Index: Granger 2003 - Spurious Regression and Cointegration

Granger 2003 - Spurious Regression and Cointegration

Routing Summary

This folder covers Clive Granger’s 2003 Nobel Lecture on time series, cointegration and applications, with citation-only background from Yule (1926), Granger & Newbold (1974), Phillips (1986) and Engle & Granger (1987), plus a reproducible Python Monte Carlo. Contains 7 notes spanning integration/stationarity, cointegration and error correction, spurious regression, Granger causality, and forecasting/decision-science methodology.

• Need the source map or key findings? → Granger 2003 - Spurious Regression and Cointegration - Overview
• Need what “integrated” / $I(1)$ means, or the pearls analogy? → Granger 2003 - Econometrics, Integrated Series and the String-of-Pearls Picture
• Need why regressing trending series gives fake significance, the $R^2>DW$ rule, Yule/Granger-Newbold/Phillips? → Granger 2003 - Spurious Regression from Yule to Granger-Newbold
• Need code to demonstrate spurious regression, the Engle-Granger test or an ECM? → Granger 2003 - Spurious Regression Monte Carlo in Python
• Need cointegration, the error-correction model, the Granger representation theorem? → Granger 2003 - Cointegration and the Error-Correction Representation
• Need Granger causality, or why cointegration implies it? → Granger 2003 - Granger Causality and Its Link to Cointegration
• Need forecasting stages, the decision-maker criterion, aggregation? → Granger 2003 - Forecasting, Decision Science and Aggregation

Concept Map

Concept	Note	Type	Depends On	Key Result
Integrated series $I(d)$	Granger 2003 - Econometrics, Integrated Series and the String-of-Pearls Picture	definition	Single Marketing Time Series	${\Delta }^d{x}_t$ stationary; changes/returns closer to stationary (p. 361)
Pearls and magnets analogies	Granger 2003 - Econometrics, Integrated Series and the String-of-Pearls Picture	example	—	smooth series = linked pearls; cointegration = magnetised chains
Cointegration	Granger 2003 - Cointegration and the Error-Correction Representation	definition	$I(d)$	${\mathbf{\beta }}^{\prime }{\mathbf{x}}_t\sim I(0)$; “a surprise when it occurs”
Granger representation theorem	Granger 2003 - Cointegration and the Error-Correction Representation	theorem	cointegration	cointegration ⇔ ECM; common factor; constant-ratio forecasts
Engle-Granger two-step	Granger 2003 - Cointegration and the Error-Correction Representation	algorithm	cointegration	residual ADF test with EG critical values, then ECM
Spurious regression	Granger 2003 - Spurious Regression from Yule to Granger-Newbold	definition	$I(1)$	independent random walks look related
Phillips asymptotics	Granger 2003 - Spurious Regression from Yule to Granger-Newbold	theorem	spurious regression	$t=O_p(\sqrt{T})$, $R^2$ non-degenerate, DW $\to 0$
$R^2>DW$ rule	Granger 2003 - Spurious Regression from Yule to Granger-Newbold	heuristic	DW statistic	flag for spurious levels regressions
Spurious-regression Monte Carlo	Granger 2003 - Spurious Regression Monte Carlo in Python	example	all above	67-90% false rejections in levels, ~5% in differences
Granger causality	Granger 2003 - Granger Causality and Its Link to Cointegration	definition	VAR	precedence + unique information
Toda-Yamamoto causality test	Granger 2003 - Granger Causality and Its Link to Cointegration	algorithm	VAR, $I(d)$	levels VAR with $p+d_{\max }$ lags; Wald test on first $p$ is ${\chi }_p^2$
Yule’s conjunct series	Granger 2003 - Spurious Regression from Yule to Granger-Newbold	definition	—	positive serial correlation; with random or conjunct differences
Cointegration ⇒ causality	Granger 2003 - Granger Causality and Its Link to Cointegration	theorem	ECM	at least one adjustment coefficient nonzero
Decision-maker criterion; forecasting stages	Granger 2003 - Forecasting, Decision Science and Aggregation	concept	—	evaluate analyses by decision usefulness; evaluate past forecasts
Aggregation and limit theorems	Granger 2003 - Forecasting, Decision Science and Aggregation	concept	—	aggregates over ~$10^8$ units should show special properties

