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)
Check if a process is invertible:
TimeSeriesInvertibility[ARMAProcess[.1, {.2, .3}, {-.4}, 1]]TimeSeriesInvertibility[ARMAProcess[.1, {.2, .3}, {4}, 1]]Generate conditions for a process to be invertible:
TimeSeriesInvertibility[MAProcess[{a, b}, σ^2]]Scope (3)
Visualize conditions for an MAProcess to be invertible:
RegionPlot[TimeSeriesInvertibility[MAProcess[{a, b}, v]], {a, -2, 2}, {b, -2, 2}]RegionPlot3D[Evaluate@TimeSeriesInvertibility[MAProcess[{a, b, c}, v]], {a, -2, 2}, {b, -2, 2}, {c, -2, 2}, ViewPoint -> {0, 0, -2}, PlotPoints -> 50, AxesLabel -> Automatic]Find an invertible MAProcess:
proc = MAProcess[c, {a, b}, v, {x}];FindInstance[TimeSeriesInvertibility[proc] && a ≠ 0 && b ≠ 0, {a, b}]TimeSeriesInvertibility[proc /. First[%]]Check if a given time series is invertible:
TimeSeriesInvertibility[proc = MAProcess[{.2, 1, 4}, 1]]Plot zeros of transfer function:
PoleZeroPlot[TransferFunctionModel[proc], AspectRatio -> Automatic]Since there are no zeros on the unit circle, the time series has invertible representation:
iproc = ToInvertibleTimeSeries[proc]Check if zeros of the transfer function are inside the unit circle:
PoleZeroPlot[TransferFunctionModel[iproc], AspectRatio -> Automatic]Properties & Relations (2)
Every ARProcess is invertible:
TimeSeriesInvertibility[ARProcess[c, {Subscript[a, 1], Subscript[a, 2]}, σ^2]]The conditions for an ARMAProcess to be invertible depend only on the moving-average parameters:
TimeSeriesInvertibility[ARMAProcess[c, {a, b}, {k, m}, v]]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