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I used auto_arima function with seasonality to forecast covid19 and got ARIMA(0,1,1)(2,0,2) Can anyone explain me the reason for each parameter (p,d,q)(P,D,Q)? (Ex: why AR is 0 meanwhile SAR is 2)

Jose
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1 Answers1

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For Samira is decompose (p,d,q) and (P, D, Q) with the seasonal.

AR(0) or p = 1. The time serie does not depend on time spent.

d = 1 cov(Xt, Xt-1) = No Constant. The serie is stationnary with one differentiable. Yt = Xt - Xt-1 cov(Xt, Yt) = Constant

AM(1). The times serie depend a one random evenement.

idem for seasonal. For exemple (P,D,Q)12 months, you have for every year.

P = 2 The time serie by Years(month) depend Year-1(month) and Year-2(month). With july, you have July 2021 depend July 2020 and July 2019 but with AR(0) July 2021 not depend of June

D = 0 The procesus is stationnary. cov(month 2021, month 2020) = constant for every months.

Q = 2 The time serie depend a random event with mean equal 0 (Noise white), exemple : July 2021 depend event at July 2020 and July 2019, and for all month you have month 2021 depend event same month 2020 and same month 2019.

Best regard,

gregory l
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