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Quantitative Finance · शब्दावली

Out-of-sample R-squared, predictability ceiling क्या है?

अन्य नाम: out-of-sample R-squared · predictability ceiling

Definition 1.5 Machine Learning for Markets · अध्याय 1 — Why Financial Machine Learning Is Different

The out-of-sample R-squared of forecasts $\hat y_i$ of returns $y_i$ on a test set is

R^2_{\mathrm{oos}} = 1 - \frac{\sum_i(y_i - \hat y_i)^2}{\sum_i y_i^2},

measured against a forecast of zero, not against the sample mean. The predictability ceiling of a dataset is $R^2_{\mathrm{oos}}$ of the true conditional expectation $\mu(x_i) = \E[y_i\mid x_i]$ : the best any model of those features can score.

	500 stocks, ceiling 0.60% out of sample			strong signal, Bayes 0.95
model	in sample	out of sample	corr. with the truth	in sample	out of sample
ridge regression	0.39%	0.38%	0.74	0.72	0.72
boosted trees	1.45%	0.57%	0.92	0.92	0.92
neural network	0.64%	0.28%	0.74	0.94	0.93

Table 1.1. Three models on two tasks: twenty years of training and ten of test on firm.mlsynth’s 500 stocks, and 20 000 training examples of a task with a strong signal. R-squared against zero for the stocks, against the mean for the generic task. Data: ml_why.compare and ml_why.strong_signal.

The 120 test months, one R-squared per month over 500 stocks, for the boosted trees and for the planted truth itself. Bars left of the dashed line are months where the forecast did worse than zero: 18% of them for the model, and some for the truth. Data: ml_why.compare on firm.mlsynth. — Figure 1.2. The 120 test months, one R-squared per month over 500 stocks, for the boosted trees and for the planted truth itself. Bars left of the dashed line are months where the forecast did worse than zero: 18% of them for the model, and some for the truth. Data: ml_why.compare on firm.mlsynth.

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