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I'm analysing weekly sales data for a product which is highly seasonal. I would like to capture the seasonality in the regression model. I have read that if you have quarterly or monthly data, in that case you can create 3 and 11 dummy variables respectively — but can I deal deal with weekly data?

I have nearly 3 years of weekly data. The independent variables are average price, advertising spend, promotions, a couple of competitive indexes, school.holidays (1/0), temperature and others. The dependent variable is sales of that product. I am not looking for a time series model as I am using a multiple regression model and I'm trying to understand the influence of the independent variables and not making any forecast.

Thanks!! :)

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You can use 51 dummies to represent the weekly effects. Care should be taken to deal with one or more trends , one or more level shifts, one or more pulse outliers AND/OR any significant autocorrelation in the residuals as any of these will vitiate any of your results. There can also be a change in weekly effects say the week1 effect in year 1 is a -20 whereas the week1 effect in years 2 and 3 is +10 . An incorrect analysis wll suggest that there is no week1 effect. Simple approaches sometimes work when the data is simple . In general simple approaches should simply be tested for possible violations using software/procedures that are aggressive. If you want to see a possibly more correct/rigorous approach to your data (highlighting the implications of under-modeeling) why don't you post it.

By the way time series model are a superset of regression models as they can include regressor variables of the type you specified i.e. fixed/deterministic ( and even more powerful types enabling lead and lag structures. When you use the term time series model you are simply referring to pure ARIMA models. The more correct/general reference to time series models includes causal variables but it all depends on who your teachers were or what textbook you used..

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As mentioned, you can create 51 dummy variables to represent the weeks, but I would suggest testing that model's performance (using RMSE or other) against a more simple model that uses a monthly predictor instead. If seasonality is the most powerful predictor, then weekly indicators may be worth the added complexity - but if your goal is interpretability, monthly indicators may be much more simple to explain/communicate, especially true if the predictive power is similar.

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  • $\begingroup$ quite true .... But how do you take 52 weeks and exactly convert them to 12 months .... only if you have daily data and if you have daily data then you should model daily data .... but that's just my opinion ..try searching SE for DAILY stats.stackexchange.com/questions/240863/… $\endgroup$ – IrishStat Dec 6 '16 at 19:34
  • $\begingroup$ Fair point... but if that problem occurs, it should be evident in the RMSE comparison between the two models. The more complex model must out-perform the more simple model to be worth it. $\endgroup$ – B.Frost Dec 6 '16 at 20:04
  • $\begingroup$ agreed ! but over-archingly one needs to know when forecasts need to be recomputed. Higher frequency data analysis such as weeks compared to months enable "quicker assesments" to be made and certainly daily data analysis could even be better as there is a "time value of information" . $\endgroup$ – IrishStat Dec 6 '16 at 20:15
  • $\begingroup$ My suggestion was to trial weekly sales modeling with a month indicator as one of the predictors, so the frequency would be identical. $\endgroup$ – B.Frost Dec 6 '16 at 20:23
  • $\begingroup$ can you be more specific ? do you mean 1,1,1,1,2,2,2,2,3,3,3,3,, $\endgroup$ – IrishStat Dec 6 '16 at 20:37

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