realized_garch_with_rv_exog – GARCH(1,1) with realised-variance series fed as the exogenous regressor (NOT Hansen-Huang-Shek 2012 joint MLE).#

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Operational op under axis family, sub-layer L4_A_model_selection, layer l4. Standalone callable: mf.functions.realized_garch_fit.

Function signature#

mf.functions.realized_garch_fit(
    X: np.ndarray | pd.DataFrame,
    y: np.ndarray | pd.Series,
) -> RealizedGARCHFitResult

Parameters#

name

type

default

constraint

description

X

`np.ndarray

pd.DataFrame`

—

—

y

`np.ndarray

pd.Series`

—

—

Returns#

RealizedGARCHFitResult — frozen dataclass with fit results.

Attribute

Type

Description

.conditional_mu

float

Fitted conditional mean mu.

.n_obs

int

Number of non-missing observations.

.params_

dict

Fitted model parameters dict.

.predict(X)

np.ndarray

Conditional mean broadcast over len(X) rows.

.predict_variance(h)

np.ndarray

h-step-ahead variance forecast.

.summary()

str

Table: conditional mean and fitted parameters.

Behavior#

Phase C-3 audit-fix (M9) honest rename. The L4 wrapper consumes params['realized_variance'] (a column name in X) as the RV series and feeds it as the exogenous regressor x= into a vanilla GARCH(1,1) spec. This is useful in practice (RV improves volatility forecasts), but it is NOT the Hansen-Huang-Shek (2012) joint return + measurement-equation MLE: there is no ξ, φ, δ_1, δ_2 measurement-equation parameters in the fitted output. The proper RealizedGARCH spec is reserved as FUTURE under the name realized_garch (awaiting native arch.RealizedGARCH API or manual joint-MLE implementation).

Returns the conditional mean as the point forecast; predict_variance(h_steps) exposes the variance path.

Defaults: mean_model = 'constant', dist = 'normal'. Falls back to a squared-returns proxy when the RV column is unavailable.

When to use

Volatility forecasting when intraday realised variance is observable as a leading indicator (RV-as-exogenous improves vol forecast); honest baseline labelling for studies that need to distinguish from the proper Hansen-Huang-Shek MLE.

When NOT to use

When the proper joint-MLE Realized GARCH is required (the family name realized_garch is FUTURE / unrunnable until upstream supports it); without [arch] extra installed; without an RV measurement available.

In recipe context#

Set params.family = "realized_garch_with_rv_exog" in the relevant layer to activate this op within a recipe:

# Layer L4 recipe fragment
params:
  family: realized_garch_with_rv_exog

References#

  • macroforecast design Part 2, L4: ‘forecasting model is the layer where every authoring iteration ends – pick family, tune, repeat.’

  • Hansen, Huang & Shek (2012) ‘Realized GARCH: A Joint Model for Returns and Realized Measures of Volatility’, Journal of Applied Econometrics 27(6): 877-906 — the target spec, not implemented here.