Metric to measure the time series similarity

[sarahmish]

Problem Description

Current time series metrics in SDMetrics are detection/classifier based. It would be beneficial to have a metric that assesses the quality of the synthetic time series and the original one. An example of such metric would be something to compare the autocorrelation of the original time series and the correlation of the synthetic one.

In this case, the sampled sequences do not preserve the correlation of the time series with itself.

Discussion

Since the most important value in autocorrelation are the ones with low lag values, we can take the maximum as a "metric" of how well AC is. Other ideas of how we can construct a metric to assess the seasonality/periodicity of the signal can be constructed around the FFT of the two signals.