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 all close allBasic Examples (2)
Scope (3)
Visualize conditions for an MAProcess to be invertible:
Find an invertible MAProcess:
Check if a given time series is invertible:
Plot zeros of transfer function:
Since there are no zeros on the unit circle, the time series has invertible representation:
Check if zeros of the transfer function are inside the unit circle:
Properties & Relations (2)
Every ARProcess is invertible:
The conditions for an ARMAProcess to be invertible depend only on the moving-average parameters:
Text
Wolfram Research (2012), TimeSeriesInvertibility, Wolfram Language function, https://reference.wolfram.com/language/ref/TimeSeriesInvertibility.html.
CMS
Wolfram Language. 2012. "TimeSeriesInvertibility." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TimeSeriesInvertibility.html.
APA
Wolfram Language. (2012). TimeSeriesInvertibility. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TimeSeriesInvertibility.html