## Correlation between event and its effect on a time series

For the discussion of math. Duh.

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csiko
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Joined: Sun Nov 04, 2012 7:51 pm UTC

### Correlation between event and its effect on a time series

I have a time series, e.g. the daily number of visitors on my blog. I have a set of events of some class, like the days when I made a new posting. I want to measure the effect of a new posting on the visitors. However, the effect of a new posting is not limited to the same day the posting was made. It could be days later.

So to generalize it: There is a (either discrete time or continous time) series of data points. There is a set of events given by their time instants. All events are believed to have a similar effect on the series, beginning from the event time and lasting for some time t_L.

Is there a statictical method to approach this problem? Or do I need some extra assumptions?

Thanks in advance for any tips, ideas, help on this.

Treatid
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### Re: Correlation between event and its effect on a time serie

As a general resource I would imagine that various analysis relating to stock market data could provide some useful algorithms.

To some degree the problem can be considered as a "best fit curve" problem. In this case you would have the underlying data - which presumably is fairly linear - on top of which you have the response to each event. One might guess that the general response to an event will be an initial spike that decays over time - so some form of decay graph and an iterated approach to best fit of parameters.

If your initial event provokes further events (responses in turn provoke discussion...) then a more complex curve may be appropriate.

As mentioned above - for better or worse - curve fitting is a favourite sport among market watchers and there are many well developed algorithms for matching curves to stochastic data.

mouseposture
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### Re: Correlation between event and its effect on a time serie

FancyHat
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### Re: Correlation between event and its effect on a time serie

Would autocorrelation be suitable?
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ConMan
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### Re: Correlation between event and its effect on a time serie

FancyHat wrote:Would autocorrelation be suitable?

Well, autocorrelation is better for understanding how a series without any assumed external input behaves. To deal with the effect of external factors, you need to incorporate some form of intervention analysis. While probably overpowered for your purpose, I think X-12-ARIMA from the US Bureau of Labour Statistics includes some suitable intervention analysis methods.
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