API Reference

This page lists contains a list of the essential end-user API functions and classes.

Volatility Modeling


arch_model(y[, x, mean, lags, vol, p, o, q, …])

Initialization of common ARCH model specifications

Mean Specification

ConstantMean([y, hold_back, volatility, …])

Constant mean model estimation and simulation.

ZeroMean([y, hold_back, volatility, …])

Model with zero conditional mean estimation and simulation

HARX([y, x, lags, constant, use_rotated, …])

Heterogeneous Autoregression (HAR), with optional exogenous regressors, model estimation and simulation

ARX([y, x, lags, constant, hold_back, …])

Autoregressive model with optional exogenous regressors estimation and simulation

LS([y, x, constant, hold_back, volatility, …])

Least squares model estimation and simulation

Volatility Process Specification

GARCH([p, o, q, power])

GARCH and related model estimation

EGARCH([p, o, q])

EGARCH model estimation


Heterogeneous ARCH process

FIGARCH([p, q, power, truncation])


MIDASHyperbolic([m, asym])

MIDAS Hyperbolic ARCH process


Exponentially Weighted Moving-Average (RiskMetrics) Variance process

RiskMetrics2006([tau0, tau1, kmax, rho])

RiskMetrics 2006 Variance process


Constant volatility process

FixedVariance(variance[, unit_scale])

Fixed volatility process

Shock Distributions


Standard normal distribution for use with ARCH models


Standardized Student’s distribution for use with ARCH models


Standardized Skewed Student’s distribution for use with ARCH models


Generalized Error distribution for use with ARCH models

Unit Root Testing

ADF(y[, lags, trend, max_lags, method, …])

Augmented Dickey-Fuller unit root test

DFGLS(y[, lags, trend, max_lags, method, …])

Elliott, Rothenberg and Stock’s GLS version of the Dickey-Fuller test

PhillipsPerron(y[, lags, trend, test_type])

Phillips-Perron unit root test

ZivotAndrews(y[, lags, trend, trim, …])

Zivot-Andrews structural-break unit-root test

VarianceRatio(y[, lags, trend, debiased, …])

Variance Ratio test of a random walk.

KPSS(y[, lags, trend])

Kwiatkowski, Phillips, Schmidt and Shin (KPSS) stationarity test

Cointegration Testing

engle_granger(y, x[, trend, lags, max_lags, …])

Test for cointegration within a set of time series.

phillips_ouliaris(y, x[, trend, test_type, …])

Test for cointegration within a set of time series.

Cointegrating Relationship Estimation

CanonicalCointegratingReg(y, x[, trend, x_trend])

Canonical Cointegrating Regression cointegrating vector estimation.

DynamicOLS(y, x[, trend, lags, leads, …])

Dynamic OLS (DOLS) cointegrating vector estimation

FullyModifiedOLS(y, x[, trend, x_trend])

Fully Modified OLS cointegrating vector estimation.


IIDBootstrap(*args[, random_state])

Bootstrap using uniform resampling

IndependentSamplesBootstrap(*args[, …])

Bootstrap where each input is independently resampled

StationaryBootstrap(block_size, *args[, …])

Politis and Romano (1994) bootstrap with expon distributed block sizes

CircularBlockBootstrap(block_size, *args[, …])

Bootstrap using blocks of the same length with end-to-start wrap around

MovingBlockBootstrap(block_size, *args[, …])

Bootstrap using blocks of the same length without wrap around

Block-length Selection


Estimate optimal window length for time-series bootstraps

Testing with Multiple-Comparison

SPA(benchmark, models[, block_size, reps, …])

Test of Superior Predictive Ability (SPA) of White and Hansen.

MCS(losses, size[, reps, block_size, …])

Model Confidence Set (MCS) of Hansen, Lunde and Nason.

StepM(benchmark, models[, size, block_size, …])

StepM multiple comparison procedure of Romano and Wolf.

Long-run Covariance (HAC) Estimation

Bartlett(x[, bandwidth, df_adjust, center, …])

Bartlett’s (Newey-West) kernel covariance estimation.

Parzen(x[, bandwidth, df_adjust, center, …])

Parzen’s kernel covariance estimation.

ParzenCauchy(x[, bandwidth, df_adjust, …])

Parzen’s Cauchy kernel covariance estimation.

ParzenGeometric(x[, bandwidth, df_adjust, …])

Parzen’s Geometric kernel covariance estimation.

ParzenRiesz(x[, bandwidth, df_adjust, …])

Parzen-Reisz kernel covariance estimation.

QuadraticSpectral(x[, bandwidth, df_adjust, …])

Quadratic-Spectral (Andrews’) kernel covariance estimation.

TukeyHamming(x[, bandwidth, df_adjust, …])

Tukey-Hamming kernel covariance estimation.

TukeyHanning(x[, bandwidth, df_adjust, …])

Tukey-Hanning kernel covariance estimation.

TukeyParzen(x[, bandwidth, df_adjust, …])

Tukey-Parzen kernel covariance estimation.