Clive Granger

Overview

Clive W. J. Granger (1934–2009) was an econometrician at the University of California, San Diego, and co-recipient (with Robert Engle) of the 2003 Nobel Prize in Economics. He invented the concept of cointegration (1981) and gave it empirical and theoretical foundations through the Granger Representation Theorem, the two-step estimation method (with Engle 1987), and a long research program on extensions. He also originated the concept of Granger causality (1969), contributed to long-memory modeling, forecast combination, and nonlinear time-series analysis.

Key Contributions / Features

• Spurious regression (Granger and Newbold 1974) — showed via simulation that OLS on independent random walks produces spuriously significant t-statistics and high $R^2$ with strongly autocorrelated residuals; foundational motivation for cointegration.
• Cointegration concept (Granger 1981) — introduced the I(d) integration order taxonomy; defined cointegration as the existence of a stationary linear combination of I(1) variables; uniqueness of the cointegrating vector for n=2 (contradiction proof).
• Granger Representation Theorem (Granger and Weiss 1983; Engle and Granger 1987) — cointegration is equivalent to an error-correction representation; a cointegrated I(1) system always has a VECM form with at least one nonzero loading coefficient α.
• Engle-Granger two-step (Engle and Granger 1987) — OLS estimate $\hat\beta$ is superconsistent (rate $T^{-1}$, Stock 1987); fix β̂, estimate (α, Γ) by ML → asymptotically normal second-stage estimators. First systematic method for estimating cointegrated systems.
• Granger causality (Granger 1969) — predictive causality definition: $y_3$ Granger-causes $y_1$ if past $y_3$ improves forecasts of $y_1$ beyond the past of $y_1$ alone; testable as zero restrictions in VAR coefficient matrices.
• Seasonal cointegration (Hylleberg, Engle, Granger, and Yoo 1990) — extension to seasonally integrated variables ($\Delta_4 x_t = I(0)$); seasonal unit roots at frequencies $\omega = \pi/2, \pi$.
• Multicointegration (Granger and Lee 1990) — when $x_t$ and $y_t$ are cointegrated, the cumulated disequilibrium $\sum(y_t - \beta x_t)$ is I(1) and may be cointegrated with $x_t$ or $y_t$; useful for stock-flow models.
• Long-memory / fractional integration (Granger and Joyeux 1980) — I(d) for non-integer d; slow hyperbolic decay of autocorrelations; ARFIMA models.
• Forecast combination (Granger and Bates 1969) — early contribution to combining forecasts; laid groundwork for the forecast combination literature.
• Stochastic unit root (Granger and Swanson 1994) — $X_t = \alpha_t X_{t-1} + \varepsilon_t$ with $E(\alpha_t)=1$, $\alpha_t$ stationary; not rejected by DF tests yet variance grows exponentially (vs. linearly for pure I(1)); shows failing to reject I(1) ≠ the process is I(1).
• Gonzalo-Granger common trends (Gonzalo and Granger 1995) — in a cointegrated system with $m$ variables and rank $r$, the $m-r$ common stochastic trends are $W_t = \alpha_\perp' x_t$ identified by the requirement that equilibrium errors $z_t$ do not Granger-cause $W_t$ at low frequencies; multivariate analogue of Beveridge-Nelson permanent/transitory decomposition.
• "On modelling the long run" (1997) — methodological essay defining "extended memory" ($E(X_{t+h}|I_t) \not\to \text{const}$ as $h \to \infty$); 8-step ECM workflow (Johansen → Gonzalo-Granger → general-to-specific with BIC); I(2) skepticism (unappealing IRFs: WWI shock > WWII shock > Gulf War shock); non-linear ECMs with threshold error-correction terms; model competition philosophy.
• Nonlinear cointegration (Granger and Swanson 1996) — nonlinear error correction models incorporating transaction costs and threshold behavior.
• Power-GARCH (Ding, Granger, and Engle 1993) — generalization of GARCH where $h_t^\delta$ is parameterized; S&P 500 daily data gives $\hat\delta = 1.43$, rejecting both δ=1 and δ=1/2.

Related

• Cointegration
• Spurious Regression
• Granger Causality
• GARCH and BEKK-GARCH
• Robert Engle