Question

Explain how to use MSPE(mean square prediction error) to compare the fits of LPM, Probit and Logit. Explain the difference between MSPE and MSFE(mean squared forecast error)

Answer 1

Mean squared errors measures the expected squared distance between a estimator and the true underlying parameter.

MSE (θ^) = E [(θ^ - θ)2] ; it measure the equality of estimator.

The mean squared prediction error measure the expected square distance between what your predictor predicts for a specific value and what the true value is,

MSPE (L) = E(g(xi)−gˆ(xi))2 , here measures the quality of predictor.

The value of MSPE is close to zero, which shows that your predictor is close to the true value.

The mean squared forecast error is the difference between an observed value and its forecast. Forecast errors are different from residuals in two ways, firstly, residual are calculated on the training set and the residuals are based on one step forecast while forecast errors can involve multi step forecasts.