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

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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:

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.

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

BibTeX

@misc{reference.wolfram_2024_timeseriesinvertibility, author="Wolfram Research", title="{TimeSeriesInvertibility}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/TimeSeriesInvertibility.html}", note=[Accessed: 24-June-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_timeseriesinvertibility, organization={Wolfram Research}, title={TimeSeriesInvertibility}, year={2012}, url={https://reference.wolfram.com/language/ref/TimeSeriesInvertibility.html}, note=[Accessed: 24-June-2024 ]}