I have two time series data sets which contain hourly-intervalled, monthly, and yearly household electricity consumption in kWh. One data set is produced by a simulation, the other gathered from the real-world. My aim is to validate the simulated output by using the data gathered from the real-world.
I want to measure the similarity between these data sets, and be able to say if these are statistically similar. My first intuition is to use a correlation coefficient such a Pearson product moment correlation. But from what I read in previous posts that in general the correlation coefficient between two time-series may be a very poor metric.
I'm not very keen on statistics related to time series, but would something like a cross-correlation or maybe ARIMA do the trick? Could someone please point me in the direction for a technique which I can use in SPSS?