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Table 6 Forecasting Performance Before and Since 2006

From: Robust monitoring machine: a machine learning solution for out-of-sample R\(^2\)-hacking in return predictability monitoring

Forecast

1947–2005

2006–2017

Out-of-sample

\(E[d_{\cdot }]\)

\(Var[d_{\cdot }]\)

Diebold-Mariano

Out-of-sample

\(R^2\) (%)

(\(\times 10^{-6}\))

(\(\times 10^{-8}\))

Test (p-value)

\(R^2\) (%)

Robust (m)

0.65

11.2

0.275

0.004

0.17

Proposed (a)

0.64

11.1

0.519

0.040

− 0.25

  1. This table reports forecasting performance measures for two sub-periods: 1947–2005 and 2006–2017. \(E[d_{i}]\) and \(Var[d_{i}]\) for \(i \in \{a, m\}\) denote the expected value and variance of loss difference, which represent average forecasting performance and its relative risk, respectively. Diebold-Mariano tests are to show if a forecast has significantly different predictability from a benchmark. All forecasts are free from look-ahead bias