non-linear AR model - NLAR(1)

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non-linear AR model - NLAR(1)

Unread postby ac_1 » Sat Mar 13, 2021 4:54 pm

Hi Tom,

For a simple non-linear AR model - NLAR(1), e.g. y(t) = c + beta1*y(t-1) + beta2*(y^2)(t-1) + beta3*(y^3)(t-1) + u(t), I think can be estimated via either LINREG or BOXJENK ???

If so then to generate one-step ahead forecasts is straightforward using UFORECAST. How about multi-step ahead forecasts, do these have to be simulated e.g bootstrap?

many thanks,
Amarjit
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Re: non-linear AR model - NLAR(1)

Unread postby TomDoan » Sun Mar 14, 2021 10:15 am

BOXJENK really wouldn't apply to that---the AR(1) term is really no different in its use from the squared and cubed lags. You can use LINREG (after creating separate series for the square and cube), or you can estimate it using NLLS. (It's linear in the parameters, but non-linear in the variables). If you estimate by NLLS, you can use FORECAST (UFORECAST doesn't apply to non-linear FRML's) which will do chain rule forecasts (replacing y^2 and y^3 by their point estimates) out-of-sample. You can also do bootstrapping or simulation if you want to forecast the process mean.
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Re: non-linear AR model - NLAR(1)

Unread postby ac_1 » Mon Mar 15, 2021 5:53 am

Thanks. I will use LINREG and I can generate one-step-ahead & multi-step-ahead forecasts via FORECAST. I can also generate forecasts via bootstrap method, however I have not seen a simulation example...
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Re: non-linear AR model - NLAR(1)

Unread postby TomDoan » Tue Mar 16, 2021 2:10 pm

ac_1 wrote:Thanks. I will use LINREG and I can generate one-step-ahead & multi-step-ahead forecasts via FORECAST. I can also generate forecasts via bootstrap method, however I have not seen a simulation example...


Not LINREG, NLLS. An EQUATION or FRML generated by LINREG won't include the connections among the powers of Y.

You can do simulations with SIMULATE rather than FORECAST---that will give you one realization. You have to loop over that to generate many realizations and figure out what you want to do with the results. Bootstrapping is done as show in the User's Guide except you have only one set of residuals, not three. Again, you have to figure out what you want to do with the results.
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