Some autoregressive moving average processes with generalized Poisson marginal distributions

1993 ◽  
Vol 45 (2) ◽  
pp. 223-232 ◽  
Author(s):  
A. A. Alzaid ◽  
M. A. Al-Osh
Keyword(s):  
Moving Average ◽  
Autoregressive Moving Average ◽  
Marginal Distributions ◽  
Generalized Poisson ◽  
Moving Average Processes

Autoregressive moving-average processes with negative-binomial and geometric marginal distributions

1986 ◽  
Vol 18 (03) ◽  
pp. 679-705 ◽  
Author(s):  
Ed McKenzie
Keyword(s):  
Negative Binomial ◽  
Moving Average ◽  
Random Variables ◽  
Autoregressive Moving Average ◽  
Marginal Distributions ◽  
Alternative Derivation ◽  
Discrete Random Variables ◽  
Moving Average Processes ◽  
Negative Exponential ◽  
Interval Lengths

Some simple models are described which may be used for the modelling or generation of sequences of dependent discrete random variates with negative binomial and geometric univariate marginal distributions. The models are developed as analogues of well-known continuous variate models for gamma and negative exponential variates. The analogy arises naturally from a consideration of self-decomposability for discrete random variables. An alternative derivation is also given wherein both the continuous and the discrete variate processes arise simultaneously as measures on a process of overlapping intervals. The former is the process of interval lengths and the latter is a process of counts on these intervals.

Autoregressive moving-average processes with negative-binomial and geometric marginal distributions

1986 ◽  
Vol 18 (3) ◽  
pp. 679-705 ◽  
Author(s):  
Ed McKenzie
Keyword(s):  
Negative Binomial ◽  
Moving Average ◽  
Random Variables ◽  
Autoregressive Moving Average ◽  
Marginal Distributions ◽  
Alternative Derivation ◽  
Discrete Random Variables ◽  
Moving Average Processes ◽  
Negative Exponential ◽  
Interval Lengths

Some simple models are described which may be used for the modelling or generation of sequences of dependent discrete random variates with negative binomial and geometric univariate marginal distributions. The models are developed as analogues of well-known continuous variate models for gamma and negative exponential variates. The analogy arises naturally from a consideration of self-decomposability for discrete random variables. An alternative derivation is also given wherein both the continuous and the discrete variate processes arise simultaneously as measures on a process of overlapping intervals. The former is the process of interval lengths and the latter is a process of counts on these intervals.

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.

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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