"Frontmatter". In: Analysis of Financial Time Series

REFERENCES 171P(s t = 2 | s t−1 = 1) = 0.15, P(s t = 1 | s t−1 = 2) = 0.05.Suppose that a 100 = 6.0, σ100 2 = 50.0 ands 100 = 2 with probability 1.0; whatis the 1-step ahead volatility forecast at the forecast origin t = 100? Also, ifthe probability of s 100 = 2 is reduced to 0.8, what is the 1-step ahead volatilityforecast at the forecast origin t = 100?4. Again, consider the monthly log returns of GE stock from January 1926 toDecember 1999. Reserve the returns in 1998 and 1999 for forecasting evaluation.• Fit a 3-2-1 feed-forward neural network to the return series and calculatethe mean squared error of the 1-step ahead forecasts in the forecasting subsample.Write down the biases and weights of the network in the estimationsubsample.• Suppose that we are interested in forecasting the direction of the 1-monthahead stock movement. Fit a 6-5-1 feed-forward neural network to the returnseries using a Heaviside function for the output node. Compute the 1-stepahead forecasts in the forecasting subsample and compare them with theactual movements.5. Because of the existence of inverted yield curves in the term structure of interestrates, the spread of interest rates should be nonlinear. To verify this, considerthe weekly U.S. interest rates of (a) Treasury 1-year constant maturity rate, and(b) Treasury 3-year constant maturity rate. As in Chapter 2, denote the two interestrates by r 1t and r 3t , respectively, and the data span is from January 5, 1962 toSeptember 10, 1999. The data are in files “wgs3yr.dat” and “wgs1yr.dat” on theWeb.• Let s t = r 3t − r 1t be the spread in log interest rates. Is {s t } linear? Performsome nonlinearity tests and draw the conclusion using the 5% significancelevel.• Let st∗ = (r 3t − r 3,t−1 ) − (r 1t − r 1,t−1 ) = s t − s t−1 be the change in interestrate spread. Is {st ∗ } linear? Perform some nonlinearity tests and draw theconclusion using the 5% significance level.• Build a threshold model for the s t series and check the fitted model.• Build a threshold model for the s ∗ t series and check the fitted model.REFERENCESAkaike, H. (1974), “A New Look at the Statistical Model Identification,” IEEE Transactionson Automatic Control, AC-19, 716–723.Andrews, D. W. K., and Ploberger, W. (1994), “Optimal tests when a nuisance parameter ispresent only under the alternative,” Econometrica, 62, 1383–1414.