Global warming

Now that you have some experience fitting an ARIMA model to simulated data, your next task is to apply your skills to some real world data.

The data in globtemp (from astsa) are the annual global temperature deviations to 2015. In this exercise, you will use established techniques to fit an ARIMA model to the data. A plot of the data shows random walk behavior, which suggests you should work with the differenced data. The differenced data diff(globtemp) are also plotted.

After plotting the sample ACF and PACF of the differenced data diff(globtemp), you can say that either

The ACF and the PACF are both tailing off, implying an ARIMA(1,1,1) model.
The ACF cuts off at lag 2, and the PACF is tailing off, implying an ARIMA(0,1,2) model.
The ACF is tailing off and the PACF cuts off at lag 3, implying an ARIMA(3,1,0) model. Although this model fits reasonably well, it is the worst of the three (you can check it) because it uses too many parameters for such small autocorrelations.

After fitting the first two models, check the AIC and BIC to choose the preferred model.

This exercise is part of the course

ARIMA Models in R

Exercise instructions

Plot the sample ACF and PACF of the differenced data, diff(globtemp), to discover that 2 models seem reasonable, an ARIMA(1,1,1) and an ARIMA(0,1,2).
Use sarima() to fit an ARIMA(1,1,1) model to globtemp. Are all the parameters significant?
Use another call to sarima() to fit an ARIMA(0,1,2) model to globtemp. Are all the parameters significant? Which model is better?

Hands-on interactive exercise

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

# Plot the sample P/ACF pair of the differenced data 


# Fit an ARIMA(1,1,1) model to globtemp


# Fit an ARIMA(0,1,2) model to globtemp. Which model is better?

Edit and Run Code

This exercise is part of the course

ARIMA Models in R

IntermediateSkill Level

5.0+

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 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

Current Exercise

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!