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I have a set of seasonal time series data and I would like to know what method I can use to determine if the data is decaying to 0 or if what I am seeing is actually part of a seasonal drop. By decay I mean that over time the metric is going to 0.

Here is a chart as an example: Seasonal data plot w/ forecast

How can I differentiate the gradual failure from a seasonal drop?

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  • $\begingroup$ Has it ever gone to 0? Is there any data on what that typically looks like, or do you just want to identify when it is dropping faster than normal? $\endgroup$ – gung Jan 29 '16 at 16:48
  • $\begingroup$ No, it's never gone to 0 and I should clarify that the data I am looking at goes back 7 days and it is in 5m increments. I basically would just like to identify when the data is headed to 0 or if I am just in a seasonal drop. I have performed a Holt-Winters forecast of the data and that's nice to see but I still am having trouble differentiating. $\endgroup$ – Eric Jan 29 '16 at 16:50
  • $\begingroup$ A simple linear model could give you the general trend. If you know the length of the season, try x(t) = x(t-length of season) and a lag plot could give you some simple insight. If the trend is decreasing, then you have your answer. $\endgroup$ – YCR Feb 1 '16 at 14:38
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IMHO, you could do a lag plot, it is the most simple visual technique, very efficient.

More technical, another way to answer your question is to ask if the average of your series change over time when the seasonality effect is discarded.

For the stationarity, you could see that one.

In your case, it is a bit different, as you have a seasonality. It is lightly discussed here.

In the end, the easiest way is to aggregate your time series to get rid of the seasonality then to test this new time serie with the tests in the first link.

The hard way is to do a Threshold Autoregressive model.

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