Enable JavaScript to interact with content and submit forms on Wolfram websites. Learn how

TimeSeriesInvertibility

TimeSeriesInvertibility[tproc]

gives conditions for the time series process tproc to be invertible.

Details

A time series process is invertible if it can be written as an autoregressive time series, possibly of infinite order, such that the autoregressive coefficients are absolutely summable.
An invertible time series representation with preserved moments can be found using ToInvertibleTimeSeries.
TimeSeriesInvertibility can be used with time series processes such as MAProcess, ARMAProcess, ARIMAProcess, and FARIMAProcess.

Examples

open allclose all

Basic Examples (2)

Check if a process is invertible:

Generate conditions for a process to be invertible:

Scope (2)

Visualize conditions for an MAProcess to be invertible:

For three parameters:

Find an invertible MAProcess:

Check:

Properties & Relations (2)

Every ARProcess is invertible:

The conditions for an ARMAProcess to be invertible depend only on the moving-average parameters:

Top