Contents
What is the autocorrelation function of an ARIMA model?
Here is the autocorrelation function (ACF) of the UNITS series, before any differencing is performed: The autocorrelations are significant for a large number of lags–but perhaps the autocorrelations at lags 2 and above are merely due to the propagation of the autocorrelation at lag 1.
Which is the forecasting equation for an ARIMA model?
Now, the forecasting equation for an AR (1) model for a series Y with no orders of differencing is: If the AR (1) coefficient ϕ 1 in this equation is equal to 1, it is equivalent to predicting that the first difference of Y is constant–i.e., it is equivalent to the equation of the random walk model with growth:
What are the rules for identifying ARIMA models?
Summary of rules for identifying ARIMA models ARIMA models with regressors The mathematical structure of ARIMA models (pdf file) Summary of rules for identifying ARIMA models Identifying the order of differencing and the constant:
What are the parameters of the Arima function?
The important parameters of the function are: The time-series to which you fit the ARIMA model. start_p: the starting value of p, the order of the auto-regressive (AR) model. This must be a positive integer. start_q: the starting value of q, the order of the moving-average (MA) model.
How to calculate residuals for an ARIMA model?
Lesson 3.1gives the basic ideas for determining a model and analyzing residuals after a model has been estimated. Lesson 3.2gives a test for residual autocorrelations. Lesson 3.3gives some basics for forecasting using ARIMA models. We’ll look at other forecasting models later in the course.
When to use maximum likelihood and ARIMA estimation?
If the residuals do have an ARIMA structure, use maximum likelihood to simultaneously estimate the regression model using ARIMA estimation for the residuals. Examine the ARIMA structure (if any) of the sample residuals from the model in step 3. If white noise is present, then the model is complete.
When to revise a non-seasonal ARIMA model?
If non-constant variance is a concern, look at a plot of residuals versus fits and/or a time series plot of the residuals. If something looks wrong, you’ll have to revise your guess at what the model might be. This might involve adding parameters or re-interpreting the original ACF and PACF to possibly move in a different direction.