Consider testing for presence of autocorrelation of lag order up to $h$ in the residuals from a regression model $$ y_t = \mathbf x_t^\top \beta + u_t $$ where $\mathbf x_t$ may or may not include lags of $y_t$. The Breusch-Godfrey test would employ an auxiliary regression $$ \hat u_t = \mathbf x_t^\top \gamma + \varphi_1\hat u_{t-1} + \dots + \varphi_h\hat u_{t-h} + \varepsilon_t $$ and derive its test statistic from there.

Instead of the usual regression model, consider an MA(q) model $$ y_t = \theta_0+\theta_1 u_{t-1} + \dots + \theta_q u_{t-q} + u_t. $$ How do I carry out the Breusch-Godfrey test on residuals from this model? (The null hypothesis being that the residuals are not autocorrelated against an alternative that autocorrelation of lag order up to $h$ is present in them.) Concretely:

  1. How do I construct the auxiliary regression?
    Will it be $\hat u_t=\varphi_1\hat u_{t-1}+\dots+\varphi_s\hat u_{t-s}+\varepsilon_t$ where $s$ somehow depends on $h$ and $q$?
  2. How do I construct the test statistic?
  3. What is its asymptotic distribution under the null hypothesis of zero autocorrelation?

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.