Index

An alphabetical subject index of the book’s concepts, named results, and people. Each entry links to the section(s) where the term is defined or plays a central role. “Ch. IX”, “Ch. X” and “Investment Under Uncertainty” (Ch. XIV) refer to the preparatory and capstone chapters; all other links point to sections of the Linear Time Series part and its postscripts. Works cited are collected separately in the Bibliography.

A

• adaptive expectations — Prediction Examples; Money Demand in Hyperinflations; Ch. X

• adjustment cost of capital — Investment Under Uncertainty

• aggregation over time — Aggregation over Time

• annihilation operator \([\,\cdot\,]_+\) — Representation Theory; Partial Fractions; Granger Causality; Exact Linear RE

• anticipative (non-realizable) representation — Explosive Decomposition; Ch. IX; Investment Under Uncertainty

• approximation error formula (Sims) — Seasonality & Approximation; Money Demand in Hyperinflations; Lucas & Whiteman; Exercises

• approximation criterion (Kullback–Leibler / Whittle) — Seasonality & Approximation

• ARMA process (mixed moving average, autoregressive) — Wold ARMA; Signal Extraction; Prediction Examples

• autoregressive process (first-, second-order) — Preliminary Concepts; Spectrum

• autoregressive representation — Linear Prediction; Vector SDEs; Multivariate Prediction

• averaged periodogram (Bartlett, Welch) — FFT Estimation

B

• backward (anticausal) filtering — Orthogonality & Filtering; Solutions

• Bartlett window — Complex Demodulation

• Beveridge–Nelson decomposition — Exercises; Solutions; Explosive Decomposition

• bicoherence — Nonlinear Representations; FFT Estimation

• bilinear process — Nonlinear Representations

• bispectrum (and its estimation) — Nonlinear Representations; FFT Estimation; Complex Demodulation

• Blackman–Tukey estimator — FFT Estimation

• Blanchard, O., and Watson, M. — Bubbles

• Blanchard–Kahn condition — Signal Extraction

• Blaschke factor (root flipping) — Solutions; Interpreting VARs; Exact Linear RE

• bubble, rational — Bubbles

• Burns, A., and Mitchell, W. — Business Cycle Definitions; Index Models

• business cycle — Business Cycle Definitions; Spectrum; Index Models

C

• Cagan model (hyperinflation, portfolio balance) — Rational Expectations; Optimal Prediction; One-Sided Projections; Money Demand in Hyperinflations; Ch. X; Exercises

• Cass–Koopmans optimum growth problem — Ch. IX

• Cauchy–Schwarz inequality — Uncertainty Principle; Preliminary Concepts

• cepstrum — Representation Theory

• certainty equivalence (separation principle) — Investment Under Uncertainty

• chain rule of forecasting — Chain Rule

• characteristic equation and roots — Ch. IX

• coherence (and its estimation) — Cross Spectrum; FFT Estimation; Leading Indicators; Business Cycle Definitions; Complex Demodulation

• companion form (compact notation) — Compact Notation

• complex demodulation — Complex Demodulation

• continuous-time process — Aggregation over Time; Sims’s Formula

• convolution (↔ multiplication of transforms) — Fourier & z-Transforms

• cospectrum — Cross Spectrum

• covariance generating function — Preliminary Concepts; Cross Covariogram; Index Models; Wold ARMA; Signal Extraction; Filtering & Projections

• covariance stationarity (wide-sense) — Preliminary Concepts

• covariogram — Preliminary Concepts; Deriving the MA; Business Cycle Definitions

• cross covariogram — Cross Covariogram

• cross spectrum — Cross Spectrum; Leading Indicators; Complex Demodulation

• cross-equation restrictions — Rational Expectations; Optimal Prediction; Multivariate Prediction; Exact Linear RE; Exercises; Investment Under Uncertainty

