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mfe — Financial Econometrics for Python

mfe is a Python port of Kevin Sheppard's Oxford MFE Toolbox, optimised for HFT data and quantitative research. It complements the arch package — covering everything arch is missing.

What's inside

Full HFT realized-measure library with Cython-accelerated hot paths:

  • Realized variance, BPV, MedRV, MinRV, pre-averaged RV, semivariance
  • Realized kernel (6 weight functions, auto-bandwidth)
  • Two-scale RV (TSRV) and multi-scale RV (MSRV) — noise-robust
  • Realized quantile variance — jump-robust
  • Hayashi-Yoshida covariance — O((N₁+N₂) log N) sweep-line in Cython
  • Multivariate realized kernel — PSD-guaranteed (K,K) covariance matrix
  • BNS jump test, realized range, microstructure noise estimation

Every model missing from arch:

  • DCC (Engle 2002), cDCC (Aielli 2013)
  • CCC (Bollerslev 1990)
  • BEKK scalar + diagonal (Engle & Kroner 1995)
  • O-GARCH (Alexander 2001)
  • GO-GARCH — ICA or moments rotation (van der Weide 2002)
  • RCC (Noureldin, Shephard & Sheppard 2014) — rotated conditional correlation

Models not in arch:

  • HAR-RV — standard, matrix-interval, MODIFIED spec, jump-augmented (HAR-RV-J)
  • HEAVY — joint model of returns + realized variance (Shephard & Sheppard 2010)

The gap vs. statsmodels VAR:

  • VAR with 4 VCV options: homo/het × corr/uncorr
  • Granger causality — LR, LM, Wald tests with robust VCV
  • Impulse response functions with delta-method standard errors
  • Beveridge-Nelson decomposition — permanent/transitory components
  • Wild bootstrap for realized volatility statistics
  • SPA test — Hansen (2005) Superior Predictive Ability
  • StepM — Romano & Wolf (2005) stepdown FWER control
  • ARCH-LM, Ljung-Box Q, HAC-robust LM serial correlation
  • Diebold-Mariano (MSE/MAE/QLIKE), Mincer-Zarnowitz
  • Fama-MacBeth with Shanken correction
  • OLS / OLSNW — White and Newey-West standard errors
  • PCA with factor interpretation and reconstruction

Quick example

from mfe.realized import (
    price_filter, returns_from_prices,
    realized_variance, realized_kernel, bns_jump_test,
)
from mfe.realized.sampling import SamplingType

# Filter raw ticks to 5-minute grid
prices_5m, times_5m = price_filter(
    tick_prices, tick_times,
    sampling_type=SamplingType.CALENDAR_TIME,
    sampling_interval=300,
)
r = returns_from_prices(prices_5m)

# Realized variance and kernel
rv  = realized_variance(r)
rk  = realized_kernel(r)           # noise-robust
jmp = bns_jump_test(r)             # jump detection

print(f"RV  = {rv.value:.6f}")
print(f"RK  = {rk.rk_adjusted:.6f}  (H = {rk.bandwidth})")
print(f"Jump significant: {jmp.significant}  (p = {jmp.p_value:.3f})")

from mfe.multivariate import DCC, RCC, GOGARCH
from mfe.univariate import HEAVY

# DCC-GARCH on daily returns
dcc = DCC().fit(returns)          # (T, K) return matrix
print(dcc.conditional_covariances.shape)   # (T, K, K)

# Rotated Conditional Correlation — covariance-targeting by construction
rcc = RCC().fit(returns)
print(f"RCC: a={rcc.a:.3f}  b={rcc.b:.3f}")

# HEAVY — use realised variance to sharpen daily vol forecasts
heavy = HEAVY().fit(daily_returns, realized_variances)
h_r, h_rm = heavy.h_returns, heavy.h_realized

Installation

pip install mfe

Cython extensions (optional, ~10-800x speedup on hot paths):

pip install mfe[cython]
# or build from source:
python setup_cython.py build_ext --inplace

Design principles

  • Results are dataclasses — immutable, no state mutation bugs.
  • ConvergenceWarning always fires on non-converged optimisers — never silent.
  • Cython extensions with pure-Python fallbacks — wheels ship as binaries; pure installs work without a C compiler.
  • No duplication of arch — univariate GARCH estimation stays in arch.
  • HFT-first — all realized estimators operate on raw tick arrays, not DataFrames.

Relationship to the MATLAB MFE Toolbox

This package ports the MATLAB MFE Toolbox (Kevin Sheppard, Oxford) to Python, fixing known bugs:

MATLAB issue Python fix
gogarch.m closes over volData in loop → memory leak No closures; all state explicit
Convergence warning fires then parameters silently used ConvergenceWarning raised
realized_kernel.m mixes validation into hot path Separated: realized_kernel() vs realized_kernel_validated()
dcc.m recomputes Q_bar inside likelihood loop Pre-computed, passed as constant
No sandwich VCV for multivariate estimators Sandwich estimator standard
realized_hayashi_yoshida.m has TODO for K > 2 Implemented for general K