Robert Engle

Overview

Robert F. Engle is an econometrician at NYU Stern School of Business and co-recipient (with Clive Granger) of the 2003 Nobel Prize in Economics. He is the inventor of ARCH (1982) and the originator of a family of volatility models — ARCH-in-mean, BEKK multivariate GARCH, factor-ARCH, DCC — that transformed financial risk modeling. He also made foundational contributions to the theory of exogeneity (with Hendry and Richard 1983).

Key Contributions / Features

• Dynamic Factor Model / State-Space ML (Engle-Watson 1981) — "A One-Factor Multivariate Time Series Model of Metropolitan Wage Rates," Journal of the American Statistical Association 76(376): 774–781. State-space single-factor extraction of an unobserved metropolitan wage component from five Los Angeles sectoral series via the Kalman filter; scoring algorithm for ML estimation: information matrix computed from K additional Kalman filter passes using only first derivatives (no second derivatives needed); LM serial-correlation diagnostics under the null. Factor loadings (Construction = 1.0, Retail Trade = 0.663, …, Wholesale Trade = 0.302) confirm non-traded sectors load most on the common metro factor. See State-Space Representation.
• Co-integration and Error Correction (Engle-Granger 1987) — "Co-Integration and Error Correction: Representation, Estimation, and Testing," Econometrica 55(2): 251–276. Introduced the CI(d,b) definition; proved the Granger Representation Theorem (ECM ↔ reduced-rank MA ↔ AR equivalence); established superconsistency of OLS for the cointegrating vector; developed the two-step estimator; proposed seven cointegration tests (ADF on residuals recommended) with Monte Carlo critical values. See Cointegration.
• ARCH (1982) — "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica 50: parameterized time-varying conditional variance as $h_t = \alpha_0 + \sum \alpha_j \varepsilon_{t-j}^2$; developed ML estimation theory; Lagrange multiplier test for no-ARCH. First application: UK inflation series.
• ARCH-in-mean (Engle, Lilien, Robins 1987) — introduced the ARCH-M model $r_t = \beta + \delta h_t^{1/2} + \varepsilon_t$; first formal link between conditional volatility and expected asset returns; applied to excess returns of 6-month US T-bills.
• IGARCH (Engle and Bollerslev 1986) — "Modeling the Persistence of Conditional Variances": defined the integrated GARCH model ($\alpha_1 + \beta_1 = 1$); special case gives the EWMA formula used in RiskMetrics VaR.
• Co-persistence in Variance (Bollerslev-Engle 1993) — "Common Persistence in Conditional Variances," Econometrica 61(1): 167–186. Introduced co-persistence as the second-moment analogue of cointegration: IGARCH series can have a stationary-variance linear combination (co-persistent vector), which is the null space of the explosive eigenvalues of $A(1)+B(1)$. Factor GARCH connection: co-persistence exists iff the number of persistent variance factors is less than $N$. Empirical application: DM/BP bilateral rate non-persistent ($t$-stat for $\hat\alpha+\hat\beta=1$ equals 6.03) while both individual USD rates are near-IGARCH — persistence is dollar-specific news.
• Exogeneity (Engle, Hendry, and Richard 1983) — three-way taxonomy of weak, strong, and super-exogeneity used throughout applied econometrics and VAR modeling.
• Factor-ARCH (Engle 1987; Engle, Ng, and Rothschild 1990) — factor structure $r_t = B\xi_t + \varepsilon_t$ with ARCH factors; reduces parameter count for large $n$; applied to Treasury bills of different maturities.
• BEKK (Engle and Kroner 1995) — "Multivariate Simultaneous Generalized ARCH," Econometric Theory 11: positive-definite multivariate GARCH via the outer-product form $H_t = C'C + A_1'\varepsilon_{t-1}\varepsilon_{t-1}'A_1 + G_1'H_{t-1}G_1$; standard model for multivariate volatility.
• News impact curve (Engle and Ng 1993) — misspecification tests for GARCH; concept of the news impact curve: isolates the effect of a single innovation $\varepsilon_{t-1}$ on $h_t$; symmetric for standard GARCH, asymmetric for EGARCH and power-GARCH.
• DCC-GARCH (Engle 2002a) — "Dynamic Conditional Correlation," Journal of Business and Economic Statistics 20: time-varying correlation matrix with constant unconditional targets; extends the constant conditional correlation model (Bollerslev 1990); widely used in multivariate financial applications.
• ACD (Engle and Russell 1998) — "Autoregressive Conditional Duration," Econometrica 66: GARCH-like model for inter-trade durations; applied to ultra-high-frequency market microstructure data.
• CAViaR (Engle and Manganelli 1999) — conditional autoregressive VaR; directly models the conditional quantile without distributional assumptions.
• GARCH 101 (Engle 2001) — "GARCH 101: An Introduction to the Use of ARCH/GARCH Models in Applied Econometrics," Journal of Economic Perspectives 15(4): 157–168. Pedagogical derivation of GARCH(1,1) long-run variance $V_L=\omega/(1-\alpha-\beta)$ and multi-step geometric mean-reversion forecast $\sigma^2_{t+k|t}=V_L+(\alpha+\beta)^k(\sigma^2_t-V_L)$; DJIA+bond empirical example ($\hat\alpha+\hat\beta=0.9922$); VaR calculation; survey of EGARCH, GJR/TARCH, DCC, and meteor showers extensions. See GARCH and BEKK-GARCH and Value at Risk.
• Multiplicative Error Model / Multiple Indicators Model (Engle and Gallo 2006) — "A Multiple Indicators Model for Volatility Using Intra-Daily Data," Journal of Econometrics 131: 3–27. Introduced the MEM ($x_t = \mu_t\varepsilon_t$, $\varepsilon_t\sim\text{Gamma}$, GARCH-like dynamics for $\mu_t$) and joint MIM system for three S&P 500 volatility proxies (absolute returns, daily high-low range, realized volatility); BIC cross-equation lag selection; non-monotonic multi-step forecasts; CBOE VIX tracking. See Multiplicative Error Model and Multiple Indicators Model.

Related

• GARCH and BEKK-GARCH
• Multiplicative Error Model and Multiple Indicators Model
• Value at Risk
• Cointegration
• State-Space Representation
• Clive Granger
• Luc Bauwens
• Giampiero Gallo
• Mark W. Watson