• cumulants (higher-order moments) — Nonlinear Representations; FFT Estimation

• cycle (from complex roots) — Preliminary Concepts; Business Cycle Definitions

D

• delta function (generalized function) — Representation Theory; Fourier & z-Transforms

• difference equation, linear — Ch. IX; Introduction

• Dirichlet kernel — Uncertainty Principle; Complex Demodulation

• distributed lag, sum of coefficients \(h(0)\) — Lucas & Whiteman; Solutions

• dominant-player dynamic game — Ch. IX

• DSGE model — Lucas & Whiteman

• duopoly (dynamic Nash equilibrium) — Ch. IX

• dynamic factor model — see index model

• dynamic supply and demand curves — Investment Under Uncertainty; Interpreting VARs; Rational Expectations

E

• Eckstein, Z. — Investment Under Uncertainty

• econometric exogeneity — Granger Causality; Vector SDEs; Money Demand in Hyperinflations

• eigenvalue decomposition — Compact Notation

• energy (of a sequence) — Uncertainty Principle

• errors in variables — Errors in Variables

• Euler equation (and stochastic Euler equation) — Ch. IX; Deriving the MA; Rational Expectations; Investment Under Uncertainty

• exact linear rational expectations models — Exact Linear RE

• expectations hypothesis (term structure) — Ch. X; Multivariate Prediction

• explosive autoregression (decomposition; anticipative representation) — Explosive Decomposition; Exercises; Solutions; Ch. IX

• exponential order (of a sequence) — Ch. IX; Investment Under Uncertainty

• externality (in dynamic equilibrium) — Investment Under Uncertainty

F

• fast Fourier transform (FFT); periodogram estimation — FFT Estimation

• feedback and feedforward parts (of a solution) — Ch. IX; Interpreting VARs; Investment Under Uncertainty

• Fejér kernel — FFT Estimation

• Fibonacci sequence / golden ratio — Ch. IX; Ch. X

• filter — Filter Kit; Slutsky & Kuznets; Spectrum

• filter, low-pass (Lucas’s exponential filter) — Lucas & Whiteman; Uncertainty Principle; Complex Demodulation

• filtering formula (fundamental) — Spectrum; Cross Spectrum

• final form — Money & Income

• first-difference filter \(1-L\) — Filter Kit; Slutsky & Kuznets

• forward filtering — Orthogonality & Filtering; One-Sided Projections

• forward rate — Ch. X

• Fourier transform — Fourier & z-Transforms

• frequency dispersion — Uncertainty Principle

• Friedman, Milton — Prediction Examples; Ch. X

• Frisch, Ragnar — Introduction

• fundamental representation (fundamentalness) — Deriving the MA; Wold MA; Representation Theory; Interpreting VARs

• Futia, Carl — Geometric Leads

G

• gain — Cross Spectrum; Filter Kit; Slutsky & Kuznets

• Gaussianity, tests for — Nonlinear Representations; FFT Estimation

• generalized least squares (consistency of) — Filtering & Projections

• generalized method of moments (GMM) — Solutions

• geometric distributed lag — Prediction Examples; Ch. IX

• geometric distributed lead — Geometric Leads; Seasonal Adjustment

• Geweke, John — Sims’s Formula; Index Models

• Godfrey (bispectrum) — Complex Demodulation

• golden ratio — Ch. IX; Ch. X

• Golden rule (and modified Golden rule) — Ch. IX

• Gordon and Hynes — Investment Under Uncertainty

• Granger, C. W. J.; typical spectral shape — Business Cycle Definitions

• Granger causality (Wiener–Granger) — Granger Causality; Leading Indicators; Money & Income; Filtering & Projections; Errors in Variables; Money Demand in Hyperinflations; Exercises

H

• habit persistence (seasonal) — Seasonality & Approximation

• Hammerstein model — Nonlinear Representations

• Hannan’s inefficient estimator — Cross Spectrum

• Hanning (spectral smoothing) — FFT Estimation

• Hansen–Sargent formula (geometric lead) — Geometric Leads; Seasonal Adjustment; Solutions

