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CPS1947 Hsein K. et al.
premium (which is 1.52%). The confidence interval is constructed by the
procedure described in Section 3. The sample period is 1952:Q1 through
2017:Q4.
As an illustration of the nonlinear predictability, consider the pair of
quarterly lty and tbl with the cointegrating relation ̂ −1 = 0.674 −1 −
0.739 −1 shown in Figure 2. The average quarterly equity risk premium in
the post-1952 sample is 1.52 percent. The predicted value of quarterly equity
premium, ̂(̂ −1 ), exceeds this 1.52 percent beginning at ̂ −1 = 0.0038 and
then peaks at 3.39 percent at ̂ −1 = 0.0147. This peak occurs in the first
quarter of 2016 when the annualized long-term yield is 2.43% and 3-month T-
bill rate is 0.23%.
Panel A in Table 1 shows that the pair of baa and aaa gives the largest
quarterly in the full sample and this pair explains 8 percent of the variation
̅
2
in next quarter equity premium. As in previous empirical studies, we document
in Table 1 small statistics but they can signal economically significant
̅
2
predictability, as explained in Campbell and Thompson (2008) and Fama and
French (1988).

4. Conclusion
This paper considers a semi-parametric single index predictive model with
cointegrated predictors. We apply our model to study the predictability of U.S.
stock returns. We provide new evidence that quarterly stock returns are
predictable using the following pairs of cointegrated predictors: earning-price
ratio and dividend-price ratio; 3-month T-bill rate and long-term yield; baa
and aaa rated corporate bond yields; and dividend-price ratio and dividend
yield using data over the 1927-2017 period and the post-1952 period.

References
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3. Dong, C., Gao, J. and Tjostheim, D. (2016), `Estimation for single-index and
partially linear singleindex integrated models', The Annals of Statistics
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4. Fama, E. F. and French, K. R. (1989), `Business conditions and expected
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