Parameter Space Restrictions in State Space Models

The state space model is widely used to handle time series data driven by related latent processes in many fields. In this article, we suggest a framework to examine the relationship between state space models and autoregressive integrated moving average (ARIMA) models by examining the existence and positive-definiteness conditions implied by auto-covariance structures. This study covers broad types of state space models frequently used in previous studies. We also suggest a simple statistical test to check whether a certain state space model is appropriate for the specific data. For illustration, we apply the suggested procedure in the analysis of the United States real gross domestic product data. Copyright © 2011 John Wiley & Sons, Ltd.

[1]  Duk Bin Jun,et al.  State space trend‐cycle decomposition of the ARIMA(1,1,1) process , 1997 .

[2]  Drew D. Creal,et al.  The relationship between the Beveridge–Nelson decomposition and other permanent–transitory decompositions that are popular in economics , 2008 .

[3]  Tommaso Proietti,et al.  Trend–Cycle Decompositions with Correlated Components , 2006 .

[4]  Mark W. Watson,et al.  Univariate detrending methods with stochastic trends , 1986 .

[5]  Daisuke Nagakura.  A Note on the Two Assumptions of Standard Unobserved Components Models , 2008 .

[6]  Andrew Harvey,et al.  Trends and Cycles in Macroeconomic Time Series , 1985 .

[7]  Eric Zivot,et al.  Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different? , 2003, Review of Economics and Statistics.

[8]  P. Clark,et al.  The Cyclical Component of U. S. Economic Activity , 1987 .

[9]  C. Nelson,et al.  Trends and random walks in macroeconmic time series: Some evidence and implications , 1982 .

[10]  C. Nelson,et al.  A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the ‘business cycle’☆ , 1981 .

[11]  L. Reichlin,et al.  On persistence of shocks to economic variables: a common misconception , 1992 .

[12]  C. Nelson.  Spurious Trend and Cycle in the State Space Decomposition of a Time Series with a Unit Root , 1987 .

[13]  Tommaso Proietti,et al.  A Beveridge-Nelson smoother , 2000 .

[14]  How Are Shocks to Trend and Cycle Correlated? A Simple Methodology for Unidentified Unobserved Components Models , 2011 .