Volume 14, Issue 2

In this paper we consider tests for lack of fit in a class of seasonal periodic autoregressive moving average (SPARMA) models under the assumption that the errors are uncorrelated but non-independent (i.e. weak SPARMA models). We derive the asymptotic distributions of residual and normalized residual empirical autocovariances and autocorrelations of these weak SPARMA models. We then deduce the modified portmanteau statistics. We establish the asymptotic behavior of the proposed statistics, which can be quite different from the usual chi-squared approximation used under independent and identically distributed (iid) assumptions on the noise. We also propose another test based on a self-normalization approach to cheek the adequacy of SPARMA models. A set of Monte Carlo experiments and an application to the daily returns of the SP500 are presented.

We are interested in a class of seasonal autoregressive moving average (SARMA) models with periodically varying parameters, so-called seasonal periodic autoregressive moving average (SPARMA) models under the assumption that the errors are uncorrelated but non-independent (i.e. weak SPARMA models). Relaxing the classical independence assumption on the errors considerably extends the range of application of the SPARMA models, and allows one to cover linear representations of general nonlinear processes. We establish the asymptotic properties of the quasi-generalized least squares (QLS) estimator of these models. Particular attention is given to the estimation of the asymptotic variance matrix of the QLS estimator, which may be very different from that obtained in the standard framework. A set of Monte Carlo experiments are presented.

For large multivariate models of generalized autoregressive conditional heteroskedasticity (GARCH), it is important to reduce the number of parameters to cope with the ‘curse of dimensionality’. Recently, Laurent, Rombouts and Violante (2014 “Multivariate Rotated ARCH Models” Journal of Econometrics 179 : 16–30) developed the rotated multivariate GARCH model, which focuses on the parameters for standardized variables. This paper extends the rotated multivariate GARCH model by considering a hyper-rotation, which uses a more flexible structure for the rotation matrix. The paper shows an alternative representation based on a random coefficient vector autoregressive and moving-average (VARMA) process, and provides the regularity conditions for the consistency and asymptotic normality of the quasi-maximum likelihood (QML) estimator for VARMA with hyper-rotated multivariate GARCH. The paper investigates the finite sample properties of the QML estimator for the new model. Empirical results for four exchange rate returns show the new specifications works satisfactory for reducing the number of parameters.

A multivariate vector autoregressive model is used to construct the distribution of the impulse-response functions of macroeconomics shocks. In particular, the paper studies the distribution of the short-, medium-, and long-term effects after a shock. Structural and reduced form quantile vector autoregressive models are developed where heterogeneity in conditional effects can be evaluated through multivariate quantile processes. The distribution of the responses can then be obtained by using uniformly distributed random vectors. An empirical example of exchange rate pass-through in Argentina is presented.