Notes

• Granger 2003 - Spurious Regression and Cointegration - Overview — CONTAINS: research question, contribution, 6 key findings, note-set table, full page-by-page Source Map including citation-only sources
• Granger 2003 - Econometrics, Integrated Series and the String-of-Pearls Picture — CONTAINS: opening framing (both laureates econometricians; deterministic variable; probability and Statistics); definition of econometrics by genealogy (p. 360); “internal visualization” instead of figures; string-of-pearls example; data-frequency table; stationarity and $I(d)$ definitions; Box-Jenkins remark; two-chains/magnets example; marketing classification example
• Granger 2003 - Cointegration and the Error-Correction Representation — CONTAINS: formal cointegration definition ($CI(d,b)$, cointegrating rank); 5-part consequences theorem (common factor, ECM, converse, constant-ratio forecasts, causality) with proof sketch; ECM definition with half-life; Sargan/Johansen/Hylleberg/Teräsvirta/Hendry history; users (central banks, Federal Reserve Bank, model builders) and reception; Engle-Granger algorithm (asymptotic -3.34 vs finite-T -3.37 critical value); simulated ECM example; brand-share example
• Granger 2003 - Spurious Regression from Yule to Granger-Newbold — CONTAINS: spurious regression definition; Granger’s p. 363 account; Yule (1926) terms (random vs conjunct series with random or conjunct differences), card-drawn design, 11-term construction, 600-correlation sampling scheme, Series X1 re-run and results table; Granger-Newbold (1974) motivation, Table 1 ($S$ distribution, factor 5.6), full Table 2 (random walk and ARIMA(0,1,1), levels and changes, % $R^2>0.7$), Section 5 recommendations and Sheppard example, G&N-vs-vault comparison table; Phillips (1986) results (all citation only); $R^2>DW$ rule; Phillips theorem with proof idea; levels/differences decision table; 6-step screening algorithm; simulation summary; KPI-vs-media and driver-search examples
• Granger 2003 - Spurious Regression Monte Carlo in Python — CONTAINS: ADEMP table; full runnable script; Experiments 1-5 result tables (levels vs differences; $k$ regressors; Yule correlation shapes; Engle-Granger test; ECM recovery); plotting script and three figures (sample spurious pair, Yule histograms, $\sqrt{T}$ growth of $t$); persistence-matched null procedure
• Granger 2003 - Granger Causality and Its Link to Cointegration — CONTAINS: origin story (Tukey, Morgenstern, Gabor, Wiener); two-component definition and formal/VAR versions; forecasting-consequence theorem; reception quotes; cointegration ⇒ causality theorem with proof sketch and differenced-VAR corollary; VECM joint test and Toda-Yamamoto lag-augmented procedure; nonlinear extension; marketing VAR example
• Granger 2003 - Forecasting, Decision Science and Aggregation — CONTAINS: models-assume-themselves-correct remark (p. 362); Popper (“I do not always agree”, The Logic of Scientific Discovery) and probability; personal detour (AEA Fellow, two department chairs, economics by osmosis, thin theoretical core); decision-maker criterion; uses and forecastability table; 5-stage forecasting algorithm; panels; Amazon scenario model (scale, five authors, fallow land vs European ex-forest land); data variety; aggregation conjecture with formal reading; laureate statistics and table of laureates met (Gabor 1970/1971 discrepancy); reference list table with Anderson/Andersen and Popper 1934/1959 discrepancies; MMM decision example

Sources

• Granger 2003 - Time Series Analysis Cointegration and Applications (Nobel Lecture) — Granger (2003) Nobel Lecture, Les Prix Nobel 2003, pp. 360-366
• Citation only (not in raw/): Yule (1926) JRSS 89(1); Granger & Newbold (1974) J. Econometrics 2(2); Phillips (1986) J. Econometrics 33(3); Engle & Granger (1987) Econometrica 55(2)

See Also

• Multivariate Persistence and Cointegration — marketing-notation cointegration, Johansen test, persistence modelling
• Single Marketing Time Series — stationarity, ARIMA, unit roots
• Empirical Causal Ordering — Granger causality and impulse responses in marketing VARs
• Optimal Marketing Decisions and Forecasting — VAR/ECM forecasting for long horizons under cointegration
• Carryover Effects and Distributed Lags — hysteresis and long-run effects
• Bergmeir Hyndman Koo 2018 - CV for Time Series - Overview — sibling source on time-series cross-validation
• Morris White Crowther 2019 - Simulation Studies (ADEMP) - Overview — simulation-study design