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Model card — Realized volatility

Family: realized_measures, har_rv, realized_quarticity, tripower_quarticity, bns_jump_test, realized_range

Measuring and forecasting volatility from high-frequency data. Where GARCH models latent volatility from daily returns, realized measures observe it: sum intra-day squared returns to estimate a day's integrated variance, use jump-robust variants to separate the smooth diffusion from discrete jumps, test whether a given day contained a jump, and forecast realized variance with the HAR model that has become the field's workhorse. When only OHLC bars are available, range estimators recover much of the same signal.

Function Role
realized_measures RV, bipower variation, and the jump component for one day
realized_quarticity Integrated-quarticity estimate (RV's own standard error scale)
tripower_quarticity Jump-robust quarticity
bns_jump_test Barndorff-Nielsen-Shephard ratio jump test
har_rv HAR-RV forecasting regression (Corsi 2009)
realized_range Range-based variance from OHLC bars

What it estimates

  • realized_measures(returns) — from one day of intraday returns: the realized variance RV = Σrᵢ² (a consistent estimate of the day's integrated variance plus jumps), the jump-robust bipower variation BV (integrated variance only), and the jump component max(RV − BV, 0).
  • realized_quarticity(returns) — RQ = (n/3)Σrᵢ⁴, the integrated quarticity that sets the scale of RV's sampling error. tripower_quarticity is the jump-robust counterpart, used to make the jump test robust to jumps in the variance-of-variance.
  • bns_jump_test(returns) — the Barndorff-Nielsen-Shephard ratio statistic (with the Huang-Tauchen 2005 refinement): a standardized measure of the gap between RV and BV; large positive values signal a jump occurred that day.
  • har_rv(rv) — the Corsi (2009) Heterogeneous AutoRegressive model: regress RV_t on a constant and the daily, weekly, and monthly averages of past RV, with HAC standard errors. Its cascade of horizons captures RV's long memory with three regressors.
  • realized_range(high, low) — the Parkinson (or Garman-Klass, given open and close) range estimator of variance from OHLC bars — far more efficient than close-to-close when intraday returns are unavailable.

Assumptions

  • realized_measures, quarticity, and the jump test each take one day's intraday returns — a 1-D array of the intra-period log returns (e.g. 78 five-minute returns). They return per-day scalars; loop over days to build a series.
  • har_rv takes a series of daily RV, not intraday returns. It needs at least ~a month of history (the monthly component averages 22 days) plus the start burn-in; nobs in the output reflects the usable rows.
  • Sampling frequency is a bias-variance tradeoff. Too-fine sampling lets market-microstructure noise inflate RV; the classic 5-minute grid is a common compromise. These estimators assume you have already chosen a sensible grid — they do not implement noise-robust (two-scale / pre-averaging) corrections.
  • Jump separation is asymptotic. RV − BV is a noisy jump proxy in finite samples; the bns_jump_test ratio is the disciplined way to decide whether a day's gap is a real jump rather than sampling noise.
  • Range estimators assume continuous trading and no drift within the bar; Garman-Klass additionally uses the open and close and is more efficient when those are reliable.

When to use

  • realized_measures — the daily volatility proxy for any high-frequency dataset, and the input to HAR forecasting.
  • bns_jump_test (+ tripower_quarticity) — to flag jump days before modeling, or to build a jump indicator / separate continuous and jump variation for a HAR-CJ style regression.
  • realized_quarticity — to attach a standard error to RV or to construct the jump-test denominator by hand.
  • har_rv — the default realized-volatility forecast: simple, robust, hard to beat, and interpretable (daily/weekly/monthly loadings).
  • realized_range — when you only have OHLC bars (most historical equity and FX data), recovering most of the efficiency of true realized variance.

Key arguments and defaults

Call Argument Default Notes
realized_measures returns — one day's intraday returns
har_rv rv — a series of daily realized variance
start 22 burn-in (needs the monthly window)
variant "level" "level", "log", or "sqrt"
hac_maxlags 5 Newey-West lags on the HAR SEs
use_correction False small-sample HAC correction
realized_range method "parkinson" or "garman_klass" (needs open, close)
open / close None required for Garman-Klass

How to read the output

  • realized_measures → {"rv", "bipower", "jump"}, all scalars in variance (squared-return) units. jump = max(rv − bipower, 0); a jump of 0 means no jump was detected that day. On a small quiet sample bipower can exceed rv, which is why the jump is floored at 0.
  • realized_quarticity, tripower_quarticity → scalars.
  • bns_jump_test → {"ratio"}. The ratio is (asymptotically standard normal under no jump) large and positive on jump days; compare to a normal quantile (e.g. > 1.96 flags a jump at 5%). Negative or small values indicate no jump.
  • har_rv → {"params", "bse", "tvalues", "rsquared", "nobs"} with params ordered [const, daily, weekly, monthly] and HAC bse. The persistence shows up as positive daily+weekly+monthly loadings; variant controls whether the regression is in levels, logs, or square roots (logs keep RV positive and tame outliers).
  • realized_range → a scalar variance.

