Granger 2003 - Spurious Regression and Cointegration - Overview
Summary
Source: Clive Granger’s Nobel Lecture (8 December 2003), a non-technical account of why economic time series need special methods. Research question: how should one model groups of smooth, integrated series without being fooled by them? Contribution (as recounted): the concept of cointegration — a linear combination of integrated series that is stationary — and its consequences (common factor, error-correction representation, constant-ratio long-run forecasts, implied Granger causality), which explained and resolved the spurious regression problem that Granger and Newbold (1974) had demonstrated by simulation. Key findings for model validation: standard regression inference is invalid for independent integrated series (it “would very often appear to ‘find’ a relationship whereas in fact there was none”, p. 363); many published macro relationships had to be re-examined; the cure is differencing or an error-correction model; and models should be judged by their usefulness to decision makers through forecast evaluation with uncertainty bounds. This vault set adds the citation-only background (Yule 1926, Granger-Newbold 1974, Phillips 1986, Engle-Granger 1987) and a reproducible Python Monte Carlo.
Overview
The lecture (7 pages, no section headings) moves from what econometrics is, through integrated series and cointegration, to spurious regression, the Hendry anecdote, a personal detour, the purpose of economics, forecasting practice, aggregation, Granger causality and closing remarks. Because it is a lecture, the formal content is implicit; the notes below state it formally, clearly separating Granger’s words (quoted, with page) from standard results (labelled as from the literature).
Why it belongs in a model-validation collection: spurious regression is the canonical example of a modelling procedure that produces confident, publishable, wrong findings purely because an assumption (stationarity) fails, with error rates that worsen as data grow. Every analysis of trending marketing data — media-mix models of drifting KPIs, driver analyses on macro series, geo-test counterfactuals assuming stationarity — inherits the risk.
Main Content
Note Set
| Note | Covers |
|---|---|
| Granger 2003 - Econometrics, Integrated Series and the String-of-Pearls Picture | Motivation/setup: econometrics, time series, data frequencies, stationarity vs integration , pearls and magnets pictures |
| Granger 2003 - Cointegration and the Error-Correction Representation | Formal cointegration, Granger representation theorem (5 consequences), ECM, Engle-Granger two-step algorithm, history (Sargan, Johansen, Hendry, Popper) |
| Granger 2003 - Spurious Regression from Yule to Granger-Newbold | Spurious regression definition; Yule (1926) design and results table, Granger-Newbold (1974) Tables 1-2 in full, Phillips (1986) results; rule; decision table; diagnostic algorithm |
| Granger 2003 - Spurious Regression Monte Carlo in Python | Reproducible script; 5 experiments with result tables (size distortion, multiple regressors, Yule shapes, Engle-Granger test, ECM recovery); plotting script with three figures |
| Granger 2003 - Granger Causality and Its Link to Cointegration | Two-component definition, forecasting consequence, reception, cointegration ⇒ causality theorem, nonlinear extension |
| Granger 2003 - Forecasting, Decision Science and Aggregation | Discussion: model purpose, decision-maker criterion, forecastability, forecasting stages, panels, Amazon scenario model, aggregation, closing numbers, reference list |
Key Findings
- Integrated ≠ standard data. Smooth macro series violate the stationarity assumed by standard procedures; their changes/returns are closer to stationary (p. 361). → [[Granger 2003 - Econometrics, Integrated Series and the String-of-Pearls Picture#^def-integrated| definition]]
- Cointegration is a surprise, but common in macro. “Most pairs of integrated series will not have the property” (p. 361). → definition
- Cointegration ⇔ error correction. Cointegrated series can be represented by an ECM, and data generated by an ECM are cointegrated (pp. 361-362). → representation theorem
- Spurious regression. Independent integrated series regressed on each other “very often” show a relationship; editors re-examined accepted papers; the ECM resolves many of the difficulties (p. 363). → definition, Phillips asymptotics, simulation
- Cointegration ⇒ Granger causality in at least one direction (p. 366). → theorem
- Decision value is the yardstick and forecasting needs central forecast, uncertainty bounds and evaluation of past errors (p. 364). → forecast stages
Source Map
The lecture has no numbered sections, theorems, tables or figures; the map is by page and paragraph topic. Every item is captured in the note listed.
