Degree of approximation

allowable for $h_k$

Region of Non-duality

Remark

AR(2) Process

MA(2) Process

${\varphi }_1$

${\varphi }_2$

${\theta }_1$

${\theta }_2$

1

$\left[-0.30,0.30\right]$

$\left[-0.30,0.30\right]$

$\left[-0.37,0.37\right]$

$\left[-0.43,0.32\right]$

positive values $\left({\varphi }_1,{\varphi }_2\right)$ are mapped into negative values of $\left({\theta }_1,{\theta }_2\right)$ and vice versa

2

$\left[-0.30,0.30\right]$

$\left[-0.20,0.20\right]$

$\left[-0.30,0.30\right]$

$\left[-0.22,0.20\right]$

positive values $\left({\varphi }_1,{\varphi }_2\right)$ are mapped into negative values of $\left({\theta }_1,{\theta }_2\right)$ and vice versa

3

$\left[-0.10,0.10\right]$

−0.10

$\left[-0.10,0.10\right]$

0.09

positive values $\left({\varphi }_1,{\varphi }_2\right)$ are mapped into negative values of $\left({\theta }_1,{\theta }_2\right)$ and vice versa