Multiple Regression - Weekly Data Modelling

Question

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!! :)

Answer 1

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..

Answer 2

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.