Forecasting simulated ARIMA

Now that you are an expert at fitting ARIMA models, you can use your skills for forecasting. First, you will work with simulated data.

We generated 120 observations from an ARIMA(1,1,0) model with AR parameter .9. The data are in y and the first 100 observations are in x. These observations are plotted for you. You will fit an ARIMA(1,1,0) model to the data in x and verify that the model fits well. Then use sarima.for() from astsa to forecast the data 20 time periods ahead. You will then compare the forecasts to the actual data in y.

The basic syntax for forecasting is sarima.for(data, n.ahead, p, d, q) where n.ahead is a positive integer that specifies the forecast horizon. The predicted values and their standard errors are printed, the data are plotted in black, and the forecasts are in red along with 2 mean square prediction error bounds as blue dashed lines.

The astsa package is preloaded and the data (x) and differenced data (diff(x)) are plotted.

This exercise is part of the course

ARIMA Models in R

Exercise instructions

Plot the sample ACF and PACF of the differenced data to determine a model.
Use sarima() to fit an ARIMA(1,1,0) to the data. Examine the output of your sarima() command to assess the fit and model diagnostics.
Use sarima.for() to forecast the data 20 time periods ahead. Compare it to the actual values.

Hands-on interactive exercise

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

# Plot P/ACF pair of differenced data 


# Fit model - check t-table and diagnostics


# Forecast the data 20 time periods ahead
sarima.for(x, n.ahead = ___, p = ___, d = ___, q = ___) 
lines(y)

Edit and Run Code

This exercise is part of the course

ARIMA Models in R

IntermediateSkill Level

4.9+

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You will investigate the nature of time series data and learn the basics of ARMA models that can explain the behavior of such data. You will learn the basic R commands needed to help set up raw time series data to a form that can be analyzed using ARMA models.

Exercise 1: First things first Exercise 2: Data play Exercise 3: Elements of time series Exercise 4: Stationarity and nonstationarity Exercise 5: Differencing Exercise 6: Detrending data Exercise 7: Dealing with trend and heteroscedasticity Exercise 8: Stationary time series: ARMA Exercise 9: Simulating ARMA models

You will discover the wonderful world of ARMA models and how to fit these models to time series data. You will learn how to identify a model, how to choose the correct model, and how to verify a model once you fit it to data. You will learn how to use R time series commands from the stats and astsa packages.

Exercise 1: AR and MA models Exercise 2: Fitting an AR(1) model Exercise 3: Fitting an AR(2) model Exercise 4: Fitting an MA(1) model Exercise 5: AR and MA together Exercise 6: Fitting an ARMA model Exercise 7: Identify an ARMA model Exercise 8: Model choice and residual analysis Exercise 9: Model choice - I Exercise 10: Model choice - II Exercise 11: Residual analysis - I Exercise 12: Residual analysis - II Exercise 13: ARMA get in

Now that you know how to fit ARMA models to stationary time series, you will learn about integrated ARMA (ARIMA) models for nonstationary time series. You will fit the models to real data using R time series commands from the stats and astsa packages.

Exercise 1: ARIMA - integrated ARMA Exercise 2: ARIMA - plug and play Exercise 3: Simulated ARIMA Exercise 4: Global warming Exercise 5: ARIMA diagnostics Exercise 6: Diagnostics - simulated overfitting Exercise 7: Diagnostics - global temperatures Exercise 8: Forecasting ARIMA Exercise 9: Forecasting simulated ARIMA

Current Exercise

Exercise 10: Forecasting global temperatures

You will learn how to fit and forecast seasonal time series data using seasonal ARIMA models. This is accomplished using what you learned in the previous chapters and by learning how to extend the R time series commands available in the stats and astsa packages.

Exercise 1: Pure seasonal models Exercise 2: P/ACF of pure seasonal models Exercise 3: Fit a pure seasonal model Exercise 4: Mixed seasonal models Exercise 5: Fit a mixed seasonal model Exercise 6: Data analysis - unemployment I Exercise 7: Data analysis - unemployment II Exercise 8: Data analysis - commodity prices Exercise 9: Data analysis - birth rate Exercise 10: Forecasting seasonal ARIMA Exercise 11: Forecasting monthly unemployment Exercise 12: How hard is it to forecast commodity prices?Exercise 13: Congratulations!