• Hayashi, F. (forward filtering) — Orthogonality & Filtering

• Heisenberg bound — Uncertainty Principle

• Hermite polynomials (Hermite chaos) — Nonlinear Representations

• Hilbert space — Representation Theory; Solutions

• Hinich, M. J., and Clay, C. S. — FFT Estimation

• Howrey, E. P. — Slutsky & Kuznets; Compact Notation

I

• ideal bandpass filter — Spectrum

• identification (and underidentification) — Money Demand in Hyperinflations; Exact Linear RE; Investment Under Uncertainty

• index model (unobservable / dynamic-factor) — Index Models

• inflation tax; revenue-maximizing inflation — Money Demand in Hyperinflations

• innovation accounting (impulse responses, variance decompositions) — Interpreting VARs; Errors in Variables

• innovation (one-step-ahead forecast error) — Representation Theory; Linear Prediction; Optimal Filtering

• instrumental variables estimation — Orthogonality & Filtering

• interrelated factor demand — Ch. IX; Interpreting VARs

• inverse optimal control problem — Ch. IX; Investment Under Uncertainty; Exercises

• inverse optimal predictor problem — Ch. IX; Exercises

• inverse z-transform — Inverse z-Transform; Partial Fractions

• investment under uncertainty — Investment Under Uncertainty

• isometric isomorphism (\(\ell_2 \leftrightarrow L_2\)) — Fourier & z-Transforms

K

• Kalman filter (recursive projection) — Ch. X; Interpreting VARs; Exact Linear RE

• Kalman gain; Riccati equation — Ch. X; Investment Under Uncertainty

• Kolmogorov, Andrei; Kolmogorov formula — Introduction; Linear Prediction; Representation Theory; Optimal Filtering

• Koopmans, T. C. — Index Models

• Kuznets, Simon; Kuznets’s transformations; long swings — Slutsky & Kuznets

• Kydland, F., and Prescott, E. — Index Models

L

• lag operator \(L\) — Ch. IX

• Laurent expansion — Partial Fractions; Exact Linear RE; Solutions

• law of iterated projections — Ch. X; Chain Rule; Money & Income; One-Sided Projections

• leading indicator — Leading Indicators

• leakage (spectral) — FFT Estimation

• leaning against the wind — Money & Income

• learning by doing — Ch. IX

• likelihood-ratio test (overfitting) — Money Demand in Hyperinflations

• linear least squares projection — Ch. X; Representation Theory; Linear Prediction

• linearly deterministic / indeterministic process — Representation Theory; Linear Prediction

• Lucas aggregate supply curve — Exercises

• Lucas critique — Ch. X; Ch. IX; Lucas’s Critique (Ch. XIV §3); Lucas & Whiteman

• Lucas’s two illustrations of the quantity theory — Lucas & Whiteman

• Lucas–Prescott model — Investment Under Uncertainty

M

• martingale — Ch. X; Bubbles; Explosive Decomposition; Seasonality & Approximation

• maximum likelihood estimation — Exact Linear RE; Seasonality & Approximation; Money Demand in Hyperinflations

• mean lag — Cross Spectrum

• measurement error — Errors in Variables

• Meiselman error-learning model — Ch. X

• minimum phase condition — Deriving the MA

• misspecified model (approximation) — Seasonality & Approximation; Money Demand in Hyperinflations; Lucas & Whiteman; Seasonal Adjustment

• money illusion — Ch. X

• money–income causality; mongrel coefficients — Money & Income; Money Demand in Hyperinflations

• moving average representation — Preliminary Concepts; Linear Prediction; Representation Theory

