egarch – Exponential GARCH with leverage asymmetry (Nelson 1991).#

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

Function signature#

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

Parameters#

name

type

default

constraint

description

X

`np.ndarray

pd.DataFrame`

—

—

y

`np.ndarray

pd.Series`

—

—

Returns#

EGARCHFitResult — 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 EGARCH 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#

EGARCH(p, o, q) on log-variance: ln σ²_t = ω + Σ α_i (|z_{t-i}| − E|z|) + Σ γ_i z_{t-i} + Σ β_j ln σ²_{t-j}. The asymmetry term γ captures the leverage effect (negative shocks raise volatility more than positive ones), and the log specification removes any need for non-negativity constraints on the parameters.

Defaults (Nelson 1991 §3): p = o = q = 1, mean_model = 'constant', dist = 'normal'. Wraps arch.arch_model(vol='EGARCH') – requires [arch] extra.

When to use

Asymmetric / leverage volatility; equity returns where bad news amplifies vol; macro variables with sign-asymmetric volatility responses.

When NOT to use

Without [arch] extra installed; symmetric volatility series where GARCH(1,1) is sufficient (parsimony).

In recipe context#

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

# Layer L4 recipe fragment
params:
  family: egarch

References#

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

  • Nelson (1991) ‘Conditional Heteroskedasticity in Asset Returns: A New Approach’, Econometrica 59(2): 347-370.