The Wilkie investment model

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CHAPTER THREE

METHODOLOGY

3.1 Research Design

The ultimate purpose in this paper was to describe and compare a number of published models, to provide some comparison of the distributions that result from them, and to determine which best suit the Ghanaian economic data. This research focuses on the strategic asset allocation models. This is because these models have the tendency to capture several investment series in a single model development procedure. The data used for the empirical analysis in this paper were taken from the Bank of Ghana data base. Yearly data were considered because the stochastic asset models used in the study (Wilkie, 1986; 1995; Whitten & Thomas, 1999) used similar data frequency. The selection of the models is purely purposive and convenience. Models’ parameters are calculated using the Ghanaian economic data. Subsequently, some statistics are investigated for easy comparison of the models. This helped in identifying the best model for the Ghanaian economic data. The models considered were; (a) The Wilkie model, as described in Wilkie (1995); (b) The ARCH variation of the Wilkie model, also described in Wilkie (1995) (c) The Whitten & Thomas model, as described in Whitten & Thomas (1999). Before the models comparison, I also looked at the characteristics of the data in other to understand and present the nature of the Ghanaian economic variables. Statistical univariate time series analysis were conducted, also, basic assumptions for stochastic modelling were checked. Actuarial stochastic modelling usually follow the standard assumption that the model errors are independent and identically distributed (i.i.d.) normal random variables and that, in practice the variables used in the actuarial applications, such as the inflation or interest rate, are assumed to be autoregressive and have constant unconditional means (Sherris, 1997). The existence of unit roots in the series for models show the nature of the trends in the series. If a series contains a unit root then the trend in the series is stochastic and shocks to the series will be permanent and this can be an accumulation of past random shocks otherwise, the series is termed as “trend stationary”. An investigation concerning the unit root and stationarity of the series were also conducted. This is because trend stationary has major implications for investment models in actuarial applications (Sherris et al. 1999). The Dickey and Fuller (1979) test is employed for this purpose. 3.2 DATA Stochastic modeling requires the use of data from the past to combine with the present to model the future. For a good model, the structure should be consistent with validated or widely accepted economic and financial theory. These theories and the developed models depend on empirical data for validation. Statistically analysing the historical data provides a better insights into the features of past experience inherent in the variable that the model must capture. Good models are consistent with historical data since the parameter estimations are usually based on the historical data. The data considered were:

  • Consumer Price Index (CPI);

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