• moving (evolutionary) spectrum and cross spectrum — Complex Demodulation

• Mundell–Tobin effect — Lucas & Whiteman

• Muth, John — Signal Extraction; Ch. X; Ch. IX; Partial Fractions

N

• NBER minor / major cycle — Leading Indicators; Business Cycle Definitions

• nonanticipative representation — Ch. IX; Investment Under Uncertainty

• nonfundamental representation — Deriving the MA; Interpreting VARs; Exact Linear RE

• nonlinear Wold theorem — Nonlinear Representations

• nonnegative definite sequence — Preliminary Concepts; Deriving the MA

• normal equations — Ch. X

• Nyquist frequency — Uncertainty Principle

O

• one-sided projection — Cross Spectrum; Granger Causality; Filtering & Projections; One-Sided Projections; Optimal Filtering

• optimal filtering (Wiener–Kolmogorov) — Optimal Filtering

• optimal prediction (compact / state-space) — Optimal Prediction

• orthogonality principle — Ch. X; Representation Theory

• oscillatory covariogram — Preliminary Concepts; Compact Notation

• outer (minimum-phase) function — Solutions; Deriving the MA

P

• Parseval’s relation — Fourier & z-Transforms

• partial fractions — Ch. IX; Partial Fractions; Granger Causality

• Parzen window — Complex Demodulation

• Pascal (Solow) lag distribution — Ch. IX; Exercises

• periodic model — Seasonality & Approximation

• periodogram (inconsistency; resolution–variance trade-off) — FFT Estimation

• permanent income — Ch. X; Prediction Examples; Optimal Filtering; Ch. IX

• phase — Cross Spectrum; Filter Kit; Leading Indicators

• phase lead — Leading Indicators; Complex Demodulation

• Phillips curve (Lucas’s) — Ch. X; Exercises

• Pigouvian (corrective) tax — Investment Under Uncertainty

• Poisson kernel — Uncertainty Principle

• pole (order of a pole) — Inverse z-Transform; Partial Fractions

• policy invariance, failure of — Lucas & Whiteman; Ch. IX; Investment Under Uncertainty

• polyspectra — Nonlinear Representations

• prediction-error variance — Representation Theory; Linear Prediction

• Prescott, Edward — Index Models; Investment Under Uncertainty

Q

• quadrature spectrum — Cross Spectrum

• quantity theory of money — Lucas & Whiteman

• quasi-differencing — Solutions

R

• random walk — Money Demand in Hyperinflations; Explosive Decomposition; Exercises; Solutions; Seasonal Adjustment

• rational expectations — Introduction; Prediction Examples; Rational Expectations; Exact Linear RE; Investment Under Uncertainty

• rational expectations equilibrium — Investment Under Uncertainty

• realization — Preliminary Concepts

• reciprocal pair of roots — Deriving the MA; Wold MA; Ch. IX

• recursive projection — Ch. X

• remodulation — Complex Demodulation

• residue; residue theorem — Inverse z-Transform; Partial Fractions; Ch. IX

• Riesz–Fischer theorem — Fourier & z-Transforms

• Romer, Paul — Investment Under Uncertainty

S

• saddle path — Ch. IX

• Samuelson multiplier–accelerator model — Ch. IX

• Samuelson, Paul (properly anticipated prices) — Ch. X

• Sargent, T. J., and Sims, C. A. (business cycle modeling) — Index Models

• Sargent, T. J.; interest rates in the nineteen-fifties — Complex Demodulation

• seasonal adjustment — Seasonal Adjustment; Seasonality & Approximation; Business Cycle Definitions; Complex Demodulation

• seasonal filter — Filter Kit; Seasonal Adjustment

• Shiller, Robert — Chain Rule; One-Sided Projections

• signal extraction — Ch. X; Signal Extraction; Errors in Variables; Exercises; Solutions

• Sims, Christopher A. — Granger Causality; Money & Income; Leading Indicators; Aggregation over Time; Sims’s Formula; Seasonality & Approximation; Interpreting VARs; Money Demand in Hyperinflations; Lucas & Whiteman

