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183

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Abraham, B.

Ali, M.M.

Amemiya, T.

Anderson, B.D.O.

Ansley, C.F.

Arato, M.

Astrom, K.J.

Balestra, P.

Beach, C.M.

Bertsekas, D.P.

Box, G.E.P.

Carvalho, J.L.

Chow, G.C.

Cramer, J.S.

Deist1er, M.

Dhrymes, P.J.

Domowitz, I.

Duncan, D.B.

Durbin, J.

Friedman, A.

Fuller, W.A.

Godfrey, L.G.

Goldberg, S.

Goodwin, G.C.

Gooijer, J.G. de

Grether, D.M.

AUTHOR INDEX

93, 177

7, 183

8, 131, 132, 137, 177

56, 74, 76, 177

2, 8, 11, 12, 25, 34, 47, 51, 54, 59, 60, 177

180

2, 25, 177

56, 64, 74, 76, 177

7, 24, 25, 26, 177

11, 177

68, 76, 177

20, 33, 36, 57, 172, 177, 180

181

56, 62, 74, 76, 134, 178

153, 178

3, 56, 76, 78, 79, 179

133, 178

171, 172, 183

3, 72, 178

8, 19, 137, 178

42, 178

131, 132, 137, 177

5, 159, 160, 161, 170-175, 178

98, 178

56, 74, 76, 178

8, 25, 178

181

186

Griffiths, W.E.

Gupta, Y.P.

Hamilton, J.D.

Hannan, E.J.

Harvey, A.C.

Hatanaka, M.

Hill, R.C.

Horn, S.D.

Jenkins, G.M.

Jones, R.H.

Judge, G.G.

Kailath, T.

Kalman, R.E.

Kapteyn, A.

Kashyap, A.K.

Kedem, G.

Kiviet, J.F.

Klein, L.R.

Kmenta, J.

Knottnerus, P.

Kohn, R.

Koyck, L.M.

Ledo1ter, J.

Lee, T.C.

Levinson, N.

Liviatan, N.

Ljung, G.M.

179

131, 132, 178

95, 179

3, 56, 76, 78, 79, 179

2, 3, 8, 55-57, 59, 66, 72, 73, 75, 85

88-93, 98, 109, 114, 117, 123, 124, 131,

134, 137, 138, 143, 158, 179, 181

137, 141, 179

179

3, 73, 178

20, 33, 57, 172, 177

123, 179

100, 130, 131, 152, 179

56, 67, 76, 124, 179

56, 67, 74, 76, 179

3, 97, 98, 100, 107, 108, 110, 183

4, 159, 160, 170, 174, 181

54, 181

113, 175, 179

131, 132, 138, 148, 152, 180

130, 139, 152, 181

4, 159, 160, 164, 180

2, 34, 180

131, 132, 134, 149, 180

93, 177

179

8, 19, 180

130, 180

33, 36, 180

MacKinnon, J.G.

Magnus, J .R.

McAvinchey, I.D.

McLeod, A. I.

Me1ard, G.

Mentz, R.P.

Moore, J.B.

Ner1ove, M.

Neudecker, H.

Oberhofer, W.

Palm, F.C.

Pesaran, M.H.

Phadke, M.S.

Phillips, G.D.A.

Pierse, R.G.

Porter, R.D.

Richardson, S.M.

Sargan, J.D.

Savin, N.E.

Schmidt, P.

Shaman, P.

Shilov, G.E.

Sin, K.S.

Sneek, J.M.

Spanos, A.

Steyn, I.J.

Stoer, J.

Theil, H.

Thursby, J.G.

11, 177

67, 110, 180

109, 143, 179

2, 34, 37, 180

55, 180

27, 28, 180

56, 74, 76, 177

27, 28, 128, 181

67, 180

130, 139, 181

170, 181

7,181

54, 181

187

2, 8, 55-57, 59, 75, 85, 88-93, 124, 179,181

123, 179

4, 159, 160, 170, 174, 181

97, 181

159, 161, 181

97, 159, 181, 182

139, 161, 182

8, 182

42, 182

56, 74, 76, 178

170, 181

62, 182

85, 182

18, 182

12, 73, 116, 137, 156, 182

4, 159-168, 170-174, 182

188

Tiao, G.C.

Wansbeek, T.J.

White, H.

White, K.J.

Zinde-Wa1sh, V.

