# How do I read an auto-correlation plot?

I'm taking a data camp lesson by Professor Rob J Hyndman. He went over the ACF plot and said that you know the period of seasonality based on the highest point in the ACF plot.

I have this timeseries-

And I have this ACF plot -

Does this mean the seasonal difference is every one or two days and the further out in time, the more strongly negatively correlated the relationship? I'm not sure how to read it with this many significant lags.

Update-

I created an arima model with auto.arima() and it suggested that I diff my timeseries one time to make it stationary. I'll add the new charts.

Autoplot on the stationary data-

ACF of the stationary data-

I added a transformation for the increasing variance.

ts %>% BoxCox(lambda = .3170305) %>% diff() %>% autoplot() where lambda is defined by BoxCox.lambda(ts)

Here's the ACF plot given these transformations -

• Your series is not stationary! It clearly shows an upward trend, which makes things quite confusing for study of autocorrelation. I would work on the differenciated series $Y_t:=X_t - X_{t-1}$ rather than on the original $X_t$ If the problem persists, then try $Z_t:=Y_t - Y_{t-1}$ and so on... Commented May 27, 2019 at 8:28
• I updated the chart. What I'm seeing is that there is a strong positive correlation at a consistent interval, a strong negative correlation at a consistent interval and a few weeker effect too. My data is daily ecommerce revenue. Does this suggest to you that the effect is a function of the day of the week?
– ivan
Commented May 27, 2019 at 15:39
• the series are not only nonstationary on mean, but the variance seems increasing too. you cant apply ACF/PACF analysis until you address mean and variance instability, e.g. by log differencing Commented May 27, 2019 at 15:39
• @Aksakal Do you think that that increase in variance as time goes on has to do with the fact that the original series was also growing? I mean, we'd have something like a constant coefficient of variation, but not constant variance. Because in that case maybe the series to work with is the "return" series $Y_t:=(X_t−X_{t−1})/X_{t-1}$ Commented May 27, 2019 at 15:48
• @David, it very well can be. The log differencing (continuous return) is similar to simple return that you refer to in this respect. It doesn't have to be the log rule though, it can be power law. Commented May 27, 2019 at 15:50