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time-seriesforecastingarimasarimax

Is autocorrelation an indication of Non Stationary Series

I have time series data and it has following ACF plot

enter image description here

I read The data should be stationary

"The data is non-stationary when there is a large spike at lag 1 that slowly decreases over several lags. If you see this pattern, you should difference the data before you attempt to identify a model. To difference the data, use differences. Once you difference the data, obtain another autocorrelation plot."

Adf test telling me the data is stationary as its p values is less than 0.05.

For stationary series , I read many places that "A stationary time series has a mean, variance, and autocorrelation function that are essentially constant through time."

do we really need to have constant autocorrelation for each lag for data to be stationary?

Based on Mauritis response here i am attaching graph highlighted with seasonal regionenter image description here

Solution

  • Is autocorrelation an indication of Non Stationary Series

    The short answer is no.

    To demonstrate, let's consider a stationary AR(1) process: I'm using R here to simulate data and plot the ACF.

    set.seed(2020)
ts <- arima.sim(model = list(ar = 0.8), n = 100)
plot(ts)

    enter image description here

    acf(ts)

    enter image description here

    Notice how the sample autocorrelation tapers off; to be specific, the ACF decreases with phi^h where h is the lag and phi is the slope in the AR(1) model (here phi = 0.8).