I have hourly data of electricity load (MW) that span 8 months (that is, 5760 data points). I also have predictions from a regression model for the same period. My goal is:
- to examine some properties of the time series (stationarity, seasonality, trend)
- to assess the performance of the regression model.
To check whether the time series is stationary I used the Dickey-Fuller test. The results of the test are:
Test Statistic -3.85795
p-value 0.00236705
#Lags Used 34
Number of Observations Used 5725
Critical Values {'5%': -2.86204498529, '1%': -3.43149274838,...
It seems that it is safe to reject the null hypothesis of the test (i.e. that the time series is non-stationary) as the test statistic lies beyond the critical values.
I have also plotted the ACF values. I used lags up to T/4 (that is 1400) and I am not sure that this makes much sense.
The plot is shown below:
Finally, a residual plot is shown:
The plot does not seem to indicate problem with the equality of variance assumption.
My questions are:
Is it possible to draw any conclusions from the ACF plot and is this the proper way to do it (i.e. use the complete time series and a lag up to 1400 or would it be possible to perform the test using a subset of the series)?
Do the findings in the ACF plot in any way contradict or reinforce the results of the Dickey-Fuller test?
What would the "proper" approach to analyzing such time series data be?