• Sims’s approximation-error formula — Exercises; Solutions; Seasonality & Approximation; Money Demand in Hyperinflations; Lucas & Whiteman

• Sims’s formula (discrete/continuous-time aggregation) — Aggregation over Time; Sims’s Formula

• Sims’s theorem (Granger causality ↔ one-sidedness) — Granger Causality; Leading Indicators

• Slutsky effect (spurious cycle) — Slutsky & Kuznets

• Slutsky, Eugen — Introduction; Slutsky & Kuznets

• social planning problem (and equilibrium–optimality) — Investment Under Uncertainty

• spectral density matrix — Vector SDEs; Compact Notation; Index Models; Granger Causality

• spectral factorization — Wold MA; Representation Theory; Errors in Variables

• spectral peak — Spectrum; Business Cycle Definitions

• spectral window (kernel) — FFT Estimation

• spectrum (spectral density; estimation) — Spectrum; FFT Estimation; Business Cycle Definitions; Representation Theory

• St. Louis (Andersen–Jordan) equation — Money & Income

• stable and unstable roots — Ch. IX; Interpreting VARs; Explosive Decomposition; Investment Under Uncertainty; Exercises

• state-space representation — Lucas & Whiteman; Interpreting VARs; Exact Linear RE; Nonlinear Representations

• stochastic Euler equation — Investment Under Uncertainty

• stochastic process — Introduction; Preliminary Concepts

T

• Taylor, John B. — Investment Under Uncertainty

• term structure of interest rates — Ch. X; Multivariate Prediction

• Theil’s specification (omitted-variable) theorem — Money & Income; Sims’s Formula

• Tiao–Grupe formula — Seasonality & Approximation

• time to build — Ch. IX

• time-varying (drifting-coefficient) VAR — Lucas & Whiteman; Complex Demodulation

• time–frequency trade-off (uncertainty principle) — Uncertainty Principle; Complex Demodulation

• Toeplitz matrix — Solutions

• transfer function \(h(e^{-i\omega})\) — Lucas & Whiteman; Seasonal Adjustment; Nonlinear Representations; Money Demand in Hyperinflations

• transversality condition — Ch. IX; Bubbles; Investment Under Uncertainty

• triangular (block-triangular) representation — Granger Causality; Money Demand in Hyperinflations; Interpreting VARs

• two-sided projection — Cross Spectrum; Granger Causality; Filtering & Projections; Errors in Variables

U

• uncertainty principle — Uncertainty Principle

• unit circle (sorting roots by) — Wold MA; Ch. IX

• unit root — Solutions; Explosive Decomposition

V

• variance decomposition by frequency — Spectrum

• vector autoregression — Introduction; Multivariate Prediction; Interpreting VARs

• vector moving average representation — Vector SDEs; Granger Causality; Exact Linear RE

• vector stochastic difference equation — Vector SDEs; Compact Notation

• Volterra series and kernels — Nonlinear Representations

W

• Wallace–Sargent value — Money Demand in Hyperinflations

• white noise — Preliminary Concepts

• Whiteman, Charles H. — Lucas & Whiteman

• Whittle, Peter; Whittle’s spectral factorization — Representation Theory; Linear Prediction; Optimal Filtering

• Wiener cascade — Nonlinear Representations

• Wiener filter — Solutions

• Wiener, Norbert — Introduction; Linear Prediction; Granger Causality

• Wiener–Itô representation — Nonlinear Representations

• Wiener–Kolmogorov prediction formula — Linear Prediction; Prediction Examples; Signal Extraction; Multivariate Prediction; Optimal Filtering

• Wold, Herman; Wold decomposition (theorem, representation) — Representation Theory; Linear Prediction; Wold MA; Wold ARMA; Chain Rule

Y

• yield curve — Ch. X

• Yule–Walker equations — Preliminary Concepts; Compact Notation; One-Sided Projections

Z

• z-transform — Fourier & z-Transforms; Inverse z-Transform; Vector SDEs