In this article, we have applied an autoregressive moving average, ARMA(2,2) model of order AR(1), AR(2), MA(1), MA(2) and SMA(12) to test the natural logarithmic monthly market returns of the of the closed – end funds of major investment banks such as Van Kampen income trust, Aberden Asia Pacific income fund, Credit Suisse asset management income, Scudder high income and Templeton global income. The purpose of this article is to eliminate the seasonality, to compare and select the maximum value of the log likelihood estimation of the different closed-end funds. We have selected the model with the best forecasting ability in terms of the lowest value of the Akaike information criterion, the Schwarz criterion, the Hannan – Quinn criterion. The software that we have used is EViews 6. We have found that the natural logarithmic monthly market price returns of all closed-end funds are a stationary series. We have concluded that the best fit model is Scudder high income, (LNMPSHI), closed-end fund as it has the maximum log likelihood value of -123.16 and the Akaike information criterion, the Schwarz criterion, and the Hannan – Quinn criterion are 1.65, 1.55 an 1.61 respectively. In terms of gradients at the estimated parameters, we have found that there are outlier values and significant fluctuations at the various observations of the coefficients vectors, C(1), C(2), C(3), C(4) and C(5) of the gradients. The gradients of the log likelihood function have been computed at the estimated parameters and the unsuccessful estimation are displayed through the outliers of the peak of the graph of the four closed-end funds. Credit Suisse asset management income, (LNMPCS), closed-end fund displayed less outlier values and not significant fluctuations at the various observations of the coefficients vectors, C(1), C(2), C(3), C(4) and C(5) of the gradients. Finally, the analytic derivatives were calculated based on the specified values. The real and minimum step sizes are identical for all coefficients vectors and very close to zero. We have used one-sided numeric derivative. The whole dataset is from 31/01/1990 to 31/12/2001. The total observations are 144 and the logarithmic monthly market returns observations are 143.The data was obtained from Thomson Financial Investment View database
