# How to align two seasonal time series

I am trying to decompose a time series using Holt Winters method and use it for forecast. I am trying to do this for weekly data of last 25-26 months.

The challenge is that the dates of the seasonal points keep on changing. E.g. Diwali was on 13th Nov in 2012, 3rd Nov in 2013 and 23rd Oct in 2014. This may not give me a very close prediction, especially around this seasonal point. In addition, there are other seasonal points that occur on same date, e.g. Christmas, Valentine Day, etc.

How do I handle this problem? Do I need to shift my time series for the seasonal points to coincide?

• It is not really clear what kind of two time series are you taking? Could you edit your question to add additional information? – Tim Mar 17 '15 at 8:24
• @Tim I am talking about the yearly time series. So, if I have data from 2012-2015, there will be three series 2012-13, 2013-14, 2014-15. In these 3 series the same seasonal point can appear in different positions – naka Mar 17 '15 at 8:54
• What's crucial is exactly when your non-calendar years start and end. If you have a choice then problems such as this can be made minor. All the specific examples you mention are accommodated quite well by years starting on 1 July. If you have no choice, then spikes such as two occurrences of Diwali in one non-calendar year may be unavoidable, but how much difference will that really make to annual totals or means? – Nick Cox Mar 17 '15 at 9:13
• If you have, or did have, weekly data, then your question is different and the answer is different. But you know when Diwali occurs, as I understand it, so the simplest remedy for forecasting is to build in an indicator variable for a week being Diwali to your model. – Nick Cox Mar 17 '15 at 9:55
• as @NickCox points out the simplest and a straight forward approach is to use a indicator variable i.e., 1 when Diwali else 0. Unfortunately there is no way to include indicator variables in exponential smoothing. so you are left with regression based approaches like ARIMA, linear regression, UCM etc., – forecaster Mar 17 '15 at 14:46