# handling spikes in ARIMA model residual components

I am trying to predict sales values using time series approach. Below graph is the sales for a store over a period of 942 days (sales will be 0 when the store is closed and are not plotted in first 2 graphs for sake for clarity in graph):

Stacking yearly sales give us a graph like below:

It looked like it may be worth investing in time series, so I tried drawing the acf and pacf graphs which are shown below:

The strong auto correlation in the curve suggest the presence of time series. So I applied, auto.arima() function from r to just look at how it performs (salesModel <- auto.arima(saleDataSeries)). Below is the residuals plot from arima. I tested the prediction on Kaggle Leaderboard and the approach did not perform that well(competition is over now).

Model Parameters:

Series: saleDataSeries
ARIMA(5,1,4)

Coefficients:
ar1      ar2      ar3      ar4      ar5      ma1     ma2     ma3
-0.0885  -0.1938  -0.5965  -0.3084  -0.3058  -0.8985  0.0040  0.7063
s.e.   0.1036   0.0634   0.0451   0.0329   0.0690   0.1202  0.0704  0.0909
ma4
-0.6996
s.e.   0.0296

sigma^2 estimated as 4621003:  log likelihood=-8555.57
AIC=17115.2   AICc=17115.43   BIC=17163.67


Currently I am also looking at multiple seasonality using tbats, but I believe that there can be certain modifications that can be made to simple ARIMA model as the ACF/PACF graph still have some spikes in the residual component. I am unsure why this is happening and any insights would be helpful

• The data is publicly available at kaggle.com/c/rossmann-store-sales/data (one would need to sign up though). The train.csv has all the data and I had grouped the data by store and analysing for each store. The data I have posted is for store 6. Let me know if you can't access it. – Aman Deep Gautam Dec 15 '15 at 19:48