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Generalized ARMA (GARMA) model is a new class of model that has been introduced to reveal some unknown features of certain time series data. The objective of this paper is to derive the autocovariance and autocorrelation structure of GARMA(1,3;δ,1)  model in order to study the behaviour of the model. It is shown that the results of this model can be reduced to the autocovariance and autocorrelation of the standard ARMA model as well as a special case. Numerical examples are used to illustrate the behaviour of the autocovariance and autocorrelation at different δ values to show the various structures that the model can represent

Autocovariance and autocorrelation structures of the generalised autoregressive moving average (GARMA(1,3;δ,1)) model