Predictive Regression Forecasts

A short description of the post.

Compare Out-Of-Sample Forecast

The out-of-sample R2 (Campbell and Thompson, 2008) is a convenient statistic for comparing MSFEs. It is analogous to the conventional in-sample R 2 and measures the proportional reduction in MSFE for the predictive regression forecast relative to the historical average:

\[ R^{2}_{OS} = 1 -\frac{(1/ n_2) \sum^{n_2}_{s=1}(r_{n_1+s} - \hat{r}_{i,n_1 + s})^2}{(1/ n_2) \sum^{n_2}_{s=1}(r_{n_1+s} - \bar{r}_{n_1 + s})^2} \]

oosres <- matrix(NA, nrow = n_col, ncol = 2)
colnames(oosres) <- c("r2os", "p_value")
rownames(oosres) <- colnames(xs[,3:ncol(xs)])

for (k in 1:n_col) {
  
  cw_res <- clark_west(actual, fc_ha, fc_econ[,k])
  
  oosres[k,1] <- cw_res[2]
  oosres[k,2] <- cw_res[4]
  
}

Monthly U.S. Equity Premium Out-of-Sample Forecasting Results
Individual Economic Variables, 1957:01–2010:12
Economic Variable	Overall	Expansion	Recession
	$$R^2_{OS}(\%)$$	$$R^2_{OS}(\%)$$	$$R^2_{OS}(\%)$$
log (DP)	−0.05 [0.10]	−1.24 [0.42]	2.41 [0.00]
log (DY)	−0.37 [0.07]	−2.28 [0.40]	3.56 [0.00]
log (EP)	−1.88 [0.28]	−2.21 [0.31]	−1.20 [0.38]
log (DE)	−2.04 [0.97]	−1.26 [0.80]	−3.67 [0.97]
SVAR	0.32 [0.17]	−0.02 [0.50]	1.01 [0.16]
BM	−1.74 [0.31]	−2.56 [0.44]	−0.04 [0.28]
NTIS	−0.91 [0.41]	0.50 [0.03]	−3.82 [0.94]
TBL	−0.01 [0.09]	−0.84 [0.30]	1.71 [0.10]
LTY	−1.17 [0.12]	−2.37 [0.38]	1.32 [0.11]
LTR	−0.08 [0.20]	−0.85 [0.63]	1.52 [0.05]
TMS	0.06 [0.16]	−0.40 [0.34]	1.00 [0.09]
DFY	−0.04 [0.59]	−0.06 [0.64]	−0.01 [0.48]
DFR	−0.01 [0.38]	0.12 [0.25]	−0.28 [0.48]
INFL	−0.09 [0.50]	0.10 [0.22]	−0.48 [0.66]