ARMA get in

By now you have gained considerable experience fitting ARMA models to data, but before you start celebrating, try one more exercise (sort of) on your own.

The data in oil are crude oil, WTI spot price FOB (in dollars per barrel), weekly data from 2000 to 2008. Use your skills to fit an ARMA model to the returns. The weekly crude oil prices (oil) are plotted for you. Throughout the exercise, work with the returns, which you will calculate.

As before, the astsa package is preloaded for you. The data are preloaded as oil and plotted.

This exercise is part of the course

ARIMA Models in R

Exercise instructions

Calculate the approximate crude oil price returns using diff() and log(). Put the returns in oil_returns.
Plot oil_returns and notice that there are a couple of outliers prior to 2004. Convince yourself that the returns are stationary.
Plot the sample ACF and PACF of the oil_returns using acf2() from the astsa package.
From the P/ACF pair, it is apparent that the correlations are small and the returns are nearly noise. But it could be that both the ACF and PACF are tailing off. If this is the case, then an ARMA(1,1) is suggested. Fit this model to the oil returns using sarima(). Does the model fit well? Can you see the outliers in the residual plot?

Hands-on interactive exercise

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

# Calculate approximate oil returns
oil_returns <-

# Plot oil_returns. Notice the outliers.


# Plot the P/ACF pair for oil_returns


# Assuming both P/ACF are tailing, fit a model to oil_returns

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

Current Exercise

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!