# ACF and differencing order of operations

When calculating ACF and PACF, what is the rule regarding differencing? For example, I have an increasing time series- looking at instrument drift. Differencing returns what looks like white noise. When I do ACF and PACF, do I use the raw values or the differenced values?

I've done both, just playing around. The raw values return positive ACF values for many lags. The differenced values return a negative value and the rest negative and insignificant.

What is the correct procedure? Since the mean increases over time. Do I difference before ACF? Or ACF on the raw data?

• Beware of overdifferendcing. Differencing is only appropriate when the original series are integrated, but not otherwise. Mean increasing over time does not warrant differencing, but rather modelling with a deterministic (e.g. linear) time trend. Sep 25, 2017 at 5:20

Edit: Valerie, what Richard is referring to might happen if your true model is something like $y_t = \beta_0 + \beta_1 t + \epsilon_t$ where $\epsilon_t$ is iid or white noise. In this case, if you incorrectly difference your series, you will have $\bigtriangledown y_t = \beta_1 + \epsilon_t - \epsilon_{t-1}$. Then, looking at the ACF plot, it will look like you have an MA(2) model. This will help you determine whether the series is trend-stationary or difference-stationary, or in other words, if it has a deterministic trend or a stationary trend.