An Application of a Linear Gaussian State Space Model and the Kalman Filter In Estimating Expectations of the Natural Logarithmic Monthly Market Returns of the US 1838 Bond Debenture Closed-End Fund

Abstract

In this article, we have tested a linear Gaussian state space model and the kalman filter in testing ARMA(2,3) models of the natural logarithmic monthly market returns of the US 1838 bond debenture closed-end fund. The aim is to estimate expectations that arises from the interaction of arbitrageurs and noise traders. 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 AR coefficients as shown in terms of C(6) and C(7) are statistically significant at 5% significance level. The MA coefficients as displayed by C(2), C(3), C(4) are not statistically significant at 5% significance level. The variance of the error is denoted by C(5) and it is statistically significant as the p-value is 0.0000. The Final one – step ahead values of the state vector, SV1, SV2, SV3 and SV4 are not statistically significant at the 5% significance level, as all the p-values are above the 5% level. We did not found unanticipated changes in the share prices of the closed-end fund. The total dataset includes monthly data starting from 31/05/1981 to 31/10/2004 and total to 282 observations. The total data for the natural logarithmic returns of the market prices are accounted to 281 observations. The data was obtained from Thomson Financial Investment View database.