# ARIMA - Regressor Effects

I am new to R and forecasting. I have access to weekly data (104 weeks) for a certain SKU, its value and volume sales and a few promo variables.

Promo 1 and Promo 2 are continuous variables (unfortunately Promo 1 is 0 here for this SKU) while Promo 3 and Promo 4 are categorical variables.

I tried forecasting the volume sales for this SKU for the next 72 weeks. I included dummy variables using seasonaldummy function

actual_vol = ts(data$Volume , frequency =52) dummy = seasonaldummy(actual_vol) xreg = cbind(data$Promo1 , data$Promo2 , data$Promo3 , data\$Promo4 , dummy)

fit = auto.arima(actual_vol , xreg = xreg)


I am trying to forecast sales for the next 72 weeks by keeping my promo variables as 0 (basically baseline sales). I used seasonaldummyf and promo variables as 0 for forecast.

The plot looks something like this

As you can see the forecast looks exactly the same as the previous data (same as using snaive) and it seems promo had no effect at all on volume sales.

Kindly let me know if the method is correct and if not how can I improve it.

https://drive.google.com/file/d/0B6sOv1da0JMeVHl1SlRMZmJDODQ/view?usp=sharing

• What are you expecting the forecasting(software) method to do? If you have prior beliefs you need to incorporate them. – forecaster Sep 18 '15 at 16:39
• You may also consider including seasonal effects via dummies due to Easter and/or other events that could be relevant to the sales of a particular SKU and that do not occur on the same date every year. Also, using 52 weeks per year is fine in the short run, but over a few years the extra day or two at the end of each year will accumulate and make your forecasts less accurate; see e.g. this (and also this) post in Rob J. Hyndman's blog. – Richard Hardy Sep 20 '15 at 14:22
• thanks a lot Richard .I shall incorporate these in my model – Abhishek Shetty Sep 21 '15 at 5:56

## 1 Answer

I took your data and used AUTOBOX ( a commercially available piece of software that I have helped develop ) to automatically analyze your data. AUTOBOX found that one of your promotional variables (PROMO2) was statistically significant. . A plot of the Actual/Fit and Forecast is of interest as it shows the dynamic buildup/change starting at week 35 of each year lasting some 21 weeks. . The plot of the forecasts is here with values here . Your solution was flawed by ignoring the 6 points in time that were "unusual" and by using seasonal arima structure rather than specific week of-the-year effects . Anomalies have a deleterious effect on parameter estimation thus they need to be treated thus any parameters that are estimated without adjusting for outliers are not robust e.g. your ar coefficient.