Modeling high-dimensional unit-root time series

Modeling High Dimensional Time Series

This paper investigates the effectiveness of the recently proposed Gaussian Process Dynamical Model (GPDM) on high dimensional chaotic time series. The GPDM takes a Bayesian approach to modeling high-dimensional time series data, using the Gaussian process Latent Variable model (GPLVM) for nonlinear dimensionality reduction combined with a nonlinear dynamical model in latent space. The GPDM is ...

Compact modeling of high-dimensional time-series

On time series with randomized unit root and randomized seasonal unit root

A time series model with possibly a randomized unit root and a randomized seasonal unit root is considered. Two statistical tests are developed for the null hypothesis of 3xed unit roots against the alternative that the roots are random and 5uctuate about the value of one. The testing problem is addressed via the score test approach. The asymptotic representations of the test statistics in term...

Symbolic Analysis of High-Dimensional Time Series

In order to extract and to visualize qualitative information from a highdimensional time series, we apply ideas from symbolic dynamics. Counting certain ordinal patterns in the given series, we obtain a series of matrices whose entries are symbol frequencies. This matrix series is explored by simple methods from nominal statistics and information theory. The method is applied to detect and to v...

Unit Root Tests for Time Series in the Presence of an Explosive Root

This paper describes a modification for the practical relevance of unit root tests for time series generated by linear stochastic difference equations with an explosive root.