BUG: Implement forecasting for ARCH-in-mean models - #859
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ARCHInMean.forecast has raised NotImplementedError since the model was added in 2021. Implement it by mirroring ARX.forecast and adding the kappa*f(sigma2) term to the mean recursion and to the simulation and bootstrap paths. The one-step analytic forecast is exact for all form specifications; multi-horizon analytic forecasts use the variance forecast recursion, which is exact when form is 'var'.
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ARCHInMean.forecasthas raisedNotImplementedErrorsince the model was added in 2021, even though the class docstring example ends atfit()and the rest of the class (simulate,resids) works. This implements it by mirroringARX.forecastand adding thekappa * f(sigma2)term to the mean recursion and the simulation/bootstrap paths.Repro:
ARCHInMean(y, lags=[1, 2], volatility=GARCH()).fit().forecast(horizon=3).The 1-step analytic forecast is exact for all
formsettings. Multi-horizon analytic forecasts use the variance forecast recursion, which is exact whenform='var'and the standard plug-in approximation otherwise. EGARCH and APARCH keep their existing analytic multi-horizon constraint (ValueError).Tests cover a hand-computed closed-form recursion for
var/vol/log, convergence of the simulation forecast to the analytic forecast forvar, thekappa=0case reducing byte-for-byte to an ARX forecast, exog composition, bootstrap, and the EGARCH h>1 constraint. Full suite: 4948 passed.