Solved – Forecasting a transformed time series

arimadata transformationforecastingr

I have fitted a seasonal ARIMA model using R to a log transformed times series which I called lnseries.

I can forecast fine for the transformed time series (lnseries) storing the ARIMA model (which I called fit) then using the command:

$\texttt{plot(forecast(fit))},$

this shows me the forecast and 95% confidence interval. But I'm stuck on how to get the actual original time series forecast plot using this model.

Help anyone!?

Best Answer

If you're trying to forecast an interval for future observations, exponentiating the limits from the log-scale forecasts should do.

If your log-data is approximately symmetric, exponentiating the log-scale forecast should give you a median forecast on the original scale; if that's good enough you're pretty much set.

If your sample sizes are quite large and you have approximate normality on the log scale you could treat your variance estimate as "known" and produce a reasonable approximation of a mean forecast by taking $\exp(\hat{y}_t+\frac{1}{2}\sigma^2_{t})$ where $\sigma^2_{t}$ is the conditional variance of the predicted observation.

Related Solutions

Solved – Initialize ARIMA simulations with different time-series

You can "fit" the model to different data and then simulate:

m2 <- Arima(z,model=m1)
simulate.Arima(m2,future=TRUE,bootstrap=TRUE)

m2 will have the same parameters as m1 (they are not re-estimated), but the residuals, etc., are computed on the new data.

However, I am concerned with your model. Seasonal models are for when the seasonality is fixed and known. With animal population data, you almost certainly have aperiodic population cycling. This is a well-known phenomenon and can easily be handled with non-seasonal ARIMA models. Look at the literature on the Canadian lynx data for discussion.

By all means, use the square root, but then I would use a non-seasonal ARIMA model. Provided the AR order is greater than 1, it is possible to have cycles. See

You can do all this in one step:

m1 <- auto.arima(y, lambda=0.5)

Then proceed with your simulations as above.

Solved – time series forecasting using auto.arima and exponential smoothing

Seasonality is probably not very strong. Different algorithms will give different results, unless seasonality is glaringly obvious.
The best measure is always to compare forecast accuracy on a holdout set: hold back the last $n$ observations, fit your models to all other observations, forecast into the last $n$ time periods with both models, then compare forecast accuracy using your error measure of choice (see 5 below).
Yes, this is a common complaint. I don't think there is an easy way to get the in-sample fit. But you can get the residuals: auto.arima(WWWusage)$residuals. Best to look into the code of auto.arima() to see whether you need to add or subtract them from the original series to get the fit. I'd say you have to subtract ("actuals=model+residuals"), but better check.
I recommend a good forecasting textbook. This is a very good start. Otherwise, read through the help pages.
The appropriate error measure will depend on your personal loss function. Is your pain symmetric, and will it increase more strongly with larger errors? Then use MSE. Is your pain proportional to absolute errors? Then use MAE. Best to look at multiple error measures.

One tip: averaging forecasts will usually improve accuracy. Consider taking the average of your two models' forecasts per future time bucket.
auto.arima() apparently fits no drift, even if you allow it.

Best Answer

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Solved – Initialize ARIMA simulations with different time-series

Solved – time series forecasting using auto.arima and exponential smoothing

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