CODEWITHSUNDEEP
rtime-series
Thai Phi
Thai Phi

Reputation: 11

R auto.arima() vs arima() giving different result with the same model

I have a question about this time series analysis, with mean monthly air temperature (Deg. F) Nottingham Castle 1920-1939:

https://datamarket.com/data/set/22li/mean-monthly-air-temperature-deg-f-nottingham-castle-1920-1939#!ds=22li&display=line

When I ran 

auto.arima(x.t,trace=True)

it gave me "ARIMA(5,0,1) with non-zero mean" and "AIC=1198.42" as the lowest AIC. However, when I manually input the arima model, I came across a model with even lower aic. 

arima(x = x.t, order = c(3, 1, 3))

aic = 1136.95. When I run the function auto.arima(x.t,trace = TRUE,d=1), It gave me ARIMA(2,1,2) with AIC of 1221.413. While ARIMA(3,1,3) with drift gives 1209.947 and ARIMA(3,1,3) gives 1207.859.

I am really confused. I thought auto.arima should automatically suggest you the number of differencing. Why is auto.arima AIC different than the arima AIC while they have the same model?

Upvotes: 0

Views: 1299

Answers (1)

Maurits Evers
Maurits Evers

Reputation: 50678

You're fitting two different ARIMA models. Obviously an ARIMA(5,0,1) model is not the same as an ARIMA(3,1,3) model. In the former, you model p=5 time lags with no differencing, whereas in the latter you consider p=3 time lags with d=1 degree of differencing. Additionally, your model's MA components are also different: q=1 vs. q=3.

Different models will obviously give you different quality metrics (i.e. different AICs).

Upvotes: 0

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