vgxqual - Qualify multivariate time series process

Synopsis

[isStable,isInvertible] = vgxqual(Spec)

[isStable,isInvertible,AReig,MAeig] = vgxqual(Spec)

Description

vgxqual determines if a multivariate time series process is stable and invertible.

A process with non-constant exogenous inputs may not be stable or invertible. This cannot be determined from the specification structure unless the number of exogenous inputs is zero. vgxqual determines if the AR and the MA portions of a VARMAX model are stable and invertible without considering exogenous inputs. Thus it is more appropriate to call a multivariate time series process AR-stable if the AR portion is stable, and MA-invertible if the MA portion is invertible.

A stable VARMAX process is stationary, but the converse is not true. Although the terms stable, stationary, and covariance-stationary are often used interchangeably, a process is truly stationary if and only if its first and second moments are independent of time.

If a VARMAX model has no autoregressive terms, it is always AR-stable.

If a VARMAX model has no moving average terms, it is always MA-invertible.

Input Argument

Spec

A multivariate time series specification structure for an n-dimensional time series process, as created by vgxset.

Output Arguments

`isStable`	Logical flag indicating if the multivariate time series process is stable. The flag is `true` if the process is stable, `false` otherwise.
`isInvertible`	Logical flag indicating if the multivariate time series process is invertible. The flag is `true` if the process is invertible, `false` otherwise.
`AReig`	Largest-magnitude eigenvalue for the AR portion of the multivariate time series process.
`MAeig`	Largest-magnitude eigenvalue for the MA portion of the multivariate time series process.

Example

Start with a 2-dimensional VARMA(2, 2) specification structure in Spec. Although the display method for a vgxset object performs this test, the explicit test is:

[isStable, isInvertible] = vgxqual(Spec)

isStable =

     1

isInvertible =

     1

This shows that Spec is a model for an AR-stable and MA-invertible time series process.

vgxproc

vgxset

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