Analysis of Financial Time Series, Third Edition

11.7 Application

In this section, we consider some applications of the state-space model in finance and business. Our objectives are to highlight the applicability of the model and to demonstrate the practical implementation of the analysis in S-Plus with SsfPack.

Example

Consider the CAPM for the monthly simple excess returns of General Motors (GM) stock from January 1990 to December 2003; see Chapter 9. We use the simple excess returns of the S&P 500 composite index as the market returns. The returns are in percentages. Our illustration starts with a simple market model

11.86

for t = 1, … , 168. This is a fixed-coefficient model and can easily be estimated by the ordinary least-squares (OLS) method. Denote the GM stock return and the market return by gm and sp, respectively. The result follows:

> da=read.table(“m-gmsp-excess-9003.txt”,header=F)

> gm=da[,1]

> sp=da[,2]

> fit=OLS(gm∼sp)

> summary(fit)

Call:

OLS(formula = gm∼sp)

Coefficients:

             Value Std. Error t value Pr(>|t|)

(Intercept) 0.1982 0.6302     0.3145  0.7535 

         sp 1.0457 0.1453     7.1962  0.0000 

Regression Diagnostics:

                         

         R-Squared 0.2378

Adjusted R-Squared 0.2332

Durbin-Watson Stat 2.0290

Residual Diagnostics:

               Stat P-Value

Jarque-Bera  2.5348  0.2816

  Ljung-Box 24.2132  0.3362

Residual standard error: 8.13 on 166 degrees of freedom

Thus, the ...