garch11 – GARCH(1,1) univariate conditional-variance model (Bollerslev 1986).#

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Operational op under axis family, sub-layer L4_A_model_selection, layer l4. Standalone callable: mf.functions.garch11_fit.

Function signature#

mf.functions.garch11_fit(
    X: np.ndarray | pd.DataFrame,
    y: np.ndarray | pd.Series,
) -> GARCH11FitResult

Parameters#

name

type

default

constraint

description

X

`np.ndarray

pd.DataFrame`

—

—

y

`np.ndarray

pd.Series`

—

—

Returns#

GARCH11FitResult — 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 GARCH 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#

Standard GARCH(1,1) volatility model: σ²_t = ω + α · ε²_{t-1} + β · σ²_{t-1}. The L4 wrapper treats y as the return-like series and ignores X; predict(X) returns the conditional mean (μ broadcast over len(X)) and the variance forecast is exposed via predict_variance(h_steps) for L7 inspection.

Defaults (paper-faithful, Bollerslev 1986 §3): p = q = 1, mean_model = 'constant', dist = 'normal'. Wraps arch.arch_model – requires the optional [arch] extra (pip install macroforecast[arch]); raises NotImplementedError with an install hint when missing.

When to use

Macro / financial volatility forecasting; baseline GARCH benchmark; volatility-targeting risk applications.

When NOT to use

Without [arch] extra installed – raises a clear NotImplementedError.

In recipe context#

Set params.family = "garch11" in the relevant layer to activate this op within a recipe:

# Layer L4 recipe fragment
params:
  family: garch11

References#

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

  • Bollerslev (1986) ‘Generalized Autoregressive Conditional Heteroskedasticity’, Journal of Econometrics 31(3): 307-327.

  • Engle (1982) ‘Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation’, Econometrica 50(4): 987-1007.