Simulated ARIMA

Before analyzing actual time series data, you should try working with a slightly more complicated model.

Here, we generated 250 observations from the ARIMA(2,1,0) model with drift given by $$Y_t = 1 + 1.5 Y_{t-1} - .75 Y_{t-2} + W_t\,$$ where \(Y_t = \nabla X_t = X_{t} - X_{t-1}\).

You will use the established techniques to fit a model to the data.

The astsa package is preloaded and the generated data are in x. The series x and the detrended series y <- diff(x) have been plotted.

This exercise is part of the course

ARIMA Models in R

Exercise instructions

Plot the sample ACF and PACF using acf2() of the differenced data diff(x) to determine a model.
Fit an ARIMA(2,1,0) model using sarima() to the generated data. Examine the t-table and other output information to assess the model fit.

Hands-on interactive exercise

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

# Plot sample P/ACF of differenced data and determine model



# Estimate parameters and examine output

Edit and Run Code

This exercise is part of the course

ARIMA Models in R

IntermediateSkill Level

5.0+

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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

Current Exercise

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!