Fit a pure seasonal model

As with other models, you can fit seasonal models in R using the sarima() command in the astsa package.

To get a feeling of how pure seasonal models work, it is best to consider simulated data. We generated 250 observations from a pure seasonal model given by $$X_t = .9 X_{t-12} + W_t + .5 W_{t-12}\,,$$ which we would denote as a SARMA(P = 1, Q = 1)_{S = 12}. Three years of data and the model ACF and PACF are plotted for you.

You will compare the sample ACF and PACF values from the generated data to the true values displayed.

The astsa package is preloaded for you and the generated data are in x.

This exercise is part of the course

ARIMA Models in R

Exercise instructions

Use acf2() to plot the sample ACF and PACF of the generated data to lag 60 and compare to actual values. To estimate to lag 60, set the max.lag argument equal to 60.
Fit the model to generated data using sarima(). In addition to the p, d, and q arguments in your sarima() command, specify P, D, Q, and S (note that R is case sensitive).

Hands-on interactive exercise

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

# Plot sample P/ACF to lag 60 and compare to the true values
acf2(___, max.lag = ___)

# Fit the seasonal model to x
sarima(x, p = 0, d = 0, q = 0, P = ___, D = 0, Q = ___, S = ___)

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 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

Current Exercise

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!