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I am working on time series with seasonality. However, the event that is repeated every year doesn't happen exactly in the same time, it advances by specific period of time. (example an event happened this year on 1st January, next year will take place on 11th January and the year after that 21st January and so on. each time it adds 10days). is there a way to work with such pattern? does it have a great impact on our work?

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is there a way to work with such pattern?

Use a causal model with a Boolean predictor, possibly lagged, or using some profile if the impact of the event changes over time. For instance, the event could have a strong impact when it happens and then a weaker and weaker effect over the next ten days. For something like this, some kind of "ramp-like" predictor would make sense.

A reasonable causal model might be regression with seasonal dummies to capture the seasonality. Consider interaction terms between the seasonal and the event dummies, if your seasonality has a short period, like day-of-week or day-of-month. If by "seasonality" you mean yearly seasonality, an interaction will likely not be necessary. Alternatively, try regression with ARIMA errors.

does it have a great impact on our work?

We can't tell you that, it will depend on your data. The specific date of Easter, which also shifts around in the year, will have a huge impact on the demand for eggs, but presumably much less so for many other products demanded, e.g., mousetraps.

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