Nobel Committee (2003) Time-Series Econometrics: Cointegration and Autoregressive Conditional Heteroskedasticity

Summary

The Royal Swedish Academy of Sciences' scientific background paper for the 2003 Nobel Prize in Economics (Clive Granger and Robert Engle) provides an authoritative pedagogical survey of two pillars of modern time-series econometrics. The cointegration half traces the path from the spurious regression problem through the Granger Representation Theorem to the Engle-Granger two-step estimator and Johansen's maximum likelihood estimator (MLE), with extensions (seasonal, multicointegration, threshold cointegration) and a purchasing power parity (PPP) application. The autoregressive conditional heteroskedasticity (ARCH) half covers Engle's original ARCH model, generalized ARCH (GARCH), ARCH-in-mean, multivariate GARCH (vech, BEKK, factor-ARCH, DCC), the news impact curve, EGARCH, power-GARCH, stochastic volatility, autoregressive conditional duration (ACD), and value-at-risk applications.

Key Claims

• Spurious regression is the starting point. Granger and Newbold (1974) showed that ordinary least squares (OLS) on independent random walks produces systematically significant t-statistics and high $R^2$ with strongly autocorrelated residuals. This pathology, given asymptotic foundations by Phillips (1986), motivated the concept of cointegration.
• Superconsistency. Stock (1987) showed the OLS estimator of the cointegrating vector $\hat\beta$ converges at rate $T^{-1}$ (instead of the usual $T^{-1/2}$). This makes the Engle-Granger two-step feasible: fix $\hat\beta$, then estimate $(\alpha, \Gamma)$ by ML $\to$ the second-stage estimators are consistent and asymptotically normal.
• Granger Representation Theorem. First formulated in Granger and Weiss (1983) and proved rigorously in Engle and Granger (1987): a bivariate I(1) system is cointegrated if and only if it has an error-correction representation. The ECM parameter $\alpha_1$ or $\alpha_2$ must be nonzero — the system always pulls back toward equilibrium.
• Johansen as second generation. Johansen (1988, 1991) derived the MLE of the cointegrating space via reduced-rank regression and sequential likelihood-ratio (LR) tests for $r$. This is "second generation" because it builds directly on ML rather than two-step OLS.
• ARCH (Engle 1982). $h_t = \alpha_0 + \sum\alpha_j\varepsilon^2_{t-j}$. Includes ML estimation theory, conditions for consistency and asymptotic normality, and a Lagrange multiplier test for no-ARCH.
• GARCH (Bollerslev 1986). Parsimonious extension with lagged $h_t$ terms; GARCH(1,1) overwhelmingly dominates in practice. Stationarity condition $\alpha_1+\beta_1<1$. S&P 500 example: $\hat{h}_t = 2\times10^{-6} + 0.091\varepsilon^2_{t-1} + 0.899h_{t-1}$; half-life 6 days; $\mathrm{VaR}_{0.99}$ ranges $12,400 (calm) to $61,500 (turbulent).
• ARCH-in-mean (Engle, Lilien, Robins 1987). $r_t = \beta + \delta h_t^{1/2} + \varepsilon_t$; expected excess return is a function of conditional risk. First link between ARCH and asset pricing; applied to 6-month US T-bill excess returns.
• Multivariate GARCH. vech-GARCH (BEW 1988): $\text{vech}(H_t) = \alpha + A\cdot\text{vech}(\varepsilon\varepsilon') + B\cdot\text{vech}(H_{t-1})$; capital asset pricing model (CAPM) betas are time-varying. Factor-ARCH (Engle-Ng-Rothschild 1990): $k \ll n$ common volatility factors. BEKK (Engle-Kroner 1995): positive definite by construction. Dynamic conditional correlation (DCC; Engle 2002a): time-varying correlations extending constant conditional correlation (CCC; Bollerslev 1990).
• Asymmetric and nonlinear GARCH. News impact curve (Engle-Ng 1993): positive and negative shocks of equal size need not affect $h_t$ equally. Exponential GARCH (EGARCH; Nelson 1991): log-parameterization; no positivity constraints. Power-GARCH (Ding-Granger-Engle 1993): $h_t^\delta$ with $\delta$ estimated; S&P 500 gives $\hat\delta=1.43$.

Concepts Introduced or Extended

• Cointegration — spurious regression origins; superconsistency; Engle-Granger two-step; extensions (seasonal, multicointegration, threshold)
• Spurious Regression — Granger-Newbold result; Phillips asymptotics
• GARCH and BEKK-GARCH — ARCH-M; vech multivariate; factor-ARCH; IGARCH/EWMA; news impact curve; EGARCH; power-GARCH; DCC; stochastic volatility
• Value at Risk — conditional VaR; GARCH-based estimation; IGARCH/EWMA; CAViaR
• Stochastic Volatility — Taylor (1982) model; latent log-variance

Entities Mentioned

• Clive Granger
• Robert Engle

Quotes

"Clive Granger can be credited with this change. He has shown that macroeconomic models containing nonstationary stochastic variables can be constructed in such a way that the results are both statistically sound and economically meaningful." (p. 2)

"The literature is wholly devoid of earlier work with a similar idea." (p. 14, on ARCH conditional variance)

My Take

This is an authoritative secondary source — the Nobel Committee's own distillation of why these contributions matter — rather than an original research paper. Its pedagogical clarity is exceptional. It is particularly useful as a bridge between the technical papers (Engle 1982, Granger-Newbold 1974, Johansen 1991) and the wiki's concept pages, especially for the ARCH and cointegration histories. One gap: the paper focuses on the original contributions and misses later Bayesian developments (no mention of Bauwens, Villani, Warne).