# ACF values in identifying non-stationarity

I have used NIST data to calculate ACF in excel which worked fine and coded in our programming language (NOT R).

Here is the plot of ACF:

Now my questions are:

1) From this ACF series how can I we find out this is stationary or not (By looking at values programatically without plotting)? Is there any statistical approach like if X number of values fall out of some MAX_VALUE, then this series fails ACF stationary check or something like that?

2) I have observed that sometimes people using "differenced" series to calculate ACF instead of using original series. Can you help us with when to use "differenced" series and when to use "original" series to calculate ACF?

2) If a series is nonstationary in the sense that $Y_t=Y_{t-1}+\epsilon_t$ (a "random walk") for (in the simplest case) iid $\epsilon_t$, its first difference $\Delta Y_t:=Y_t-Y_{t-1}$ will be stationary, because $\Delta Y_t=\epsilon_t$. Such stationary series have "more classical" statistical properties. E.g., estimated coefficients satisfy central limit theorems under suitable technical conditions and hence are normally distributed, which is not generally the case for nonstationary series. So many people prefer to model stationary series.
• Second, "nonstationary in the sense that" refers to the fact that stationarity refers to the condition that moments are stable over time, and this is violated in the above random walk case. But it would also be violated in other cases, say when a variance of a series jumps from $\sigma_1^2$ to $\sigma_2^2$ after a fraction $\tau$ of observations. Differencing the series is not going to deal with that type of nonstationarity. Mar 13, 2015 at 7:51