On the Ergodicity of First‐Order Threshold Autoregressive Moving‐Average Processes

2018 ◽  
Vol 40 (2) ◽  
pp. 256-264 ◽  
Author(s):  
Kung‐Sik Chan ◽  
Greta Goracci
Keyword(s):  
Moving Average ◽  
Autoregressive Moving Average ◽  
Threshold Autoregressive ◽  
First Order ◽  
Moving Average 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.

On the inverses of some patterned matrices arising in the theory of stationary time series

1974 ◽  
Vol 11 (01) ◽  
pp. 63-71 ◽  
Author(s):  
R. F. Galbraith ◽  
J. I. Galbraith
Keyword(s):  
Moving Average ◽  
Autoregressive Process ◽  
Stationary Time Series ◽  
Autoregressive Moving Average ◽  
Average Process ◽  
Moving Average Process ◽  
First Order ◽  
Explicit Formulae ◽  
Patterned Matrices ◽  
Autoregressive Moving Average Process

Expressions are obtained for the determinant and inverse of the covariance matrix of a set of n consecutive observations on a mixed autoregressive moving average process. Explicit formulae for the inverse of this matrix are given for the general autoregressive process of order p (n ≧ p), and for the first order mixed autoregressive moving average process.

Extending the correlation structure of exponential autoregressive–moving-average processes

1981 ◽  
Vol 18 (1) ◽  
pp. 181-189 ◽  
Author(s):  
Ed McKenzie
Keyword(s):  
Autocorrelation Function ◽  
Moving Average ◽  
Binary Sequence ◽  
Correlation Structure ◽  
Autoregressive Moving Average ◽  
Correlation Structures ◽  
Exponential Random Variables ◽  
Moving Average Processes ◽  
Negative Exponential ◽  
Exponential Sequence

Some recent constructions for the generation of dependent sequences of identically distributed negative exponential random variables with specific correlation structures are generalized. This is achieved by attributing a correlation structure to the binary sequence which controls the generation of the exponentials. The procedure causes the autocorrelation function of the exponential sequence to copy that of the binary sequence and thus be extended to include negative values and other values beyond the usual range.

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