University of Alabama

• EC 410

• CHAPTER 4. TOOLS OF THE FORECASTER SOLUTIONS by Wei Lin and Yingying Sun (University of California, Riverside) Note: The house price index for Exercises 1 to 4 is different from the house price index presented in the textbook (Section 4.1.1 and Table 4.1). Both are downloaded from Freddie Mac’s website. In the textbook, the time series is the Conventional Mortgage Home Price Index (CMHPI), which is a weighted average of nine census region indexes. In February 2011, Freddie Mac discontinued the publication of CMHPI and replaced it with the Freddie Mac House Price Index (FMHPI) http://www.freddiemac.com/finance/fmhpi. FMHPI is a weighted average of state indexes. The base month of the index is December 2000, i.e. FMHPI = 100. Consequently, the regression results in Table 4.1 of the textbook are not comparable to the regression results presented in Exercises 1 to 4. Exercise 1 We present the ACFs and PACFs of house prices (P), interest rates (R) and their changes (DP and DR) in Figures 1 to 4. The time series in levels (P and R) have similar profiles: strong autocorrelations that decay slowly towards zero in the ACFs, and a first order prominent spike, larger than 0.90 and statistically significant from zero, in the PACFs (observe the confidence bands for the null hypothesis of zero autocorrelation). The time series of changes in prices and rates exhibit much weaker autocorrelation. However, the two series are very different. While changes in interest rates are not autocorrelated (a barely significant autocorrelation of order one), changes in house prices exhibit short term (about 2 years) autocorrelation. This means that we will be able to exploit time dependence in yearly price growth for forecasting purposes but it will be difficult to do so in forecasting interest rate changes. Figure 1: ACF, PACF and Q-Statistic of P 1 Gloria Gonz´alez-Rivera Forecasting For Economics and Business 2013 Figure 2: ACF, PACF and Q-Statistic of R Figure 3: ACF, PACF and Q-Statistic of DP Figure 4: ACF, PACF and Q-Statistic of DR 2 Gloria Gonz´alez-Rivera Forecasting For Economics and Business 2013 Exercise 2 We estimate the following regression models i. ∆pt = α0 + α1∆pt−1 + α2∆pt−2 + ut ii. ∆pt = α0 + α1∆pt−1 + α2∆pt−2 + β1∆rt−1 + β2∆rt−2 + ut iii. ∆pt = α0 + α1∆pt−1 + α2∆pt−2 + α3∆pt−3 + α4∆pt−4 + ut iv. ∆pt = α0 + α1∆pt−1 + α2∆pt−2 + α3∆pt−3 + α4∆pt−4 +β1∆rt−1 + β2∆rt−2 + β3∆rt−3 + β4∆rt−4 + ut Tables 1 to 4 report the estimation results. Models (i) and (ii) are virtually identical. The goodness of fit (adjusted R-squared) is about 70% in both models. It seems that changes in interest rates are not informative to explain changes in house prices in this sample. This claim is also supported by an F-test for a null hypothesis of no effect of interest rates, which is F = (322.47−308.83)/2 308.83/(34−5) = 0.64. We compare it with the 5% critical value of an F2,29 = 3.33 and conclude that the null can