Conduct a likelihood ratio test to choose the number of lags in a GARCH model.
Compare the fit of a restricted model against an unrestricted model by testing whether the gradient of the loglikelihood function of the unrestricted model, evaluated at the restricted maximum likelihood estimates (MLEs), is significantly different from zero.
Compare the fit of a restricted model against an unrestricted model by testing whether the restriction function, evaluated at the unrestricted maximum likelihood estimates (MLEs), is significantly different from zero.
Select ARMA model using information criteria.
Fit two competing, conditional variance models to data, and then compare their fits using a likelihood ratio test.
This example shows the use of the likelihood ratio, Wald, and Lagrange multiplier tests.
Compare the fits of several conditional variance models using AIC and BIC.
Choose the state-space model specification with the best predictive performance using a rolling window.
Learn the mechanics behind the likelihood ratio, Lagrange multiplier, and Wald model-comparison tests.
Learn about the AIC and BIC measures of model-fit.
Learn how to select an appropriate regression model with ARIMA errors.
Estimate explicitly and implicitly defined state-space models using a rolling window.