Question

Consider the following ARMA(1,1) Process:

1. Describe the ACF and the PACF plot for the process.
2. Is the process stationary or invertible?

(Assume that    Also, )

Answer 1

I generate data for the given ARMA process for 500 observations. The ACF and PACF plots obtained are as follows:

Series ts 20 25 10 15 Lag

Series ts 20 25 15 10 Lag

The process is stationary since the mean and variance are not time dependent. The ACF and PACF plots of the above process has the signature of a white-noise process and hence, I'd rewrite the process as:

$Y_t = 2 + e_t$, where $e_t$ is a white-noise process with 0 mean and 0.5 standard deviations. Therefore, the given process is equivalent to a white noise process with mean 2 and variance of 0.25.

The forecast therefore for h=1,2,3,4 are all equal to 2, with a confidence interval of $\pm 1.6*0.5= 0.8$

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