| Pages | Content in the lecture | Note |
|---|---|---|
| p. 360 | Opening: both 2003 laureates are “Econometricians”; what the term means; deterministic variable defined; probabilities by the middle of the last millennium → Statistics → Biometrics/Psychometrics/Econometrics | Granger 2003 - Econometrics, Integrated Series and the String-of-Pearls Picture |
| p. 360 | Time series defined via monthly unemployment | Granger 2003 - Econometrics, Integrated Series and the String-of-Pearls Picture |
| p. 360 | ”Internal visualization” instead of a diagram (why the lecture has no figures); string-of-pearls thought experiment (smooth series) | Granger 2003 - Econometrics, Integrated Series and the String-of-Pearls Picture |
| pp. 360-361 | Data frequencies: high-frequency financial (Engle) vs quarterly/annual macro | Granger 2003 - Econometrics, Integrated Series and the String-of-Pearls Picture |
| p. 361 | Smoothness vs stationarity; “integrated” vs “non-stationary”; changes/returns closer to stationary | Granger 2003 - Econometrics, Integrated Series and the String-of-Pearls Picture |
| p. 361 | Box-Jenkins (1970) for single integrated series; missing joint feature | Granger 2003 - Econometrics, Integrated Series and the String-of-Pearls Picture |
| p. 361 | Cointegration defined (difference of integrated series stationary; “properly scaled”) | Granger 2003 - Cointegration and the Error-Correction Representation |
| p. 361 | Two chains thrown separately vs magnetised chains | Granger 2003 - Econometrics, Integrated Series and the String-of-Pearls Picture |
| p. 361 | Linear combination stationary; “a surprise when it occurs”; common in macro | Granger 2003 - Cointegration and the Error-Correction Representation |
| pp. 361-362 | Consequences: common hidden factor; ECM representation; ECM data are cointegrated | Granger 2003 - Cointegration and the Error-Correction Representation |
| p. 362 | ECM invented by Sargan (stochastic growth equations) | Granger 2003 - Cointegration and the Error-Correction Representation |
| p. 362 | Scandinavian collaborators: Johansen, Juselius, Hylleberg (seasonal), Jansen (Bank of Norway model), Teräsvirta (Finland, now Stockholm; nonlinear); all present as Granger’s guests | Granger 2003 - Cointegration and the Error-Correction Representation |
| p. 362 | ”The modern macro economy is large, diffuse, and difficult to define, measure, and control”; purpose of macro models; theorists vs econometricians; “All models simply assume that the model is correct” | Granger 2003 - Forecasting, Decision Science and Aggregation |
| p. 362 | ECMs as popular macro models; users named as central banks, the Federal Reserve Bank and various model builders (policy simulation) | Granger 2003 - Cointegration and the Error-Correction Representation |
| p. 362 | Constant-ratio long-run forecasts; equilibrium caveat | Granger 2003 - Cointegration and the Error-Correction Representation (item 4) |
| p. 362 | Multivariate extension; the name “cointegration”; “quickly picked up”, “numerous citations and applications”; “explain and remove a variety of difficulties”; “missing piece” | Granger 2003 - Cointegration and the Error-Correction Representation |
| p. 363 | Spurious regressions: Granger-Newbold 1974 simulation; re-evaluation of macro work; editors; ECM remedy | Granger 2003 - Spurious Regression from Yule to Granger-Newbold |
| p. 363 | Discovery story: Hendry’s claim, failed disproof, generalisation, proof of ECM representation | Granger 2003 - Cointegration and the Error-Correction Representation |
| p. 363 | ”I do not always agree with” Popper; The Logic of Scientific Discovery (via Hacohen 2000) on discovery; probabilistic description of economics; 1934 coincidences (Popper, Keynes); 1934 vs 1959 reference-list date | Granger 2003 - Forecasting, Decision Science and Aggregation |
| p. 363 | Lecture written at University of Canterbury, NZ (Popper connection) | Granger 2003 - Forecasting, Decision Science and Aggregation (aside, no technical content) |
| pp. 363-364 | Personal detour: AEA Distinguished Fellow; chair of two economics departments; one-third-year of formal training; economics learned by osmosis over ~40 years; “about me, or … the field?”; not the first laureate without formal training; thin core, theory concepts “not necessarily realistic”; hot-bed of ideas | Granger 2003 - Forecasting, Decision Science and Aggregation |
| p. 364 | Economics as decision science; “how will a decision maker find this result useful?” | Granger 2003 - Forecasting, Decision Science and Aggregation |
| p. 364 | Main uses of cointegration models; forecastability ranking | Granger 2003 - Forecasting, Decision Science and Aggregation |
| p. 364 | Forecasting stages: central forecast, uncertainty bounds, evaluation, learning from errors, combination | Granger 2003 - Forecasting, Decision Science and Aggregation |
| p. 364 | Panels of series (Scandinavian inflation) | Granger 2003 - Forecasting, Decision Science and Aggregation |
| pp. 364-365 | Amazon deforestation scenario model: forest larger than the EU, cut rapidly; Granger one of five authors; land cleared for food; contrast with European ex-forest land, fallow within five years | Granger 2003 - Forecasting, Decision Science and Aggregation |
