# AnalyticBridge

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# Numeric representation of the time series.

Dear All,

I have a data in which figures dip in the months of november and december. I can represent this dipping in the time series chart. But can I have some numeric figure showing that the seasonality have a significant effect over the sales.

Can anyone help me on this topic. Does the autocorrelation serve the pupose.

Thanks to you all

Atul

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### Replies to This Discussion

Atul,

The way to do this, is to divide your series by a moving average over 12 months (seasonality) or by differencing the series by 12 (seasonality factor) and hence you get seasonality indices... This can be graphed too.. I'll try to put up some arbit numbers, and hence the method to do this for you..

Instead, if you can give me your numbers, I can get it done on that as well!

- Arun
Atul,

I've attached the calculations for the seasonality indices. Hope it's of good help. Let me know if you've got more questions.

- Arun
Attachments:
Thanks for your valuable inputs. With this I can calculate the seasonality. But if there is any way by which we can say this seasonality is significant or not. Say for example I got the effect of seasonality as Observed-Seasonalyy adjusted. Now if there is any point or index which indicates that this much effect of seasonality is significant and this much is not.

thanks
Atul
According to me I don't think there's something like saying 'Seasonality is significant or not' from any statistic.

If there is seasonality/ trend present in your series, it'll come out when you use moving averages. If it is not significant, I'm guessing you'll find an almost straight line.. That's my way of saying significant or not.

There's probably a way using ARIMA to find d=?. This should help probably in making the series stationary, so ACF plots can help. But I still don't know if it'll give you whether those are statistically significant. I don't know if such a term exists for seasonality!

Will look forward to hearing from someone who knows if it exists.
How can we evaluate magnitude of the November-December dip?

First, calculate the ratio of a value to the previous one to compensate for any trend. It would be even better to do it with some moving average of width 2 (or maybe 3). The histogram of the ratios will likely be close to log normal (or an unknown distribution) with some outliers at these two months. Ignore the outliers for the moment and approximate the histogram with a smooth curve - this will be a theoretical model distribution. Now take the outliers and calculate their probability. If they are real (the probability is low) you have the seasonal effect. The degree of the dip can be defined as inversely proportional to value of the probability, or whatever you like.