On Parameter Estimation for International Market Cocoa Prices Modelling and Forecasting

Abstract

Time series analysis and forecasting has become a major tool in different applications in business phenomena, such as daily stock prices, weekly interest rates, quarterly sales, monthly supply figures, annual earnings, daily cocoa prices, etc.. It has two goals: perception or modeling random mechanism and prediction of future series quantities according to the past. In this thesis, ARIMA (Auto Regressive Integrated Moving Average) model has been used for monthly cocoa prices at the international market for years 2000 to 2014 from Bank of Ghana (BoG). Based on the inspection of the ACF, PACF autocorrelation plots, the most appropriate orders of the ARIMA models are determined and evaluated using the AIC, AICC and BIC criterion. For the monthly cocoa prices at the international market, ARIMA (0, 1, 1) or IMA (1, 1) or was appropriate for predicting future monthly prices. 1 2 1.1663 0.1663 t t t t Y e e e      In developing any time series model, parameter estimation is one of the crucial steps to consider. For this reason, this thesis focus on comparing the relative performance of model parameter estimations with Maximum Likelihood and Conditional Least Squares Estimations. A simulation exercise was carried out for the sample periods to see to which model parameter estimates could track the path of the actual estimates based on 500 simulation from ARIMA (0, 1, 1) or IMA (1, 1). This is basically to validate the method of parameter estimates of the model based on its predictive power. It was measured by Estimate, Standard Error, Bias estimate and mean square error (MSE). The simulation results suggested that with at least 50 sample size, maximum likelihood (ML) and Conditional least squares (CLS) are identical in parameter estimation. Hence, industry players and all those interested in modelling and forecasting future values can adopt any of this two method, Maximum Likelihood and Conditional Least Squares in estimation model parameter because both are identical in parameter estimation.