I have ~1500 time series data representing store sales (US$). All time series are of the same size with 52 weeks of data with no NA values. For a subset of 18 specific time series, I want to find the top 10 "control" time series that match based on similarity metrics.
The similarity matching process is:
1) Pearson Correlation between time series (negative correlations are filtered out)
2) Engle-Granger cointegration (two-step process as defined in link)
3) Euclidean Distance (the smaller the distance, the more similar the time series are)
Note that I normalize the data before applying the above process, defined as subtracting the mean and dividing by SD for each individual time series. Also, note that Dynamic Time Warping (DTW) is not ideal, as I want similarity at each time point rather than warped distance.
My two questions are:
1) Is it recommended to log-transform the data? I am uncertain at what step in the process I should do this or if it is needed.
2) Currently, I address outliers by restricting points to no more than ± 3 SD above the mean for each time series. Is there an improved way of determining outliers?
In addition, any input on the similarity matching process is appreciated. Does the order of the different similarity steps make sense, or is there anything that should be added/changed?
I appreciate any help. Thank you!