Application of a Linear Gaussian State Space Model and the Kalman Filter in Estimating Expectations of the Natural Logarithmic Monthly Nav Returns of the Open – End Funds of Major Investment Banks.

Abstract

In this article, we have tested a linear Gaussian state space model and the Kalman filter in testing ARMA(2,4) model of the natural logarithmic monthly market returns of the of the open – end funds of major investment banks such as: Merrill Lynch small cap value A, Fidelity equity income I, Goldman Sachs capital growth A, JPMorgan capital growth A, Invesco value equity investment, and Credit Suisse blue chip A. The purpose of this article is to estimate expectations that arises from the interaction of arbitrageurs and noise traders. The software that we have used is EViews 6. The state space model is composed from the observation and the state equation. It is analyzed by using the Kalman recursive algorithm filter to calculate finite sample forecasts for Gaussian ARMA models. We have found that the natural logarithmic monthly NAV returns of all open-end funds are a stationary series. The natural logarithmic monthly NAV returns for all open-end funds have no serial correlation and are not normally distributed. We have found that the AR coefficients as shown in terms of C(7) and C(8) are not statistically significant at the 5% significance level for Merrill Lynch small cap value A, Fidelity equity income I. The AR coefficient, C(7) is statistically significant and the C(8) coefficient is not statistically significant for Invesco value equity investment, Credit Suisse blue chip A, JPMorgan capital growth A, and Goldman Sachs capital growth A. The MA coefficient C(2) of the Goldman Sachs capital growth A, and Credit Suisse blue chip A, is statistically significant and C(3), C(4), and C(5) are not statistically significant at the 5% significance level. The MA coefficients as displayed by C(2), C(3), C(4), and C(5) are not statistically significant at the 5% significance level for the remaining open-end funds, namely, Merrill Lynch small cap value A, Fidelity equity income I, JPMorgan capital growth A, and Invesco value equity investment. The variance of the error is denoted by C(6) and it is statistically significant for all open-end funds as the p-value is 0.0000. The Final one – step ahead values of the state vector, SV1, SV2, SV3,SV4, SV5 are not statistically significant for all open-end funds except Merril Lynch at the 5% significance level. We did not found unanticipated changes in the NAV prices of the open-end funds. The whole dataset is from 31/01/1990 to 31/12/2001. The total observations are 144 and the logarithmic monthly NAV returns observations are 143. The data was obtained from Thomson Financial Investment View database.