Robust monitoring machine: a machine learning solution for out-of-sample R $$^2$$ -hacking in return predictability monitoring

Financial Innovation

Table 5 Certainty Equivalent Return Gains of Monitoring Forecasts

	First year in evaluation sample
	1947	1957	1967	1977	1987	1997	2007
Proposed forecast $f^{(a)}$	0.90	0.77	0.81	0.33	0.10	0.36	0.40
Robust monitoring machine: $f^{(m)}$	1.05	1.08	1.13	0.81	0.92	1.22	0.84
Shrinkage: ($f^{(a)}$+$f^{(b)}$)/2	0.51	0.44	0.46	0.21	0.10	0.23	0.18
Traditional robust monitoring forecasts
DMSFE (60 months, $\delta =1.0$)	0.69	0.59	0.76	0.45	0.26	0.30	0.54
DMSFE (60 months, $\delta =0.5$)	0.91	0.94	0.90	0.51	0.48	0.63	0.67
Logistic regression (feature engineering)	0.54	0.35	0.44	0.30	0.06	− 0.33	− 0.61
Logistic regression (no feature engineering)	0.46	0.36	0.30	0.13	− 0.17	0.01	0.14

This table repeats Table 4 reporting the forecasting performance of monitoring forecasts, but in terms of certainty equivalent returns (%, annualized). Traditional robust monitoring forecasts are based on discounted mean square forecast error (DMSFE) from Stock and Watson (2004) and logistic regressions. Each column corresponds to a different sample split year from 1947 to 2007. All evaluation period ends in December 2017