ARMA–GARCH

Joint MLE of a linear mean (ARMA / ARX / HAR / …) and conditional variance (GARCH, GJR, EGARCH, APARCH, FIGARCH) under normal, Student-t, skew-t or GED innovations.

README: makystats/armagarch/README.md · Full technical guide: DOCUMENTATION.md

Quick start

from makystats import arma_garch, select_order

res = arma_garch(y, mean="AR", ar=1, ma=1, vol="GARCH", dist="normal", trend="c").fit()
print(res.coef_table)
print(res.loglik, res.aic, res.bic)
print(res.forecast(h=5))
fig = res.plot_diagnostics(lags=20)

# d and seasonality fixed on the whole IC grid
tab = select_order(
    ylog, p_range=range(0, 3), q_range=range(0, 2),
    r_range=[1], s_range=[1], d=1,
    seasonal_order=(0, 1, 1, 12), criterion="aic",
)
tab, best = select_order(..., return_best=True)

API sketch

Argument	Role
`mean`	`Constant`, `Zero`, `AR`, `ARX`, `ARMAX`, `HAR`, `HARX`, `LS`
`in_mean`	`None` / `sigma` / `var` / `log` — GARCH-M (coef `archm`)
`trend`	`n` / `c` / `t` / `ct`
`vol`	`GARCH`, `ARCH`, `GJR`/`TARCH`, `EGARCH`, `APARCH`, `FIGARCH`
`dist`	`normal`, `t`, `skewt`, `ged`
`ar` / `ma`	Orders or lag lists (sparse ARMA)
`r` / `s`	ARCH / GARCH orders (`r=s=0` → constant variance)
`d`	Regular differences 0, 1 or 2
`seasonal_order`	`(P, D, Q, s)` additive seasonal mean

GARCH-M

res = arma_garch(y, mean="AR", ar=1, ma=1, vol="GARCH", in_mean="var").fit()
# in_mean: None | "sigma" | "var" | "log"  → coefficient archm (λ)

Value-at-Risk / Expected Shortfall

res.var(alpha=0.05, h=1, method="parametric")
res.var(alpha=0.05, h=10, aggregation="cumulative", n_sims=10000, seed=1)
res.expected_shortfall(alpha=0.05)
df = res.var_series(alpha=0.05)
res.var_backtest(alpha=0.05)
res.plot_var(alphas=(0.05, 0.01), method="parametric")

Forecast VaR/ES: aggregation="marginal" (default) or "cumulative" (MC)
In-sample 1-step: var_series, var_backtest, plot_var

Fitted series

res.fitted_values
res.residuals
res.results_frame(include_x=True, index=dates)
# Identity: y = fitted_values + residuals

Unconstrained BFGS on a reparameterised space; OPG standard errors by default. Deep technical material (likelihood, burn-in, backcast, optimisation): DOCUMENTATION.md.