Positivity conditions for stochastic state space modelling of time series

Abstract

This short paper clarifies some aspects of the balancing method for state space modelling of observed time series. This method may fail to satisfy the so-called positive real condition for stochastic processes. We illustrate this by theoretical spectral analysis and also by simulating univariate ARMA (1,1) models.

Keywords:

• Time Series Analysis
• State Space Models
• Balancing
• Positive Real Lemma