Testing for Fundamental Vector Moving Average Representations

We propose a test for invertibility or fundamentalness of structural vector autoregressive moving average models generated by non-Gaussian independent shocks. We prove that in these models the Wold innovations are serially dependent if and only if the structural shocks are non-fundamental. This simple but powerful characterization suggests an empirical strategy to assess invertibility. We propose a test based on a generalized spectral density to check for serial independence in the Wold innovations. This approach does not require to specify and estimate the economic agent’s information flows or to identify and estimate the non-invertible roots. Moreover, the proposed test statistic uses all lags in the sample and it has a convenient asymptotic (0 1) distribution under the null hypothesis of invertibility, and hence, it is straightforward to implement. In case of rejection, the test can be further used to check if a given set of additional variables provides sufficient informational content to restore invertibility. A Monte Carlo study is conducted to examine the finite-sample performance of our test. Finally, the proposed test is applied to the identification of government spending shocks. In the empirical illustration, we find that augmenting excess returns series of large military companies may solve the non-fundamentalness problem in a trivariate fiscal VAR.