Degree of approximation

allowable for $h_k$

Region of Non-duality

Remark

MA(1) Process

AR(1) Process

${\theta }_1$

${\varphi }_1$

1

$\left[-0.47,0.47\right]$

$\left[-0.38,0.38\right]$

Negative values ${\theta }_1$ are mapped into positive values of ${\varphi }_1$ and vice versa

2

$\left[-0.26,0.26\right]$

$\left[-0.24,0.24\right]$

Negative values ${\theta }_1$ are mapped into positive values of ${\varphi }_1$ and vice versa

3

$\left[-0.14,0.14\right]$

$\left[-0.14,0.14\right]$

Negative values ${\theta }_1$ are mapped into positive values of ${\varphi }_1$ and vice versa

4

$\left[-0.08,0.08\right]$

$\left[-0.08,0.08\right]$

Negative values ${\theta }_1$ are mapped into positive values of ${\varphi }_1$ and vice versa