It is common to fit a model using training data, and then to evaluate its performance on a test data set. When the data are time series, it is useful to compute one-step forecasts on the test data. For some reason, this is much more commonly done by people trained in machine learning rather than statistics.

If you are using the forecast package in R, it is easily done with ETS and ARIMA models. For example:

library(forecast)
fit <- ets(trainingdata)
fit2 <- ets(testdata, model=fit)
onestep <- fitted(fit2)

Note that the second call to ets does not involve the model being re-estimated. Instead, the model obtained in the first call is applied to the test data in the second call. This works because fitted values are one-step forecasts in a time series model.

The same process works for ARIMA models when ets is replaced by Arima or auto.arima. Note that it does not work with the arima function from the stats package. One of the reasons I wrote Arima (in the forecast package) is to allow this sort of thing to be done.