使用Auto.arima预测多元数据

Question

I am trying to forecasts sales of weekly data. The data consists of these variables week no, sales, avgprice/perunit , holiday(whether that week contains holiday or not) and promotion(if any promotion is going) of 104 weeks. So basically the last 6 obs of data set looks as:

 Week     Sales       Avg.price.unit Holiday    Promotion

  101     8,970             50       0         1

  102    17,000             50       1         1

  103    23,000             80       1         0

  104    28,000            180       1         0

  105                      176       1         0

  106                      75        0         1

Now I want to forecast for 105th and 106th week. So I created univariate time series x by using ts function and then ran auto.arima function by issuing the command:

x<-ts(sales$Sales, frequency=7)
>  fit<-auto.arima(x,xreg=external, test=c("kpss","adf","pp"),seasonal.test=c("ocsb","ch"),allowdrift=TRUE)
>fit
ARIMA(1,1,1)                    

**Coefficients:
          ar1      ma1  Avg.price.unit   Holiday  Promotion

      -0.1497  -0.9180          0.0363  -10.4181    -4.8971

s.e.   0.1012   0.0338          0.0646    5.1999     5.5148

sigma^2 estimated as 479.3:  log likelihood=-465.09
AIC=942.17   AICc=943.05   BIC=957.98**

Now when I want to forecast the values for last 2 weeks(105th and 1o6th) I supply the external values of regressors for 105th and 106th week:

forecast(fit, xreg=ext)

where ext consists of future values of regressors for last 2 weeks.

The output comes as:

 Point         Forecast    Lo 80    Hi 80    Lo 95    Hi 95

15.85714       44.13430 16.07853 72.19008 1.226693 87.04191

16.00000       45.50166 17.38155 73.62177 2.495667 88.50765

The output looks incorrect since the forecasted value of sales is very less as the sales value of previous values(training) values are generallly in range of thousands.

If anyone can tell me why it is coming incorrect/unexpected, that would be great.

Answer 1

If you knew a priori that certain weeks of the year or certain events in the year were possibly important you could form a Transfer Function that couild be useful. You might have to include some ARIMA structure to deal with short-term autoregressive structure AND/OR some Pulse/Level Shift/Local Trends to deal with unspecified deterministic series ( omitted variables ). If you would like to post all of your data I would be glad to demonstrate that for you thus providing ground zero help. Alternatively you can email it to me at dave@autobox.com and I will analyze it and post the data and the results to the list. Other commentators on this question might also want to do the same for comparative analytics.

Answer 2

Where are the 51 weekly dummies in your model? Without them you have no way to capture seasonality.