Model choice - I

Based on the sample P/ACF pair of the logged and differenced varve data (dl_varve), an MA(1) was indicated. The best approach to fitting ARMA is to start with a low order model, and then try to add a parameter at a time to see if the results change.

In this exercise, you will fit various models to the dl_varve data and note the AIC and BIC for each model. In the next exercise, you will use these AICs and BICs to choose a model. Remember that you want to retain the model with the smallest AIC and/or BIC value.

A note before you start:

sarima(x, p = 0, d = 0, q = 1) and sarima(x, 0, 0, 1)

are the same.

This exercise is part of the course

ARIMA Models in R

Exercise instructions

The package astsa is preloaded. The varve series has been logged and differenced as dl_varve <- diff(log(varve)).
Use sarima() to fit an MA(1) to dl_varve. Take a close look at the output of your sarima() command to see the AIC and BIC for this model.
Repeat the previous exercise, but add an MA parameter by fitting an MA(2) model. Based on AIC and BIC, is this an improvement over the previous model?
Instead of adding an MA parameter, add an AR parameter to the original MA(1) fit. That is, fit an ARMA(1,1) to dl_varve. Based on AIC and BIC, is this an improvement over the previous models?

Hands-on interactive exercise

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

# Fit an MA(1) to dl_varve.   


# Fit an MA(2) to dl_varve. Improvement?


# Fit an ARMA(1,1) to dl_varve. Improvement?

Edit and Run Code

This exercise is part of the course

ARIMA Models in R

IntermediateSkill Level

4.9+

Start Course for Free

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

Current Exercise

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 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!