE) for

the period between 3rd June 1996 to 31st December 2007 for the company share prices while for

the NSE 20-share index data was for period between 2nd March 1998 to 31st December 2007.The

share prices for three companies; Bamburi Cement, National Bank of Kenya and Kenya Airways

which were selected at random from each of the three main sectors as categorized in the Nairobi

Stock Exchange were used. Specifically, the different extensions of ARCH-type models were

utilized with ARMA and bilinear models for modelling the weekly mean of the chosen data set.

The model efficiency was determined based on the minimal mean squared error (MSE). The

results show that the Bilinear-GARCH model with the normal distribution assumption and the

AR-Integrated GARCH (IGARCH) model with student’s t-distribution are the best models for

modelling volatility in the Nairobi Stock Market data. The results also indicate that the volatility

in Nairobi Stock Exchange is statistically significant and persistent with the positive return

innovations having a greater impact than the negative ones. This implies that the leverage effect

experienced in most developed countries is not applicable to Nairobi Stock Market. The results

obtained are significant for planning, prediction and management of investments on shares in the

Nairobi Stock Exchange. The chosen models are also helpful for decision making especially by

the investors, stockbrokers and financial advisors regarding the trading in shares at the Nairobi Stock Exchange.