7, 183

3, 97, 98, 100, 107, 108, 110, 183

171, 172, 183

97, 159, 181, 182

2, 8, 38, 183

SUBJECT INDEX

absolute convergence adaptive expectations addition rule adjustments angle Ansley's algorithm approximate method autocorre1ated disturbances,

general

autoregressive (AR) process, general estimation,

dynamic models with missing observations

stationarity conditions tests

autoregressive-moving average (ARMA) process, general Ansley's algorithm autocovariance matrix dynamic models GLS recursions GLS transformation state space model tests

moving average (MA) process, general Ansley's algorithm GLS recursions GLS transformation Koyck transformation ML estimation state space model

autocovariances, general AR process ARMA process MA process

autocovariance matrix, general AR process and misssing data ARMA process MA process

backward shift operator Banach space band matrix bandwidth basis of a linear space

149 128, 134 42 98, 127, 129, 138, 143 43 8, 51, 54 56, 88, 93

1, 4, 5, 97, 108, 112, 133, 159, 161, 162, 165, 168-171, 174

3,7,19,40,57,65

137, 141, 146 97, 98, 100, 101, 107-110 124 112, 113, 119, 120, 159-167, 170, 172-175

2-9, 18-20, 22, 55, 56, 59, 127 51,52 32, 38 137-140, 143, 148, 152 47, 50 38, 40-42 66, 67, 85, 88-90, 123 160, 172, 173, 175

2, 7-9, 23, 37, 38, 47 51-54 47 22, 24-27, 29 131, 134 145 55, 56, 88, 93

52, 172 99, 109 20, 33, 34, 41 26

1, 2, 5, 7-9, 52, 54, 88, 124, 137 107, 108 32, 38, 42, 53, 55 23, 25, 27

33, 128 see space see matrix 51, 100, 101 12, 14, 16, 17

190

Bayesian interpretation Berndt, Hall, Hall, and Hausman

algorithm best linear unbiased estimator bias boundary conditions Box-Jenkins equations

Cauchy product Cauchy-Schwarz inequality Cauchy sequence chi-square distribution (X2) Cho1esky decomposition Cho1esky root Cochrane-Orcutt procedure cofactor complex valued conditional expectations conditional normal distribution conditional variances conjugate complex consistent

convergence of iterations correlation

correlation coefficient cosine (cos) covariance,

general covariance stationarity

covariance matrix

Cramer-Rao inequality

degrees of freedom De Moivre's theorem density function dependence of tests derivative determinant (1.1) difference equation differential operator (D) distributed lag model disturbance double precision dual problem Durbin's h-test Durbin's S-test Durbin-Watson test dynamic models

efficiency eigenvalue error covariance matrix error process

81

158 60, 131 28, 33

149 5, 6 43

62,

32,

64, 67, 68

36, 37, 44, 45

112, 114, 116, 162, 171 8, 10, 19, 47, 51-54, 59, 144 9, 25 109, 130, 162 23 30, 43, 49, 150, 151 73-75 I, 55, 60 63, 64 125 110, 127, 129-134, 136-142, 144, 148, 151, 152, 165, 172, 175 130, 139, 147 128, 130; see also autocorre1ated disturbances 153, 166, 168 28, 30, 31, 43, 49, 150, 151, 154

147, 154; see also autocovariances 9 10, 59, 61, 115, 124, 130, 132, 142, 144, 155, 171; see also autocovariance matrix I, 4, 5, 6, 81, 127, 143, 153, 156

161 30, 150 57, 58, 82, 85 163 110, 111, 114-117, 119, 121, 141-147, 153 8, II, 12, 16, 21-23, 40-42, 47, 51, 54, 58-60, 92, 108, 133 27, 30, 32, 36 114-116, 142, 143, 154-158 4, 127, 129 see auto correlated disturbances 88, 93 8,12 173,174 162, 163, 165, 168, 170, 174, 175 97, 159, 163, 164, 170, 173, 174 127, 138, 148, 151

110, 127, 129-133, 137-138, 140-144, 147, 151 12, 125 56, 64, 67, 68, 78, 81, 87, 88 see autocorre1ated disturbances

error term errors in variables error variance estimation error Euclidean distance Euclidean space exogenous

first order condition flow variable forecasts forward shift operator F-test functional form

