Simple forecasts from an estimated MA model

Now that you've estimated a MA model with your Nile data, the next step is to do some simple forecasting with your model. As with other types of models, you can use the predict() function to make simple forecasts from your estimated MA model. Recall that the $pred value is the forecast, while the $se value is a standard error for that forecast, each of which is based on the fitted MA model.

Once again, to make predictions for several periods beyond the last observation you can use the n.ahead = h argument in your call to predict(). The forecasts are made recursively from 1 to h-steps ahead from the end of the observed time series. However, note that except for the 1-step forecast, all forecasts from the MA model are equal to the estimated mean (intercept).

In this exercise, you'll use the MA model derived from your Nile data to make simple forecasts about future River Nile flow levels. Your MA model from the previous exercise is available in your environment.

This exercise is part of the course

Time Series Analysis in R

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Exercise instructions

Use predict() to make a forecast for River Nile flow level in 1971. Store the forecast in predict_MA.
Use predict_MA along with $pred[1] to obtain the 1-step forecast.
Use another call to predict() to make a forecast from 1971 through 1980. To do so, set the n.ahead argument equal to 10.
Run the pre-written code to plot the Nile time series plus the forecast and 95% prediction intervals.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Make a 1-step forecast based on MA
predict_MA <-

# Obtain the 1-step forecast using $pred[1]


# Make a 1-step through 10-step forecast based on MA


# Plot the Nile series plus the forecast and 95% prediction intervals
ts.plot(Nile, xlim = c(1871, 1980))
MA_forecasts <- predict(MA, n.ahead = 10)$pred
MA_forecast_se <- predict(MA, n.ahead = 10)$se
points(MA_forecasts, type = "l", col = 2)
points(MA_forecasts - 2*MA_forecast_se, type = "l", col = 2, lty = 2)
points(MA_forecasts + 2*MA_forecast_se, type = "l", col = 2, lty = 2)

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