ARIMA diagnostics

1. ARIMA diagnostics

Diagnostics for ARIMA models is no different than doing it for ARMA models. We'll look at an example and consider overfitting. That is, once a model seems reasonable, you can try adding a parameter to see if doing so makes a difference. If there is a difference, then you change your model. Otherwise, you are done.

2. Weekly Oil Prices ARIMA(1, 1, 1)?

In the previous video we looked at weekly oil prices in the US from 2000 to 2006. To remove the trend, we differenced the data.

3. Weekly Oil Prices ARIMA(1, 1, 1)?

Then the ACF and PACF appear to be tailing off, so we considered fitting an ARIMA(1,1,1).

4. Weekly Oil Prices ARIMA(1, 1, 1)?

Using sarima, we fit an ARIMA(1,1,1) to the oil price series. Here are the parameter estimates, and they are significant.

5. Weekly Oil Prices ARIMA(1, 1, 1)!

The residual analysis looks fine too.

6. Overfit: ARIMA(2, 1, 1) and ARIMA(1, 1, 2)

Now we can try to add an AR parameter and then an MA parameter to see if it makes a difference. In each case, the additional parameter is not significant and the other parameters are practically unchanged. Hence our original model ARIMA(1,1,1) fits well.

7. Let's practice!

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 Exercise 4: Global warming Exercise 5: ARIMA diagnostics

Current Exercise

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!