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ToInvertibleTimeSeries[tproc]

返回时间序列过程 tproc 的可逆版本.

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范例  
基本范例  
范围  
属性和关系  
可能存在的问题  
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ToInvertibleTimeSeries

ToInvertibleTimeSeries[tproc]

返回时间序列过程 tproc 的可逆版本.

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范例

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基本范例  (1)

求可逆表示法：

Wolfram Language code: ToInvertibleTimeSeries[MAProcess[1, {2, 3}, 1]]

检查新过程是否可逆：

Wolfram Language code: TimeSeriesInvertibility[MAProcess[1, {(2/3), (1/3)}, 9]]

范围  (5)

比较不可逆时间序列与可逆表示：

Wolfram Language code: TimeSeriesInvertibility[proc = MAProcess[.3, {2, 5}, 1]]

求可逆表示：

Wolfram Language code: iproc = ToInvertibleTimeSeries[proc]

比较均值：

Wolfram Language code: Mean /@ {proc[t], iproc[t]}

比较协方差函数：

Wolfram Language code: CovarianceFunction[#, s, t]& /@ {proc, iproc}

比较不可逆时间序列与可逆时间序列：

Wolfram Language code: TimeSeriesInvertibility[proc = MAProcess[{1 / 2, 2, 1}, 1]]
Wolfram Language code: iproc = ToInvertibleTimeSeries[proc]

计算 TransferFunctionModel:

Wolfram Language code: TransferFunctionModel /@ {proc, iproc}

对固定的随机种子，比较两个过程的随机样本：

Wolfram Language code: SeedRandom[2];sample = RandomFunction[proc, {1, 10 ^ 2}]; SeedRandom[2];isample = RandomFunction[iproc, {1, 10 ^ 2}]; ListLinePlot[{sample, isample}]

考虑不可逆过程和可逆过程：

Wolfram Language code: proc = MAProcess[{3, 4}, 1]; iproc = ToInvertibleTimeSeries@proc

求相应的传递函数：

Wolfram Language code: {tfm, itfm} = TransferFunctionModel[#, z]& /@ {proc, iproc}

每个过程模拟的噪声可能有所不同，但是对过去噪声的依赖越来越小：

Wolfram Language code: OutputResponse[#, {x1, x2, x3}]& /@ {tfm, itfm}

从不可逆过程和可逆表示生成随机样本：

Wolfram Language code: TimeSeriesInvertibility[proc = MAProcess[1, {2, 5}, 1]]

求不可逆表示：

Wolfram Language code: iproc = ToInvertibleTimeSeries[proc]

生成随机样本：

Wolfram Language code: SeedRandom[2];sample = RandomFunction[proc, {1, 10 ^ 2}]; SeedRandom[2];isample = RandomFunction[iproc, {1, 10 ^ 2}];

比较样本：

Wolfram Language code: ListLinePlot[{sample, isample}]

样本相关函数是可比的：

Wolfram Language code: Show[DiscretePlot[CorrelationFunction[proc, h], {h, 0, 6}, ExtentSize -> 1 / 2], ListLinePlot[CorrelationFunction[#, {6}]& /@ {sample, isample}, PlotStyle -> {Directive[Thick, StandardYellow], Directive[Dashed, Gray]}], PlotRange -> All]
Wolfram Language code: Subtract@@(CorrelationFunction[#, {6}]["Values"]& /@ {sample, isample})

检查给定的时间序列是否可逆：

Wolfram Language code: TimeSeriesInvertibility[proc = MAProcess[{.2, 1, 4}, 1]]

绘制传递函数的零点：

Wolfram Language code: PoleZeroPlot[TransferFunctionModel[proc], AspectRatio -> Automatic]

由于没有零点落在单位圆上，该时间序列可逆：

Wolfram Language code: iproc = ToInvertibleTimeSeries[proc]

检查传递函数的零点是否在单位圆内：

Wolfram Language code: PoleZeroPlot[TransferFunctionModel[iproc], AspectRatio -> Automatic]

属性和关系  (2)

可逆过程的 ToInvertibleTimeSeries 返回原来的过程：

Wolfram Language code: proc = MAProcess[.3, {.1}, 1, {.4}];
Wolfram Language code: TimeSeriesInvertibility[proc]
Wolfram Language code: ToInvertibleTimeSeries[proc] == proc

ToInvertibleTimeSeries 支队移动平均系数和噪声方差进行缩放：

Wolfram Language code: ToInvertibleTimeSeries[ARMAProcess[.1, {.2, .3}, {1, 2}, 3, {.4}]]

可能存在的问题  (2)

ToInvertibleTimeSeries requires numeric moving-average coefficients:

Wolfram Language code: ToInvertibleTimeSeries[ARMAProcess[{a, b}, {c, .2}, v]]

Use TimeSeriesInvertibility to find conditions for non-numeric coefficients:

Wolfram Language code: TimeSeriesInvertibility[ARMAProcess[{a, b}, {c, .2}, v]]

ToInvertibleTimeSeries 可能不存在：

Wolfram Language code: ToInvertibleTimeSeries[MAProcess[{.3, 1}, .2]]

单位圆上存在 TransferFunctionModel 的零点：

Wolfram Language code: tsm = TransferFunctionModel[MAProcess[{.3, 1}, .2]]
Wolfram Language code: PoleZeroPlot[tsm]

Compute the zeros:

Wolfram Language code: TransferFunctionZeros[tsm]
Wolfram Language code: Abs[%]
Wolfram Research (2012)，ToInvertibleTimeSeries，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ToInvertibleTimeSeries.html.

文本

Wolfram Research (2012)，ToInvertibleTimeSeries，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ToInvertibleTimeSeries.html.

CMS

Wolfram 语言. 2012. "ToInvertibleTimeSeries." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/ToInvertibleTimeSeries.html.

APA

Wolfram 语言. (2012). ToInvertibleTimeSeries. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/ToInvertibleTimeSeries.html 年

BibTeX

@misc{reference.wolfram_2026_toinvertibletimeseries, author="Wolfram Research", title="{ToInvertibleTimeSeries}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/ToInvertibleTimeSeries.html}", note=[Accessed: 16-July-2026]}

BibLaTeX

@online{reference.wolfram_2026_toinvertibletimeseries, organization={Wolfram Research}, title={ToInvertibleTimeSeries}, year={2012}, url={https://reference.wolfram.com/language/ref/ToInvertibleTimeSeries.html}, note=[Accessed: 16-July-2026]}