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Ferdi
Ferdi
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I would like to understand why the non-seasonal and seasonal parts are multiplied in Seasonal ARIMA models.

To be more specific: when we use the Seasonal ARIMA model we assume a multiplicative model and the ARIMA order is represented as: ARIMA (p,d,q)x(P,D,Q). (https://www.otexts.org/fpp/8/9)

so for e.g the order of SARIMA(1,0,0)x(1,0,0) can be represented mathematically as:

enter image description here

  1. so why are they multiplied from the first place?
  2. is there an additive model which can be applied here?
  3. if there is, why is it not used?

all books of time series analysis that I've checked, just assume that the non-seasonal and seasonal parts should be multiplied, but non have given an explanation why.. I've asked around people who worked with ARIMA but non could help me with that, so I would really appreciate if someone could shed a light on that! a reference would be also very helpful. Thanks!

I would like to understand why the non-seasonal and seasonal parts are multiplied in Seasonal ARIMA models.

To be more specific: when we use the Seasonal ARIMA model we assume a multiplicative model and the ARIMA order is represented as: ARIMA (p,d,q)x(P,D,Q). (https://www.otexts.org/fpp/8/9)

so for e.g the order of SARIMA(1,0,0)x(1,0,0) can be represented mathematically as:

enter image description here

  1. so why are they multiplied from the first place?
  2. is there an additive model which can be applied here?
  3. if there is, why is it not used?

all books of time series analysis that I've checked, just assume that the non-seasonal and seasonal parts should be multiplied, but non have given an explanation why.. I've asked around people who worked with ARIMA but non could help me with that, so I would really appreciate if someone could shed a light on that! a reference would be also very helpful. Thanks!

I would like to understand why the non-seasonal and seasonal parts are multiplied in Seasonal ARIMA models.

To be more specific: when we use the Seasonal ARIMA model we assume a multiplicative model and the ARIMA order is represented as: ARIMA (p,d,q)x(P,D,Q). (https://www.otexts.org/fpp/8/9)

so for e.g the order of SARIMA(1,0,0)x(1,0,0) can be represented mathematically as:

enter image description here

  1. so why are they multiplied from the first place?
  2. is there an additive model which can be applied here?
  3. if there is, why is it not used?

all books of time series analysis that I've checked, just assume that the non-seasonal and seasonal parts should be multiplied, but non have given an explanation why.. I've asked around people who worked with ARIMA but non could help me with that, so I would really appreciate if someone could shed a light on that! a reference would be also very helpful.

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Apython
Apython
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why the non-seasonal and seasonal parts are multiplied in ARIMA models?

I would like to understand why the non-seasonal and seasonal parts are multiplied in Seasonal ARIMA models.

To be more specific: when we use the Seasonal ARIMA model we assume a multiplicative model and the ARIMA order is represented as: ARIMA (p,d,q)x(P,D,Q). (https://www.otexts.org/fpp/8/9)

so for e.g the order of SARIMA(1,0,0)x(1,0,0) can be represented mathematically as:

enter image description here

  1. so why are they multiplied from the first place?
  2. is there an additive model which can be applied here?
  3. if there is, why is it not used?

all books of time series analysis that I've checked, just assume that the non-seasonal and seasonal parts should be multiplied, but non have given an explanation why.. I've asked around people who worked with ARIMA but non could help me with that, so I would really appreciate if someone could shed a light on that! a reference would be also very helpful. Thanks!