forecasting ARIMA model with extra regressors

Question

Suppose i have some time series as below and i want to forecast c1 one step a head, doing so is pretty straight forward and easy in R:

testurl = "https://docs.google.com/spreadsheets/d/1jtpQaSxNY1V3b-Xfa5OJKDCLE6pNlzTbwhSHByei4EA/pub?gid=0&single=true&output=csv"
test = getURL(testurl)
mydata = read.csv(textConnection(test), header = TRUE)
data <- ts(mydata['c1'])
fit <- auto.arima(data)
fcast <- forecast(fit)
fcast

note that the numbers is just random numbers, and the auto.arima suggest us to use an arima(0,1,0) and the forecast one step a head is 52.

however, what if one want to use c2 and c3 to improve (in terms of aic and bic for example) the out of sample forecast? how would one actually continue then?

c1   c2     c3
40   0,012  1
41   0,015  1
42   0,025  1
40  −0,015  1
44   0,000  0
50   0,015  0
52   0,015  1
51   0,020  1
50   0,025  1
52   0,030  0
53   0,045  1
52   0,030  1
52   0,025  0
52   0,000  0
51   0,010  0
50  −0,02   1
48  −0,025  1
49  −0,030  1
51  −0,040  1
52  −0,350  0

Answer 1

If I understand correctly you're trying to fit a dynamic regression model to your data with xreg in auto.arima(). You can automatically determine a model fit using something like this:

tsdata <- ts(mydata)
fit <- auto.arima(tsdata[,1], xreg = as.matrix(mydata[,2:3]))

To generate your 1-step ahead forecast you will need to supply a matrix of future values of C2 and C3 to the xreg argument in the forecast function. One way you could do this would be like this:

fc.c2 <- forecast(tsdata[,2], h = 1)
fc.c3 <- forecast(tsdata[,3], h = 1)


newxreg <- as.matrix(cbind(fc.c2$mean, fc.c3$mean))

fc.c1 <- forecast(fit, xreg = newxreg)