Factorised form of Autoregressive Polynomial
$begingroup$
I'm new to Time Series Analysis. I've read that when inverting autoregressive characteristic polynomial of arbitrary finite degree, we need to write it in its factorized form:
$$phi_p(x) = prod_{i=1}^p Big( 1-frac{x}{r_i} Big)$$
Where $r_1, ..., r_p$ are the roots of the polynomial. My question is why does this form of dividing by the roots make sense? Is there a proof for this that I can read about?
Thanks a lot.
statistics factoring time-series
asked Dec 13 '18 at 18:57
MetricianMetrician
677
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add a comment |
$begingroup$
I'm new to Time Series Analysis. I've read that when inverting autoregressive characteristic polynomial of arbitrary finite degree, we need to write it in its factorized form:
$$phi_p(x) = prod_{i=1}^p Big( 1-frac{x}{r_i} Big)$$
Where $r_1, ..., r_p$ are the roots of the polynomial. My question is why does this form of dividing by the roots make sense? Is there a proof for this that I can read about?
Thanks a lot.
statistics factoring time-series
asked Dec 13 '18 at 18:57
MetricianMetrician
677
$endgroup$
add a comment |
$begingroup$
I'm new to Time Series Analysis. I've read that when inverting autoregressive characteristic polynomial of arbitrary finite degree, we need to write it in its factorized form:
$$phi_p(x) = prod_{i=1}^p Big( 1-frac{x}{r_i} Big)$$
Where $r_1, ..., r_p$ are the roots of the polynomial. My question is why does this form of dividing by the roots make sense? Is there a proof for this that I can read about?
Thanks a lot.
statistics factoring time-series
asked Dec 13 '18 at 18:57
MetricianMetrician
677
$endgroup$
I'm new to Time Series Analysis. I've read that when inverting autoregressive characteristic polynomial of arbitrary finite degree, we need to write it in its factorized form:
$$phi_p(x) = prod_{i=1}^p Big( 1-frac{x}{r_i} Big)$$
Where $r_1, ..., r_p$ are the roots of the polynomial. My question is why does this form of dividing by the roots make sense? Is there a proof for this that I can read about?
Thanks a lot.
statistics factoring time-series
statistics factoring time-series
asked Dec 13 '18 at 18:57
MetricianMetrician
677
asked Dec 13 '18 at 18:57
MetricianMetrician
677
asked Dec 13 '18 at 18:57
MetricianMetrician
677
asked Dec 13 '18 at 18:57
MetricianMetrician
677
asked Dec 13 '18 at 18:57
MetricianMetrician
677
677
add a comment |
add a comment |
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