[pystatsmodels] Mean value of an ARMA process

[Georgios Boumis]

Hello, I'd like to know if there is a way to find the mean value of a
representation of an ARMA process. For a generated ARMA sample that would
be easy with np.mean() but how can I do it for the representation?

[Chad Fulton]

Post by Georgios Boumis
Hello, I'd like to know if there is a way to find the mean value of a
representation of an ARMA process. For a generated ARMA sample that would
be easy with np.mean() but how can I do it for the representation?

If your AR coefficients are phi_1, phi_2, ..., phi_n, and you have an
intercept nu, then the mean is:

nu / (1 - phi_1 - phi_2 - ... - phi_n)

The MA coefficients don't affect the mean.

Chad

[j***@gmail.com]

On Sun, Oct 14, 2018 at 11:17 AM Georgios Boumis <

Post by Georgios Boumis
Hello, I'd like to know if there is a way to find the mean value of a
representation of an ARMA process. For a generated ARMA sample that would
be easy with np.mean() but how can I do it for the representation?

If your AR coefficients are phi_1, phi_2, ..., phi_n, and you have an
nu / (1 - phi_1 - phi_2 - ... - phi_n)

However, the intercept/constant parameter in statsmodels ARMAs are already
the long term mean, AFAIR.

Josef

The MA coefficients don't affect the mean.
Chad

[Georgios Boumis]

So when my ARMA looks like φ(Β)(Xt-ÎŒ)=Ξ(Β)εt then the mean should be zero
if Ό=0 right?
΀η Κυριακή, 14 Οκτωβρίου 2018 - 5:50:55 ÎŒ.ÎŒ. UTC+2, ο χρήστης Chad Fulton

Post by Chad Fulton

Post by Georgios Boumis
Hello, I'd like to know if there is a way to find the mean value of a
representation of an ARMA process. For a generated ARMA sample that would
be easy with np.mean() but how can I do it for the representation?

If your AR coefficients are phi_1, phi_2, ..., phi_n, and you have an
nu / (1 - phi_1 - phi_2 - ... - phi_n)
The MA coefficients don't affect the mean.
Chad

[j***@gmail.com]

Post by Georgios Boumis
So when my ARMA looks like φ(Β)(Xt-ÎŒ)=Ξ(Β)εt then the mean should be zero
if Ό=0 right?

Yes, the long-term mean will be mu=0, e.g. a long term forecast in a
stationary arima converges to mu.
However, average value (mean) over shorter horizons will depend on the
initial state and the speed of adjustment.

mu in the statsmodels ARMA version depends on the definition of the `trend`
option and the presence of exog.

Josef

Josef

Post by Georgios Boumis
΀η Κυριακή, 14 Οκτωβρίου 2018 - 5:50:55 ÎŒ.ÎŒ. UTC+2, ο χρήστης Chad Fulton

Post by Chad Fulton

Post by Georgios Boumis
Hello, I'd like to know if there is a way to find the mean value of a
representation of an ARMA process. For a generated ARMA sample that would
be easy with np.mean() but how can I do it for the representation?

If your AR coefficients are phi_1, phi_2, ..., phi_n, and you have an
nu / (1 - phi_1 - phi_2 - ... - phi_n)
The MA coefficients don't affect the mean.
Chad