Improved Circular Model on Forecasting Arrivals from Western European Countries to Sri Lanka

Abstract

The Circular Model (CM) is a newly joined member to the family of Univariate Statistical Models. Development of the CM was based on; Newton’s Law of Circular Motion, Fourier Transformation and Multiple Regression Analysis. Most important property of the CM is that; the model could be applied for either stationary or non-stationary series. Further, the model is capable in capturing both seasonal and cyclical patterns of a time series. However, the applicability of CM is restricted to trend free series. As such, it was intended to improve the CM, by using the differencing technique. The Improved Circular Model; named as, "Sama Circular Model, is tested on tourist arrival data from Western European countries to Sri Lanka. Monthly arrival data for the period of April 2008 to December 2016 were used for the analysis. Time Series plots and Auto Correlation Functions were used for pattern recognition. The Auto Correlation Functions (ACF) of residuals and Ljung-Box Q statistics (LBQ) were used to test the independence of residuals. The Anderson Darling test was used to test the normality of residuals. Forecasting ability of the models was assessed by Mean Square Error (MSE) and Mean Absolute Deviation (MAD). Forecasting ability of Sama Circular Model (SCM) was compared with the Decomposition techniques and Seasonal Auto Regressive Moving Average (SARIMA). It is concluded that the SCM is capable in forecasting arrivals from Western European countries and the SCM is superior to the other tested models. It is recommended to test the SCM for different fields; Agriculture, Meteorology, Economics, Financial markets and many more.

Keywords: Circular Model, Fourier Transformation, Differencing