Fitting an AR(1) model
Recall that you use the ACF and PACF pair to help identify the orders \(p\) and \(q\) of an ARMA model. The following table is a summary of the results:
| AR(\(p\)) | MA(\(q\)) | ARMA(\(p,q\)) | |
|---|---|---|---|
| ACF | Tails off | Cuts off after lag \(q\) |
Tails off |
| PACF | Cuts off after lag \(p\) |
Tails off | Tails off |
In this exercise, you will generate data from the AR(1) model, $$X_t = .9 X_{t-1} + W_t,$$ look at the simulated data and the sample ACF and PACF pair to determine the order. Then, you will fit the model and compare the estimated parameters to the true parameters.
Throughout this course, you will be using sarima() from the astsa package to easily fit models to data. The command produces a residual diagnostic graphic that can be ignored until diagnostics is discussed later in the chapter.
This is a part of the course
“ARIMA Models in R”
Exercise instructions
- The package astsa is preloaded.
- Use the prewritten
arima.sim()command to generate 100 observations from an AR(1) model with AR parameter .9. Save this tox. - Plot the generated data using
plot(). - Plot the sample ACF and PACF pairs using the
acf2()command from theastsapackage. - Use
sarima()fromastsato fit an AR(1) to the previously generated data. Examine the t-table and compare the estimates to the true values. For example, if the time series is inx, to fit an AR(1) to the data, usesarima(x, p = 1, d = 0, q = 0)or simplysarima(x, 1, 0, 0).
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Generate 100 observations from the AR(1) model
x <- arima.sim(model = list(order = c(1, 0, 0), ar = .9), n = 100)
# Plot the generated data
# Plot the sample P/ACF pair
# Fit an AR(1) to the data and examine the t-table
This exercise is part of the course
ARIMA Models in R
Become an expert in fitting ARIMA (autoregressive integrated moving average) models to time series data using R.
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 modelsExercise 2: Fitting an AR(1) modelExercise 3: Fitting an AR(2) modelExercise 4: Fitting an MA(1) modelExercise 5: AR and MA togetherExercise 6: Fitting an ARMA modelExercise 7: Identify an ARMA modelExercise 8: Model choice and residual analysisExercise 9: Model choice - IExercise 10: Model choice - IIExercise 11: Residual analysis - IExercise 12: Residual analysis - IIExercise 13: ARMA get inWhat is DataCamp?
Learn the data skills you need online at your own pace—from non-coding essentials to data science and machine learning.