Gaussian noise Gauss-Newton algorithm generalized least squares (GLS) geometrically declining lag

coefficients geometric derivation geometric distributed lag geometric interpretation geometric series Gram-Schmidt orthogonalization grid (search)

Hessian heteroskedasticity consistent Hilbert space homogeneous hyperparallelepiped hyperplane hypothesis,

general null hypothesis (HO)

idempotent identity matrix imaginary value inconsistent independent,

general linearly stochastically

independently and identically normally distributed (iid)

induction inefficient information matrix initial estimate initial matrix initial values inner product inner product space innovations

67, 173 131 63, 93-95 62, 69 12 see space 98, 172

110, 157 94 56, 57 89 117, 122, 161, 170, 172, 175 159, 160; see also misspecification

83 4, 6, 137, 138, 143, 146-148 3, 7-8, 55, 73, 86, 90, 99, 109, 137, 174-175

127, 128 55, 67, 73 127, 148 1, 21, 55, 61, 64, 70, 79, 153, 156 149 6, 8, 14 111, 132, 133, 151, 167

see matrix 172 see space 27, 32, 36 21, 22 61

161, 173 112, 114, 116, 119, 161-163, 171, 175; see also tests

see matrix see matrix 174; see also complex valued 120, 130, 165, 169

13, 22, 65, 81, 158, 169, 170 13 13, 57, 61, 71, 83

22, 29, 32, 85, 92, 98, 164 see mathematical induction 139 see matrix 56, 73, 81, 130 124 67, 85, 86, 138, 141, 143, 147 12, 43, 153, 154, 156 see space 68, 70, 75, 82, 103

192

insignificant instrumental variables (IV) iterative procedure

Jacobian

joint distribution joint significance

Kalman filter equations, general derivations likelihood function missing observations prediction intervals

Kalman gain Kalman matrix Kalman regression equation Koyck equations Koyck model Koyck transformation Kronecker product(@) Kronecker delta (&tj)

lagged dependent variable lag polynomial Lagrange multiplier (LM) test,

general adjusted for missing data modified (MLM)

lag structure Laplace's expansion theorem least squares estimation,

nonlinear least squares estimation

ordinary least squares (OLS), general, OLS estimation

OLS residuals recursive OLS estimation

least squares sense least squares solution length Levinson-Durbin (LD) algorithm likelihood function,

general Ansley's algorithm dynamic models missing observations models with ARMA disturbances multivariate distribution

likelihood ratio (LR) test

linear least squares estimate (LLSE)

linear models

112, 113, 161, 165, 170, 173 130, 151, 152 130, 139, 147, 151, 158

2, 11, 32, 40-42, 58, 82, 92, 108, 117-119, 133, 142 57 113, 122

1-4, 6, 8, 55, 56, 61, 64, 65, 81, 82, 98 67, 70, 72, 75, 78 85, 86, 92, 93 123, 124 93 3, 70, 72, 92 see matrix 80 132, 134 149 4, 128, 152 11, 12, 42, 87 40, 65

137, 148, 160, 173-175 see polynomial

4, 98, 114, 115, 172 120, 123 113, 117-120, 122, 123, 163, 175 148, 151 12

12, 139, 151

1, 99, 139, 142, 145, 164 4, 7, 8, 11, 26, 109, 129-136, 141, 143, 144, 146, 165, 168, 169, 171 109, 113, 118, 122, 133, 135, 163, 165, 172 66 62, 67, 79 14, 104, 155 see norm 19, 20, 38

2, 9, 11, 12, 55, 56, 154, 158 25, 51 131, 142, 146 110, 111, 113-114, 116, 118, 124 82-85, 90, 92 57-59 4, 97, 107, 108, 112, 113, 124, 162, 163, 165, 169, 172, 173

67; see also least squares estimation 1

linear unbiased estimator linear vector space

Markov scheme mathematical induction matrix.

