How do you forecast ARIMA with multiple regressors? - r

Question

The complete R data and code for my question is here: https://pastebin.com/QtG6A7ZX.
I am new to R and still a beginner when it comes to time series analysis, so please forgive my ignorance.
I am attempting to model and forecast some enrollment data with 2 dummy-coded regressors. I have already used auto.arima to fit the model:
model <- auto.arima(enroll, xreg=x)
Before I forecast with this model, I am attempting to test its accuracy by selecting only a part of the time series (1:102 instead of 1:112), and likewise, a partial list of regressors.
Based on auto.arima, I fit the partial model as follows:
model_par <-arima((enroll_partial), c(1, 1, 1),seasonal = list(order = c(1, 0, 0), period = 5), xreg=x_par)
I have tried three different ways to forecast and get essentially the same error:
fcast_par <- forecast(model_par, h=10) #error
fcast_par <- forecast(model_par, h=10, xreg=x_par) #error
fcast_par <- forecast(model_par, h=10, xreg=forecast(x_par,h=10)) #error
'xreg' and 'newxreg' have different numbers of columns
I have tested using auto.arima with the partial data. That works, but gives me a different model and, although I specified 10 predictions, I get over 50:
model_par2 <- auto.arima(enroll_partial, xreg=x_par)
fcast_par <- forecast(model_par2, h=12, xreg=x_par)
fcast_par
So, my main question is, how do I specify an exact model and predict using more than 1 regressor given my data (see Paste Bin link above)?

Answer 1

The forecast() function is from the forecast package, and works with model functions that are from that package. This is why it is possible to produce forecasts from auto.arima() using forecast(model_par2,xreg=x_fcst).
The arima() function comes from the stats package, and so there are no guarantees that it would work with forecast(). To specify your own ARIMA model, you can use the Arima() function, which behaves very similarly to arima(), but you will be able to produce forecasts from it using forecast(model_par2,xreg=x_fcst).

Answer 2

You have two problems. One of them is that the various forecasting functions in R are making it (intentionally?) difficult on you.
The first problem is that you need to define the values of your regressors for the forecasting period. Extract the relevant data from x by using window():
x_fcst <- window(x,start=c(2017,4))
The second problem is that forecast() (which dispatches to forecast.Arima()) is a red herring here. You need to use predict() (which dispatches to predict.Arima() - note the capitalization in both cases!):
predict(model_par,newxreg=x_fcst,h=nrow(x_fcst))
which yields
$pred
Time Series:
Start = c(2017, 3)
End = c(2019, 1)
Frequency = 5
[1] 52.00451 52.00451 52.00451 52.00451 52.00451 52.00451 52.00451 52.00451
[9] 52.00451
$se
Time Series:
Start = c(2017, 3)
End = c(2017, 3)
Frequency = 5
[1] 17.13345
You can also use auto.arima(). Confusingly enough, this time forecast() (which still dispatches to forecast.Arima()) does work:
model_par2 <- auto.arima(enroll_partial, xreg=x_par)
forecast(model_par2,xreg=x_fcst)
which yields
Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
2017.40 39.91035 17.612358 62.20834 5.808514 74.01219
2017.60 59.51003 32.783451 86.23661 18.635254 100.38481
2017.80 69.81000 39.290834 100.32917 23.134962 116.48505
2018.00 57.49140 23.601444 91.38136 5.661183 109.32162
2018.20 55.45759 18.503034 92.41214 -1.059524 111.97470
2018.40 34.57866 -7.306747 76.46406 -29.479541 98.63686
2018.60 52.30199 6.702068 97.90192 -17.437074 122.04106
2018.80 61.61591 12.582055 110.64977 -13.374900 136.60672
2019.00 50.47661 -1.765945 102.71917 -29.421485 130.37471
And yes, you do get five times as many predictions. The first column is an expectation forecast, and the others give prediction intervals. These are governed by the level parameter to forecast().