| p. 365 | Variety of data analysed (supermarket pricing experiments, commodities, electricity, sunspots…) | Granger 2003 - Forecasting, Decision Science and Aggregation |
| p. 365 | Aggregation over ~100 million households and limit theorems | Granger 2003 - Forecasting, Decision Science and Aggregation |
| p. 365 | Causality: Princeton cross-spectrum, Tukey, Morgenstern, Gabor, Wiener; two-component definition; forecasting consequence | Granger 2003 - Granger Causality and Its Link to Cointegration |
| p. 366 | ”Granger causation”; pragmatic definition; ridiculous papers | Granger 2003 - Granger Causality and Its Link to Cointegration |
| p. 366 | Cointegration implies causality | Granger 2003 - Granger Causality and Its Link to Cointegration |
| p. 366 | Nonlinear and conditional-distribution generalisations; causality in generalised ECM | Granger 2003 - Granger Causality and Its Link to Cointegration |
| p. 366 | Usefulness of empirical causality studies; money-prices debate | Granger 2003 - Granger Causality and Its Link to Cointegration |
| p. 366 | Econometricians among laureates (8; 15%; 44% this millennium); 21 laureates met (Gabor 1970 [sic; 1971 on p. 365], Noel Baker 1959, Urey 1934, 18 economists); praise of laureates | Granger 2003 - Forecasting, Decision Science and Aggregation |
| p. 366 | Reference list (4 items); discrepancies Anderson/Andersen and Popper 1934/1959 | Granger 2003 - Forecasting, Decision Science and Aggregation |
| citation only | Yule (1926) nonsense correlations: marriages/mortality 0.9512 (1866-1911); harmonic warm-up; random vs conjunct series (random or conjunct differences); card-drawn random numbers; 11-term moving-sum construction; A/B/C 10-term sampling, 600 correlations per type; independent re-run (Series X1); means, SDs and shapes (Tables VIII, IX, XI; Figs. 16-18) | Granger 2003 - Spurious Regression from Yule to Granger-Newbold |
| citation only | Granger & Newbold (1974): motivation (high , low in published work); Table 1 distribution of (mean 4.5, factor 5.6, critical value 11.2; Malinvaud comparison); Table 2 in full (random walks and ARIMA(0,1,1), levels and changes, m=1-5: % rejected, average , corrected , % ); Section 5 conclusions (mis-specification, levels and changes, pre-whitening, Sheppard example, referee point); as later folk rule | Granger 2003 - Spurious Regression from Yule to Granger-Newbold, Granger 2003 - Spurious Regression from Yule to Granger-Newbold, Granger 2003 - Spurious Regression from Yule to Granger-Newbold |
| citation only | Phillips (1986) asymptotic theory | Granger 2003 - Spurious Regression from Yule to Granger-Newbold |
| citation only | Engle & Granger (1987) representation theorem and two-step test | Granger 2003 - Cointegration and the Error-Correction Representation |
| added | Reproducible simulation (Experiments 1-5) and figures: sample spurious pair, Yule’s three histograms, growth of the spurious | Granger 2003 - Spurious Regression Monte Carlo in Python, Granger 2003 - Spurious Regression Monte Carlo in Python, Granger 2003 - Spurious Regression Monte Carlo in Python, Granger 2003 - Spurious Regression Monte Carlo in Python |
| added | Granger-causality testing under cointegration: VECM joint test, Toda-Yamamoto lag-augmented VAR | Granger 2003 - Granger Causality and Its Link to Cointegration |
Examples
Using this note set to vet a trending-series regression
Setup: a weekly KPI and a media series both drift upward over about 100 weeks; a levels regression gives and with DW .
Route through the notes: (1) classify each series as or (integration); (2) the flag fires (rule of thumb); (3) at independent random walks give a median of about 4.6 (Experiment 1), so is no evidence by itself; (4) run the Engle-Granger test and fit an ECM only if the residuals are stationary; (5) judge the final model by Granger’s decision-maker criterion and by evaluating its past forecasts (forecast stages).
Connections
- Existing vault time-series notes this set builds on: Single Marketing Time Series, Multivariate Persistence and Cointegration, Empirical Causal Ordering, Model Testing and Specification, Marketing Time Series Models.
- Same-cluster sources: Bergmeir Hyndman Koo 2018 - CV for Time Series - Overview (when CV is valid for time series), Morris White Crowther 2019 - Simulation Studies (ADEMP) - Overview (simulation-study design used for the Monte Carlo).
- False discovery: Ioannidis 2005 - Why Most Published Findings Are False - Overview, Simmons Nelson Simonsohn 2011 - False-Positive Psychology - Overview, Garden of Forking Paths, Researcher Degrees of Freedom.
- Marketing forecasting and long-run effects: Optimal Marketing Decisions and Forecasting (VAR/ECM for long horizons), Carryover Effects and Distributed Lags (hysteresis, long-run multipliers), Price and Distribution Effects (persistent distribution effects).
- Marketing measurement: Chan Perry 2017 - Challenges in Media Mix Modeling - Overview, Bayesian Media Mix Modeling - Overview, TBR Design Sensitivity and the Stationarity Assumption.
See Also
- Granger 2003 - Spurious Regression from Yule to Granger-Newbold — the core validation lesson
- Granger 2003 - Spurious Regression Monte Carlo in Python — run it yourself
- Breiman 2001 - Statistical Modeling The Two Cultures - Overview — predictive validation as the arbiter
- Out-of-Sample Validation for Time-Series Models — shuffled CV is optimistic for random-walk regressors