Normality tests for latent variables - Martín Almuzara; Dante Amengual; Enrique Sentana (Quantitative Economics, 2019)
We exploit the rationale behind the Expectation Maximization algorithm to derive simple to implement and interpret LM normality tests for the innovations of the latent variables in linear state space models against generalized hyperbolic alternatives, including symmetric and asymmetric Student ts. We decompose our tests into third and fourth moment components, and obtain one-sided likelihood ratio analogues, whose asymptotic distribution we provide. When we apply our tests to a common trend model which combines the expenditure and income versions of US aggregate real output to improve its measurement, we reject normality if the sample period extends beyond the Great Moderation.
Keywords: C32; C52; E01; 330; Cointegration; gross domestic product; gross domestic income; kurtosis; Kuhn-Tucker test; skewness; supremum test; Wiener-Kolmogorov-Kalman smoother