Add HAR model for realized volatility (Corsi 2009)

[hass-nation]

Summary

Adds HAR (Heterogeneous Autoregressive model for realized volatility), the standard workhorse model for forecasting realized variance in high-frequency financial econometrics (Corsi 2009, JFE).

The model regresses today's realized variance on daily, weekly, and monthly rolling averages of past realized variance:

RV_t = c + β_d·RV_{t-1} + β_w·RV̄_{t-1:t-5} + β_m·RV̄_{t-1:t-22} + ε_t

Estimation is OLS with optional Newey-West HAC standard errors.

Interface

from arch.univariate.har import HAR

har = HAR(rv_series, lags=[1, 5, 22])   # pandas Series of realized variances
res = har.fit(cov_type='robust')
print(res.summary())
res.forecast(horizon=5)

New file

arch/univariate/har.py — HAR and HARResult classes

HARResult attributes

• params / param_names — OLS coefficients
• rsquared — R²
• pvalues, std_errors, tvalues — HAC-robust inference
• predict(start, end) — in-sample fitted values
• forecast(horizon) — recursive multi-step forecast
• summary() — formatted text table

Tests

29/29 pass (arch/tests/test_har.py). Coverage: params shape, R² range, fitted-values shape, multi-step forecast, p-values in [0,1], custom lags, HAC vs OLS SEs, manual OLS verification.

Reference

Corsi, F. (2009). A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics, 7(2), 174–196.

[codecov]

Codecov Report

❌ Patch coverage is 99.10714% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 99.53%. Comparing base (543f44c) to head (90ea290).

Files with missing lines	Patch %	Lines
arch/univariate/har.py	98.59%	1 Missing and 1 partial ⚠️
arch/tests/test_har.py	99.48%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #855      +/-   ##
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- Coverage   99.54%   99.53%   -0.01%     
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  Files          78       80       +2     
  Lines       15818    16154     +336     
  Branches     1294     1315      +21     
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+ Hits        15746    16079     +333     
- Misses         38       39       +1     
- Partials       34       36       +2     

Flag	Coverage Δ
adder	99.49% <99.10%> (-0.01%)	⬇️
subtractor	99.49% <99.10%> (-0.01%)	⬇️

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[bashtage]

This PR makes no sense. There is already a mean HAR which works as expected for RV.