Solved – Forecasting with ARIMA with outlier

arimaforecastingoutliersrtime series

Hi all I am trying to forecast with an ARIMA model with outliers.
At first 

x<-ts(data$value, start=c(2009,1), end=c(2015,12),  freq=12) # keep 7 months to evaluate foecast

SAR011011<-arima(serie,order=c(0,1,1),seasonal=list(order=c(0,1,1),period=12)); 
SAR011011                        #fit.an.ARIMA.model.with.no.outlier;

Coefficients:
          ma1     sma1
      -0.3372  -0.7815
s.e.   0.1166   0.2433

sigma^2 estimated as 198465069:  log likelihood = -784.53,  aic = 1573.06

Then I check for some outliers with the TSA package

detectIO(SAR011011)

ind     19.000000 30.000000 31.000000
lambda1  5.146045 -4.250828  4.136944

So, then I added 3 outliers at theobs 19, 30 and 31

Coefficients:
          ma1     sma1      IO-19       IO-30      IO-31
      -0.1550  -0.4761  23262.107  -41275.194  20083.911
s.e.   0.1274   0.1283   8954.079    8778.279   9112.721

All of them are sigficant and really improve AIC.

So, when I tried to forecast.. most common procedures did not work.

predict(SAR011011out, n.ahead = 7, se.fit = TRUE) -->data' must be of a vector type, was 'NULL'

forecast(SAR011011out, h=3)--> 'data' must be of a vector type, was 'NULL'

I have read here that TSA does not have a predict function. But I just do not believe that is not possible to forecast incorporating outliers.
what does the community use in this cases?

Best Answer

If you have

  • a fitted ARIMA model and
  • the last few observations and residuals ($p$ observations and $q$ residuals for an ARIMA($p,q$) model; $p+P$ and $q+Q$ for SARIMA models),

there should be no difficulty in forecasting. You have all the inputs you need. Use the model formula to obtain a one-step-ahead forecast. If you want to forecast further ahead, use the forecasted value in place of the true value and iterate forward.

If you are asking how to do that in R, that would be off topic. But it is actually quite easy: if you fit your model with arima or Arima, the method predict should work. If you want to account for outliers at known time points when fitting with arima or Arima, you can use a set of dummy variables (supplied via the argument xreg) with unit values on these time points. For forecasting, you would supply zero vectors for newxreg as presumably you cannot predict the future outliers.

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