TimeSeriesInvertibility

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`TimeSeriesInvertibility`

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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)Summary of the most common use cases

Check if a process is invertible:

In[1]:=1

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https://wolfram.com/xid/0rkhqorykf16bci-2qmqau

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0rkhqorykf16bci-w1t66d

Out[2]=2

Generate conditions for a process to be invertible:

In[1]:=1

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https://wolfram.com/xid/0rkhqorykf16bci-31770m

Out[1]=1

Scope (2)Survey of the scope of standard use cases

Visualize conditions for an MAProcess to be invertible:

In[1]:=1

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

Out[1]=1

For three parameters:

In[2]:=2

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

Out[2]=2

Find an invertible MAProcess:

In[1]:=1

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

In[2]:=2

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

Out[2]=2

Check:

In[3]:=3

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

Out[3]=3

Properties & Relations (2)Properties of the function, and connections to other functions

Every ARProcess is invertible:

In[1]:=1

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

Out[1]=1

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

In[1]:=1

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

Out[1]=1

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