I have some basic Arima questions.I built the following two Arima models in R (output below) and the R output each time mentions something about the mean being non-zero or zero.
Model 1: ARIMA(1,0,0)(1,0,0)[12] with zero mean
Coefficients: ar1 sar1 0.7232 0.3644 s.e. 0.0999 0.1434 Model 2: ARIMA(1,0,0)(1,0,0)[12] with non-zero mean
Coefficients: ar1 sar1 mean 0.9645 0.3081 70.8936 s.e. 0.0252 0.1288 18.6623
Model 1:
ARIMA(1,0,0)(1,0,0)[12] with zero mean
Coefficients:
ar1 sar1
0.7232 0.3644
s.e. 0.0999 0.1434
Model 2:
ARIMA(1,0,0)(1,0,0)[12] with non-zero mean
Coefficients:
ar1 sar1 mean
0.9645 0.3081 70.8936
s.e. 0.0252 0.1288 18.6623
In Model 1, what does it mean for the Arima model to have zero mean - does it mean the response series has zero mean or that the residuals have zero mean? What would be the corresponding model equation? Similarly, Model 2 is Arima(1,0,0)(1,0,0)[12] with non-zero mean - again is this saying something about the level of the response series or the residuals?
Also, I am confused about the intuitive meaning of a seasonal order - what does it mean to have an SAR1 term in the model in terms of the response series? Would much appreciate any replies that can help me understand the intuition or at least the model equation.
