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Hansen, Huang & Shek (2012) complete GARCH-X with a measurement equation linking realised variance to latent h_t, plus a leverage function. The daily-return-only GARCH is the nested special case. Not investment advice.
Takeaway. Realized GARCH is GARCH that believes high-frequency realised measures. Daily squared returns are a noisy variance proxy. Add RV (or another realised measure) and a measurement equation that maps latent $h_t$ → observed $x_t$, plus a leverage function $\tau(z_t)$ so yesterday’s return sign can tilt tomorrow’s vol.
Realized GARCH: A Joint Model for Returns and Realized Measures of Volatility (Peter Reinhard Hansen, Zhuo Huang, Howard Howan Shek, 2012; Journal of Applied Econometrics).
Fit for learners: Three equations: return, GARCH-X update with realised measure x_t, and a measurement equation so RV is not treated as exogenous.
This Hub note is a plain-language intro. Not investment advice.
Plain GARCH sees only one noisy square per day. GARCH-X plugs RV into the variance equation but treats $x_t$ as exogenous—you cannot write a joint likelihood or a clean leverage channel. You want a complete model: returns and realised measures together.
Canonical RealGARCH(1,1), linear sketch:
Then $h_t$ is AR(1)-like; $x_t$ has an ARMA flavour—hence the name. Log-linear versions are common. Nested trick: set $x_t = r_t^2$ and the measurement equation collapses; ordinary GARCH lives inside.
Empirics: DJIA names + an ETF; simple Realized GARCH fit much better than daily-return-only GARCH. Estimation is QMLE, parsimonious.
A volatility likelihood paper—not an options engine.
If you already compute 5-minute RV, this is the smallest complete model that uses it. Later “deep Realized GARCH” papers (also on this Hub) assume you know this skeleton.
Tiny evening exercise: from daily close and a toy RV series, plot $r_t^2$ vs RV. See which is noisier. Learning only.
Landing: DOI / journal
Not investment advice. This Hub note is educational only. Realized GARCH is academic volatility research—not a recommendation to trade variance.
Single course CTA: SoloQuant Academy’s Introduction to Python Programming—a three-line recurrence is just lagged variables; then you can read the measurement equation.