Failure modes

  • Feeding a daily RV series to realized_measures (or intraday returns to har_rv). The two operate at different granularities: realized_measures/quarticity/bns_jump_test consume one day of intraday returns; har_rv consumes a series of daily RV.
  • Too-fine sampling. Below a few minutes, microstructure noise biases RV upward without a noise-robust estimator (not implemented here). Stick to a ~5-minute grid or coarser unless you handle noise separately.
  • Reading RV − BV as a jump without the test. The difference is noisy; use bns_jump_test to decide.
  • HAR in levels with heavy-tailed RV. A few volatile days dominate the least-squares fit; variant="log" is the common, better-behaved default.
  • Garman-Klass without open/close. It requires all of high/low/open/close; with only high and low, use Parkinson.

Validated against

har_rv is validated as an OLS regression with Newey-West HAC SEs against statsmodels; realized_measures, realized_quarticity, tripower_quarticity, bns_jump_test, and realized_range reproduce the documented Barndorff-Nielsen-Shephard (2002, 2004), Huang-Tauchen (2005), Corsi (2009), Parkinson (1980), and Garman-Klass (1980) measure definitions. Golden values are pinned in fixtures/realized.json.

References

  • Barndorff-Nielsen, O. & Shephard, N. (2002). "Econometric analysis of realized volatility." JRSS-B 64.
  • Barndorff-Nielsen, O. & Shephard, N. (2004). "Power and Bipower Variation with Stochastic Volatility and Jumps." J. Financial Econometrics 2.
  • Huang, X. & Tauchen, G. (2005). "The Relative Contribution of Jumps to Total Price Variance." J. Financial Econometrics 3.
  • Corsi, F. (2009). "A Simple Approximate Long-Memory Model of Realized Volatility." J. Financial Econometrics 7.
  • Parkinson, M. (1980). "The Extreme Value Method for Estimating the Variance of the Rate of Return." J. Business 53.
  • Garman, M. & Klass, M. (1980). "On the Estimation of Security Price Volatilities from Historical Data." J. Business 53.

See the guide: Volatility: GARCH and Risk.

Runnable example

import numpy as np
import tsecon

rng = np.random.default_rng(21)

# ---- one trading day of intraday returns (e.g. 78 five-minute log returns) ----
intraday = 0.001 * rng.standard_normal(78)

# 1. Realized variance, jump-robust bipower variation, and the jump component.
rm = tsecon.realized_measures(intraday)
print("RV:", format(rm["rv"], ".2e"), " bipower:", format(rm["bipower"], ".2e"),
      " jump:", format(rm["jump"], ".2e"))

# 2. Integrated-quarticity estimators (the scale for RV's own standard error).
print("RQ:", format(tsecon.realized_quarticity(intraday), ".2e"),
      " tripower (jump-robust):", format(tsecon.tripower_quarticity(intraday), ".2e"))

# 3. BNS ratio jump test on a day WITH an injected jump: a large positive ratio flags it.
jumpy = intraday.copy(); jumpy[40] += 0.02
print("BNS ratio, no jump:", round(tsecon.bns_jump_test(intraday)["ratio"], 3),
      " with jump:", round(tsecon.bns_jump_test(jumpy)["ratio"], 3))

# ---- a persistent daily realized-variance series ----
days = 500
rv = np.empty(days); rv[0] = 1e-4
for t in range(1, days):
    rv[t] = 0.6 * rv[t - 1] + 0.4 * abs(rng.standard_normal() * 1e-4) + 1e-6

# 4. HAR-RV (Corsi): RV_t on its daily, weekly, and monthly averages, HAC SEs.
har = tsecon.har_rv(rv, variant="log")
print("HAR params [const, daily, weekly, monthly]:", np.round(har["params"], 3),
      " R^2:", round(har["rsquared"], 3))

# 5. Range-based variance from OHLC bars (no intraday returns needed).
n = 250
high = 1 + 0.01 * np.abs(rng.standard_normal(n)); low = 1 - 0.01 * np.abs(rng.standard_normal(n))
op = 1 + 0.005 * rng.standard_normal(n); cl = 1 + 0.005 * rng.standard_normal(n)
print("Parkinson:", round(tsecon.realized_range(high, low), 4),
      " Garman-Klass:", round(tsecon.realized_range(high, low, method="garman_klass",
                                                    open=op, close=cl), 4))

Expected output:

RV: 6.34e-05  bipower: 7.53e-05  jump: 0.00e+00
RQ: 3.21e-09  tripower (jump-robust): 7.25e-09
BNS ratio, no jump: -1.877  with jump: 8.306
HAR params [const, daily, weekly, monthly]: [-4.197  0.641  0.03  -0.112]  R^2: 0.419
Parkinson: 0.0284  Garman-Klass: 0.0353