We develop "Dickey-Fuller type" test statistics for seasonal unit roots when a model is fitted with deterministic seasonal trends. The asymptotic distributions of the test statistics are derived, and the asymptotic power of these statistics under a sequence of local alternatives are considered....

Using the Lagrange multiplier principle, we develop test statistics for testing seasonal unit roots in a time series with possible deterministic trends. The asymptotic distributions of the test statistics are derived: they are functionals of stochastic integrals of standard Brownian bridges....

In this study, a generalized method of moments (GMM) for the estimation of nonstationary vector autoregressive models with cointegration is considered. Two iterative methods are considered: a simultaneous estimation method and a switching estimation method. The asymptotic properties of the GMM...

An extension of Gaussian reduced rank estimation of Ahn and Reinsel ("Journal of Econometrics", Vol. 62, pp. 317-350, 1994) to seasonal periods other than four is presented. Simple adjustments for estimation that are necessary because of complex-valued seasonal unit roots are presented in detail...

This paper proposes a method for estimating the instantaneous frequency of a nonstationary signal; this method is based on a combination of empirical mode decomposition and functional data analysis. The proposed method incorporates a basis expansion technique for a functional data into...