Markovian representation of stochastic processes and its application to the analysis of autoregressive moving average processes

1974 ◽  
Vol 26 (1) ◽  
pp. 363-387 ◽  
Author(s):  
Hirotugu Akaike
Keyword(s):  
Stochastic Processes ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Markovian Representation ◽  
Moving Average Processes

Time-reversibility of linear stochastic processes

1975 ◽  
Vol 12 (04) ◽  
pp. 831-836 ◽  
Author(s):  
Gideon Weiss
Keyword(s):  
Probability Distribution ◽  
Stochastic Processes ◽  
Gaussian Processes ◽  
Moving Average ◽  
Joint Probability ◽  
Unique Property ◽  
Joint Probability Distribution ◽  
Autoregressive Moving Average ◽  
Time Reversibility ◽  
Moving Average Processes

Time-reversibility is defined for a process X(t) as the property that {X(t 1), …, X(tn )} and {X(– t 1), …, X(– tn )} have the same joint probability distribution. It is shown that, for discrete mixed autoregressive moving-average processes, this is a unique property of Gaussian processes.

Time-reversibility of linear stochastic processes

1975 ◽  
Vol 12 (4) ◽  
pp. 831-836 ◽  
Author(s):  
Gideon Weiss
Keyword(s):  
Probability Distribution ◽  
Stochastic Processes ◽  
Gaussian Processes ◽  
Moving Average ◽  
Joint Probability ◽  
Unique Property ◽  
Joint Probability Distribution ◽  
Autoregressive Moving Average ◽  
Time Reversibility ◽  
Moving Average Processes

Time-reversibility is defined for a process X(t) as the property that {X(t1), …, X(tn)} and {X(– t1), …, X(– tn)} have the same joint probability distribution. It is shown that, for discrete mixed autoregressive moving-average processes, this is a unique property of Gaussian processes.

scholarly journals A Parameterization of Models for Unit Root Processes: Structure Theory and Hypothesis Testing

Econometrics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 42
Author(s):  
Dietmar Bauer ◽  
Lukas Matuschek ◽  
Patrick de Matos Ribeiro ◽  
Martin Wagner
Keyword(s):  
Moving Average ◽  
Unit Roots ◽  
Structure Theory ◽  
Autoregressive Moving Average ◽  
Vector Autoregressive ◽  
Pseudo Likelihood ◽  
Moving Average Processes ◽  
Essential Input ◽  
Deterministic Components ◽  
Pseudo Maximum Likelihood

We develop and discuss a parameterization of vector autoregressive moving average processes with arbitrary unit roots and (co)integration orders. The detailed analysis of the topological properties of the parameterization—based on the state space canonical form of Bauer and Wagner (2012)—is an essential input for establishing statistical and numerical properties of pseudo maximum likelihood estimators as well as, e.g., pseudo likelihood ratio tests based on them. The general results are exemplified in detail for the empirically most relevant cases, the (multiple frequency or seasonal) I(1) and the I(2) case. For these two cases we also discuss the modeling of deterministic components in detail.

Sign in / Sign up

Export Citation Format

Share Document