ARFIMA was introduced in Stata 12.
ARFIMA stands for AutoRegressive Fractionally Integrated Moving Average.
Stata’s new arfima command fits ARFIMA models.
ARFIMA concerns long-memory processes. Long-memory processes are stationary processes whose autocorrelation functions decay slowly. The ARFIMA model provides a parsimonious parameterization of long-memory processes that nests the ARMA (autoregressive moving-average) model, which is widely used for short-memory processes. Long-memory processes can be obtained by fractionally integrating short-memory processes. The ARFIMA model does that. The ARFIMA model also generalizes the ARIMA model by allowing for fractional degrees of integration.
Below we analyze yearly data on the widths of the rings of a tree. This one tree survived 5,000 years! In any case, larger widths represent good years for the tree and narrower widths represent harsh years. Below we estimate the parameters of an ARFIMA model with the fractional difference parameter and a constant. With only those parameters, we will account for the long memory of the process.
Below we plot the original series and the fractionally differenced component of the predicted series, which reflects the short-memory component of the process:
For a complete list of what’s new in time-series analysis, click here.
See New in Stata 18 to learn about what was added in Stata 18.
Classroom & web training
Teaching with Stata
Statalist: The Stata Forum
Last updated: 16 November 2022
StataCorp LLC (StataCorp) strives to provide our users with exceptional products and services. To do so, we must collect personal information from you. This information is necessary to conduct business with our existing and potential customers. We collect and use this information only where we may legally do so. This policy explains what personal information we collect, how we use it, and what rights you have to that information.
These cookies are essential for our website to function and do not store any personally identifiable information. These cookies cannot be disabled.
Please note: Clearing your browser cookies at any time will undo preferences saved here. The option selected here will apply only to the device you are currently using.