Hessian idempotent identity matrix information matrix inverse Kalman matrix lower triangular transformation

matrix nonsingular partitioned regression matrix singular Toepli tz matrix

maximum likelihood (ML)

measurement equation measurement noise metric space minimum error variance minimum variance estimator missing observations

misspecification (MS) Monte Carlo experiments

moving average (MA) process multiple correlation

coefficient (R) multiplication rule multiplicity multivariate analysis

Newton-Raphson algorithm nonlinear equations nonlinear least squares

estimation nonlinear regression nonlinear restrictions nonnegative definite nonstationarity norm (11.11) normal distribution normal equations

null hypothesis (HO) numerical (in)stabi1ity

one step ahead prediction error one step ahead predictor ordered hypotheses ordinary least squares (OLS)

67 see space

1. 97. 124. 130 23. 67. 89

142 116 10 142. 157 8. 18. 21. 25. 31. 36. 144. 157 61-64. 155

see transformation 9. 10, 12, 13, 21. 31, 61 31, 36. 60 69 73, 88, 158 9. 19. 27 2. 8, 10, 11, 55, 56, 74, 90, 92, 93, 97, 108, 110-112, 132, 133, 138, 146-148, 173 65 65, 67, 84, 86 see space 63 60, 64, 81 3, 97, 98, 100, 101, 108, 110, 112, 113, 118, 119, 120 4, 159, 170, 171

193

4, 56, 88, 93, 108, 162-164, 166, 167, 170, 171 see auto correlated disturbances

153, 156, 157 42 30, 48, 49 55-57, 60, 64, 80-82, 95

158 131, 134

see least squares estimation 139 162, 164, 165, 168, 170 124 20, 38 12-15, 17, 21, 41, 43, 44, 153-156 I, 9, 12, 22, 57, 63-65, 75 14, 27, 45, 61, 69, 70, 73, 80, 104, 132, 155,169 see hypothesis 18, 20, 21, 38

68, 80, 82, 88, 91-93, 124 73 160 see least squares estimation

194

orthogonal orthogonal remainder orthonormal orthonormal basis orthonorma1ization

paradox partial adjustment parti tioned perpendicular polynomial,

characteristic lag polynomial

positive definite positive semidefinite posterior power powerful Prais-Winsten procedure predetermined prediction prediction interval prediction stage prior probability limit (p1im) projection Pythagorean illustration Pythagorean theorem

quadratic equation quadratic form

R2 random walk rank real number field regressand regression model regression specification error

test (RESET) regressor

regularity conditions remainder residuals,

general OLS residuals recursive

residual vector restrictions Riccati equation robust roots of

characteristic polynomials lag polynomials

rounding errors

12, 14, 53, 71, 76, 78, 61, 69, 71, 80, 81, 83, 39, 40 14, 16, 17 8, 13, 14

120 129 see matrix 13, 21, 41, 103

125 32, 41, 57, 88, 152 54, 73, 88 67, 155 81 98, 120, 123, 165, 169 161, 164 97, 108, 143 115, 141, 147, 170 93,94 56, 57, 93, 94 67 67,81

83, 104-106, 103, 155

135, 136, 165, 166, 168-170 13, 16, 39, 41, 61, 76, 103, 155 6 4,6,17,127,153,156

132, 136 9, 60

153, 156, 157 66 116 42 80 19, 32, 41, 47, 55, 56

4, 161, 163, 170, 171, 174, 175

154, 155

71, 80, 83, 141, 144, 146, 147, 157, 160, 170, 171 63, 154 139; see also orthogonal remainder

133, 137, 139, 151, 165, 166, 170, 175 see least squares estimation 91 60, 143, 154 139, 171 72 161, 171, 174

27, 30, 48, 49, 125 37,57,88,149 38, 57

sample, size small

scalar, general product variable

seasonal, autocorrelation pattern process

seemingly unrelated regression equations (SURE)

serial correlation significance level significant simulation sine (sin) singular Slutzky's theorem space,

general

Banach space Euclidean space Hilbert space inner product space linear vector space metric space subspace

spectral analysis square root algorithm standard deviation starting values state space model state vector stationarity,

general conditions covariance

stationary steady state solution stochastic stochastic error variable subspace supply function system equation system noise

Taylor series expansion t-distribution tests,

general procedure statistic strategy

time varying parameters

98, 164, 165 138, 143, 160, 174, 175

84, 88, 90 43 1, 72

164, 166, 173 5, 172 41

7, 9, 10, 12, 18

195

see auto correlated disturbances 113, 163, 175 112, 113, 159, 163 109 28, 30, 31, 49, 150, 151 see matrix 165

1, 12-14, 21, 42, 55, 61, 68, 69, 76, 104, 153, 155 43 1, 43, 156 43 43 12, 43 13 13, 16, 17, 39, 41, 53, 103, 104 38 93, 124 12 3, 93; see also initial values 2, 55, 65-67, 73, 74, 76, 85, 86, 92, 93, 123 56, 65

