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It is a classical misunderstanding, your model is right, you always have a acf equal to one at lag zero (and not one) since if there is no lag acf = covariance(x , x_lag 0) / variance x = variance x / variance x = 1. So you need to pay attention to the x axis , some software displays ACF starting at lag zero and some others from 1 (which make better ...

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The Autocorrelation Function (ACF) $\rho_k=Corr(y_t,y_{t-k})$ expresses the strength of linear dependency between the $k$-lagged realizations and hence represents an important tool for identification of the lag orders of ARMA and GARCH processes: $$\rho_k:=Corr(y_t,y_{t-k})=\frac{\gamma_k}{\gamma_0},\,\,k\in\mathbb{Z}$$ where the Autocovariance $\gamma_k$ is ...

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I go through the following steps when determing the ARMA(p,q) order for my data. First, you must determine whether any transformation is needed, such as a degree of differencing or taking the log. Remember the data must be stationary to fit an ARMA model. This can be done in a number of ways, but my preference is to run an augmented-dickey fuller test on ...

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