Diagnostics - simulated overfitting

One way to check an analysis is to overfit the model by adding an extra parameter to see if it makes a difference in the results. If adding parameters changes the results drastically, then you should rethink your model. If, however, the results do not change by much, you can be confident that your fit is correct.

We generated 250 observations from an ARIMA(0,1,1) model with MA parameter .9. First, you will fit the model to the data using established techniques.

Then, you can check a model by overfitting (adding a parameter) to see if it makes a difference. In this case, you will add an additional MA parameter to see that it is not needed.

As usual, the astsa package is preloaded and the generated data in x has been plotted for you. The differenced data diff(x) are also plotted. Note that it looks stationary.

This exercise is part of the course

ARIMA Models in R

Exercise instructions

Plot the sample ACF and PACF of the differenced data using acf2() and note that the model is easily identified.
Fit an ARIMA(0,1,1) model to the simulated data using sarima(). Compare the MA parameter estimate to the actual value of .9, and examine the residual plots.
Overfit the model by adding an additional MA parameter. That is, fit an ARIMA(0,1,2) to the data and compare it to the ARIMA(0,1,1) run.

Hands-on interactive exercise

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

# Plot sample P/ACF pair of the differenced data


# Fit the first model, compare parameters, check diagnostics


# Fit the second model and compare fit

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

Current Exercise

Exercise 7: Diagnostics - global temperatures Exercise 8: Forecasting ARIMA Exercise 9: Forecasting simulated ARIMA 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!