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Second-Order stationarity condition for complex-valued autoregressive process

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0

$begingroup$

Let $c_n$ be a complex-valued discrete autoregressive process of order $p$, $mathsfAR(p)$, such that:
beginequation
labelcn
c_n = sumnolimits_i=1^prho_i c_n-i + w_n, quad n in (-infty,infty),
endequation
where $w_n: forall n$ are textitcircularly symmetric independent and identically distributed (i.i.d.) complex random variables with finite second-order moments.

Which is the Second-Order Stationarity condition for this $mathsfAR(p)$? Is it enough to require that the complex coefficients $rho_i_i=1^p$ are such that all the roots of the polynomial $P(z)triangleq 1- sumnolimits_i=1^prho_i z^i$ lie outside the unit disk?

probability random-variables time-series

share|cite|improve this question

edited Mar 12 at 11:22

Vuk

asked Mar 12 at 11:00

VukVuk

768

$endgroup$

add a comment | 

0

$begingroup$

Let $c_n$ be a complex-valued discrete autoregressive process of order $p$, $mathsfAR(p)$, such that:
beginequation
labelcn
c_n = sumnolimits_i=1^prho_i c_n-i + w_n, quad n in (-infty,infty),
endequation
where $w_n: forall n$ are textitcircularly symmetric independent and identically distributed (i.i.d.) complex random variables with finite second-order moments.

Which is the Second-Order Stationarity condition for this $mathsfAR(p)$? Is it enough to require that the complex coefficients $rho_i_i=1^p$ are such that all the roots of the polynomial $P(z)triangleq 1- sumnolimits_i=1^prho_i z^i$ lie outside the unit disk?

probability random-variables time-series

share|cite|improve this question

edited Mar 12 at 11:22

Vuk

asked Mar 12 at 11:00

VukVuk

768

$endgroup$

add a comment | 

$begingroup$

Let $c_n$ be a complex-valued discrete autoregressive process of order $p$, $mathsfAR(p)$, such that:
beginequation
labelcn
c_n = sumnolimits_i=1^prho_i c_n-i + w_n, quad n in (-infty,infty),
endequation
where $w_n: forall n$ are textitcircularly symmetric independent and identically distributed (i.i.d.) complex random variables with finite second-order moments.

Which is the Second-Order Stationarity condition for this $mathsfAR(p)$? Is it enough to require that the complex coefficients $rho_i_i=1^p$ are such that all the roots of the polynomial $P(z)triangleq 1- sumnolimits_i=1^prho_i z^i$ lie outside the unit disk?

probability random-variables time-series

share|cite|improve this question

edited Mar 12 at 11:22

Vuk

asked Mar 12 at 11:00

VukVuk

768

$endgroup$

share|cite|improve this question

edited Mar 12 at 11:22

Vuk

asked Mar 12 at 11:00

VukVuk

768

share|cite|improve this question

edited Mar 12 at 11:22

Vuk

asked Mar 12 at 11:00

VukVuk

768

asked Mar 12 at 11:00

VukVuk

768

asked Mar 12 at 11:00

VukVuk

768