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Test VARMAX model for stability/invertibility

`[isStable,isInvertible] = vgxqual(Spec)`

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

`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.

Spec | A multivariate time series specification structure for
an |

isStable | Logical flag indicating if the multivariate time series
process is stable. The flag is |

isInvertible | Logical flag indicating if the multivariate time series
process is invertible. The flag is |

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. |

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