Discussion:
[pystatsmodels] statsmodels works with Lag Transfer Function?
Wei CHEN
2018-11-12 09:01:18 UTC
Permalink
Hi, All,



I created a free-form SARIMAX models like this:

[image: 1.png]

where, Y(t) is endog, X(t),...X(t-10) are time lagged exogs, C is a
constant level, N(t) is an autocorrelated residual.



Obviouly, it is ax SARIMAX model with exogenous regressors, the ARIMAX
method works and fits well with this free-form model. However, with this
model, we have large number of weights to estimate, from beta(0) to
beta(10) for X(t) term. For sake of parsimony, some time series analysis
and forecast books suggest to use RATIONAL TRANSFER FUNCTION model, which
has less coefficients to estimated and is writen in form as below:

[image: 2.png]


B is a backshift notation, equivalent to L(means lag notation) in
statsmodels package's documentation.



Specially for my case, the model with transfer function can be written as:

[image: 3.png]


So, the model is simplified, and therefore there 2 coefficients to
estimated with X(t) term. Is there any method in statsmodel can realize the
distributed lag transfer function model like this?



Thank you.

Wei CHEN
Chad Fulton
2018-11-13 00:52:50 UTC
Permalink
Post by Wei CHEN
Hi, All,
[image: 1.png]
where, Y(t) is endog, X(t),...X(t-10) are time lagged exogs, C is a
constant level, N(t) is an autocorrelated residual.
Obviouly, it is ax SARIMAX model with exogenous regressors, the ARIMAX
method works and fits well with this free-form model. However, with this
model, we have large number of weights to estimate, from beta(0) to
beta(10) for X(t) term. For sake of parsimony, some time series analysis
and forecast books suggest to use RATIONAL TRANSFER FUNCTION model, which
[image: 2.png]
B is a backshift notation, equivalent to L(means lag notation) in
statsmodels package's documentation.
[image: 3.png]
So, the model is simplified, and therefore there 2 coefficients to
estimated with X(t) term. Is there any method in statsmodel can realize the
distributed lag transfer function model like this?
Thank you.
Wei CHEN
Hi,

We don't have a general transfer function model. If the SARIMAX class
doesn't fit what you're planning to do, then you can construct a custom
state space model.

If you'd like to go the latter route and create a custom model, feel free
to post your code / questions to the mailing list and I'd be happy to help.

Best,
Chad
Wei CHEN
2018-11-13 01:34:22 UTC
Permalink
Chad,

OK. Thank your for the clue. It seems transer function is a special case of
state space model. I will try to customize a state space model.

Best regards
Wei

圚 2018幎11月13日星期二 UTC+8䞊午8:53:04Chad Fulton写道
Post by Chad Fulton
Post by Wei CHEN
Hi, All,
[image: 1.png]
where, Y(t) is endog, X(t),...X(t-10) are time lagged exogs, C is a
constant level, N(t) is an autocorrelated residual.
Obviouly, it is ax SARIMAX model with exogenous regressors, the ARIMAX
method works and fits well with this free-form model. However, with this
model, we have large number of weights to estimate, from beta(0) to
beta(10) for X(t) term. For sake of parsimony, some time series analysis
and forecast books suggest to use RATIONAL TRANSFER FUNCTION model, which
[image: 2.png]
B is a backshift notation, equivalent to L(means lag notation) in
statsmodels package's documentation.
[image: 3.png]
So, the model is simplified, and therefore there 2 coefficients to
estimated with X(t) term. Is there any method in statsmodel can realize the
distributed lag transfer function model like this?
Thank you.
Wei CHEN
Hi,
We don't have a general transfer function model. If the SARIMAX class
doesn't fit what you're planning to do, then you can construct a custom
state space model.
If you'd like to go the latter route and create a custom model, feel free
to post your code / questions to the mailing list and I'd be happy to help.
Best,
Chad
Wei CHEN
2018-11-13 01:35:32 UTC
Permalink
Chad,

OK. Thank your for the clue. It seems transer function is a special case of
state space model. I will try to customize a state space model.

Best regards
Wei

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