85, 87, 125 98, 124, 125, 148 9 22, 32, 55, 59, 90, 98 147 12, 13, 55, 104, 153, 154, 156 68 see space 128 65, 89 65

4, 122, 138-140, 143, 145, 151, 153, 157 94; see also t-test

112, 159, 161, 163, 165, 166, 171-173 97, 164, 165, 168, 173, 174 112-115, 159, 161, 165, 170, 171, 173, 174 1, 159, 160 65, 82

196

Toeplitz matrix trace (tr) transformation,

general data first order autocorrelation transformation matrix,

general lower triangular

transition matrix trend trigonometric formulae truncation parameter truncation remainder t-test two step estimator

unbiased unit circle unit vector univariate update stage

variance ratio vec(.) vector function vector space volume (V)

Wa1d test white noise

Yule-Walker equations

zero vector zig-zag procedure

see matrix 63, 64, 67, 155, 156

7, 50, 58, 82, 92, 101, 109, 118, 174, 175 7, 26, 47, 49, 52, 97, 103 1, 97, 133, 161, 169

8, 11, 18, 19, 24, 32, 33, 38, 42, 50, 91 10, 15, 16, 20, 40, 47, 51, 54, 90, 100, 102, 109, 144 125 147 49 172 132, 148, 149 117, 118, 163; see also t-distribution 97, 108, 127

67, 154 57, 88, 125, 149 86 93 68, 79

72 82, 87 64 see space 21, 22, 40, 41

172 66, 79, 107, 117, 119, 129, 130, 134, 137, 140, 161-163

19, 109, 166

42 139

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J.C. WUlems (Ed.)

From Data to Model 1989. vn, 246 pp. 35 figs. 10 tabs. Hardcover DM 98,- ISBN 3-540-51571-2

This book consists of 5 chapters. The general theme is to develop a mathematical frame­work and a language for modelling dynamical systems from observed data. Two chapters study the statistical aspects of approximate linear time-series analysis. One chapter devel­ops worst case aspects of system identifica­tion. Finally, there are two chapters on system approximation. The first one is a tutorial on the Hankel-norm approximation as an approach to model simplification in linear systems. The second one gives a philosophy for setting up numerical algorithms from which a model optimally fits an observed time series.

P.Hackl (Ed.)

Statistical Analysis and Forecasting of Economic Structural Change 1989. XIX, 488 pp. 98 figs. 60 tabs. Hardcover DM 178,- ISBN 3-540-51454-6

This book treats methods and problems of the statistical analysis of economic data in the context of structural change. It documents the state of the art, gives insights into existing methods, and describes new developments and trends. An introductory chapter gives a survey of the book and puts the following chapters into a broader context. The rest of the volume is organized in three parts: a) Identification of Structural Change; b) Model Building in the Presence of Struc­tural Change; c) Data Analysis and Modeling.

Springer-Verlag

C.D.Aliprantis, D.J.Brown, O.Burkinshaw

Existence and Optimality of Competitive Equilibria 1989. XII, 284 pp. 38 figs. Hardcover DM 110,- ISBN 3-540-50811-2

Contents: The Arrow-Debreu Model. - Riesz Spaces of Commodities and Prices. - Markets with Infinitely Many Commodities. - Produc­tion with Infinitely Many Commodities. -The Overlapping Generations Model. -References. - Index.

B.L.Golden, E.A. Wasil, P. T.Harker (Eds.)

The Analytic Hierarchy Process Applications and Studies

With contributions by numerous experts

1989. VI, 265 pp. 60 figs. 74 tabs. Hardcover DM 110,- ISBN 3-540-51440-6

The book is divided into three sections. In the first section, a detailed tutorial and an exten­sive annotated bibliography serve to introduce the methodology. The second section in­cludes two papers which present new method­ological advances in the theory of the AHP. The third section, by far the largest, is dedi­cated to applications and case studies; it contains twelve chapters. Papers dealing with project selection, electric utility planning, governmental decision making, medical deci­sion making, conflict analysis, strategic plan­ning, and others are used to illustrate how to successfully apply the AHP. Thus, this book should serve as a useful text in courses dealing with decision making as well as a valu­able reference for those involved in the appli­cation of decision analysis techniques.

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