The aim of this work is to investigate the effects of temporal aggregation and systematic sampling on periodic autoregressive moving average (PARMA) time series. Firstly, it is shown that the class of weak PARMA processes, i.e. with uncorrelated but possibly dependent errors, is closed under...

The exact likelihood function of a Gaussian vector autoregressive-moving average (VARMA) model is evaluated in two nonstandard cases: (a) a parsimonious structured form, such as obtained in the echelon form structure or the scalar component model (SCM) structure; (b) a partially nonstationary...

Here, we derive optimal rank-based tests for noncausality in the sense of Granger between two multivariate time series. Assuming that the global process admits a joint stationary vector autoregressive (VAR) representation with an elliptically symmetric innovation density, both no feedback and...

The aim of this work is to investigate the asymptotic properties of weighted least squares (WLS) estimation for causal and invertible periodic autoregressive moving average (PARMA) models with uncorrelated but dependent errors. Under mild assumptions, it is shown that the WLS estimators of PARMA...

Haugh [Journal of the American Statistical Association (1976) Vol. 71, pp. 378-85] developed an approach to the problem of testing non-correlation (at all leads and lags) between two univariate time series. Haugh's tests however have low power against two series which are related over a long...