Duality, Forecasting and Selection of Autoregressive Moving Average Models
by Khogali A. Khogali, Olorunsola E. Olowofeso, and John. O. Owino.
Based on both duality in time between time series processes and
lag transformation, we define duality in causality, invertibility
for mixed Autoregressive moving average ARMA(p,q) models.
We construct expressions, in terms of the parameters of
the parmaterized form of ARMA(p,q) models to compare the forecasting
efficiency for a given causal/invertible pattern of an arbitrarily
primary model relative to the pattern that define the corresponding
dual model. The work considered the case when the forecast lead is one period for general univariate ARMA(p,q) as well as for ARMA(1, 1) models when the lead time is more than one period. These expressions are presented in terms of inequalities to serve
as criterion for model selection. This study has shown that
we need not eliminate noncausal and non-invertible ARMA(p, q) models from
consideration if forecasting for more than one period is desired. In essence, we attempt to approach the estimation problem
via the relation between a given time series model and its dual
model. Numerical and empirical illustrations are reported.
Autoregressive moving average process, White noise process, Duality in time, Causality, Invertibility and Lag transformation
Khogali A. Khogali,
Olorunsola E. Olowofeso,
Olorunsola E. Olowofeso
John. O. Owino,
Hatemi J. Abdulnasser,
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