Updating ARIMA models at frequent intervals

Question

I am using an ARIMA model to create a model for correlated errors from my regression model. I am using the auto.arima function from the forecast package in R. I am able to get more data at some frequent interval after the regression model is created, so I get more values for the correlated errors.

My question is how do I update the ARIMA model with a gap in time interval between readings.

Answer 1

Suppose x contains the first series of observations and y contains the second series of observations, where there is a gap between them consisting of m time periods. Let z be the complete time series, given by

z <- ts(c(x,rep(NA,m),y), frequency=??, start=??)

I assume you will set the start and frequency to suitable values.

Then you fit the first model using

fit <- auto.arima(x)

After you have obtained the additional observations, you can update the model in several ways. First, you might just compute the residuals on the new observations without revising the parameters or model order:

fit1 <- Arima(z,model=fit)

Alternatively, you might not revise the model order, but you do update the parameter estimates. In that case:

fit2 <- Arima(z,order=fit$arma[c(1,6,2)])

(Here I have assumed it is a non-seasonal ARIMA model. For seasonality, you would need to add a seasonal argument.)

Lastly, you might revise both the model order and the parameter estimates. Then

fit3 <- auto.arima(z)