TimeSeriesInvertibility
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TimeSeriesInvertibility
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 allBasic Examples (2)Summary of the most common use cases
Scope (2)Survey of the scope of standard use cases
Visualize conditions for an MAProcess to be invertible:

https://wolfram.com/xid/0rkhqorykf16bci-mn0j0h


https://wolfram.com/xid/0rkhqorykf16bci-ss40mj

Find an invertible MAProcess:

https://wolfram.com/xid/0rkhqorykf16bci-wmghrt

https://wolfram.com/xid/0rkhqorykf16bci-flczwd


https://wolfram.com/xid/0rkhqorykf16bci-besqgr

Properties & Relations (2)Properties of the function, and connections to other functions
Every ARProcess is invertible:

https://wolfram.com/xid/0rkhqorykf16bci-ttmjof

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

https://wolfram.com/xid/0rkhqorykf16bci-zjyi97

Wolfram Research (2012), TimeSeriesInvertibility, Wolfram Language function, https://reference.wolfram.com/language/ref/TimeSeriesInvertibility.html.
Text
Wolfram Research (2012), TimeSeriesInvertibility, Wolfram Language function, https://reference.wolfram.com/language/ref/TimeSeriesInvertibility.html.
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.
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
Wolfram Language. (2012). TimeSeriesInvertibility. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TimeSeriesInvertibility.html
BibTeX
@misc{reference.wolfram_2025_timeseriesinvertibility, author="Wolfram Research", title="{TimeSeriesInvertibility}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/TimeSeriesInvertibility.html}", note=[Accessed: 02-April-2025
]}
BibLaTeX
@online{reference.wolfram_2025_timeseriesinvertibility, organization={Wolfram Research}, title={TimeSeriesInvertibility}, year={2012}, url={https://reference.wolfram.com/language/ref/TimeSeriesInvertibility.html}, note=[Accessed: 02-April-2025
]}