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Statistical Foundations of Econometric Modelling - Aris Spanos

Statistical Foundations of Econometric Modelling

By: Aris Spanos, David F. Hendry (Foreword by)

Paperback Published: 29th December 1986
ISBN: 9780521269124
Number Of Pages: 720

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This book provides an introduction to econometrics through a thorough grounding in probability theory and statistical inference. The emphasis is on the concepts and ideas underlying probability theory and statistical inference, and on motivating the learning of them both at a formal and an intuitive level. By basing its approach on the underlying theory, it is able to cover fully the econometric theory required up to the intermediate level; its emphasis on mastering the concepts makes it an ideal introduction to the advanced texts and the econometric literature.

Forewordp. xi
Prefacep. xv
Acknowledgementsp. xx
List of symbols and abbreviationsp. xxi
Introduction
Econometric modelling, a preliminary viewp. 3
Econometrics--a brief historical overviewp. 3
Econometric modelling--a sketch of a methodologyp. 15
Looking aheadp. 22
Descriptive study of datap. 23
Histograms and their numerical characteristicsp. 23
Frequency curvesp. 27
Looking aheadp. 29
Probability theory
Probabilityp. 33
The notion of probabilityp. 34
The axiomatic approachp. 37
Conditional probabilityp. 43
Random variables and probability distributionsp. 47
The concept of a random variablep. 48
The distribution and density functionsp. 55
The notion of a probability modelp. 60
Some univariate distributionsp. 62
Numerical characteristics of random variablesp. 68
Random vectors and their distributionsp. 78
Joint distribution and density functionsp. 78
Some bivariate distributionsp. 83
Marginal distributionsp. 85
Conditional distributionsp. 89
Functions of random variablesp. 96
Functions of one random variablep. 96
Functions of several random variablesp. 99
Functions of normally distributed random variables, a summaryp. 108
Looking aheadp. 109
The normal and related distributionsp. 110
The general notion of expectationp. 116
Expectation of a function of random variablesp. 116
Conditional expectationp. 121
Looking aheadp. 127
Inequalitiesp. 129
Stochastic processesp. 130
The concept of a stochastic processp. 131
Restricting the time-heterogeneity of a stochastic processp. 137
Restricting the memory of a stochastic processp. 140
Some special stochastic processesp. 144
Summaryp. 162
Limit theoremsp. 165
The early limit theoremsp. 165
The law of large numbersp. 168
The central limit theoremp. 173
Limit theorems for stochastic processesp. 178
Summaryp. 180
Introduction to asymptotic theoryp. 183
Introductionp. 183
Modes of convergencep. 185
Convergence of momentsp. 192
The 'big O' and 'little o' notationp. 194
Extending the limit theoremsp. 198
Error bounds and asymptotic expansionsp. 202
Statistical inference
The nature of statistical inferencep. 213
Introductionp. 213
The sampling modelp. 215
The frequency approachp. 219
An overview of statistical inferencep. 221
Statistics and their distributionsp. 223
The empirical distribution functionp. 228
Estimation I--properties of estimatorsp. 231
Finite sample propertiesp. 232
Asymptotic propertiesp. 244
Predictors and their propertiesp. 247
Estimation II--methodsp. 252
The method of least-squaresp. 253
The method of momentsp. 256
The maximum likelihood methodp. 257
Hypothesis testing and confidence regionsp. 285
Testing, definitions and conceptsp. 285
Optimal testsp. 290
Constructing optimal testsp. 296
The likelihood ratio test procedurep. 299
Confidence estimationp. 303
Predictionp. 306
The multivariate normal distributionp. 312
Multivariate distributionsp. 312
The multivariate normal distributionp. 315
Quadratic forms related to the normal distributionp. 319
Estimationp. 320
Hypothesis testing and confidence regionsp. 323
Asymptotic test proceduresp. 326
Asymptotic propertiesp. 326
The likelihood ratio and related test proceduresp. 328
The linear regression and related statistical models
Statistical models in econometricsp. 339
Simple statistical modelsp. 339
Economic data and the sampling modelp. 342
Economic data and the probability modelp. 346
The statistical generating mechanismp. 349
Looking aheadp. 352
Datap. 355
The Gauss linear modelp. 357
Specificationp. 357
Estimationp. 359
Hypothesis testing and confidence intervalsp. 363
Experimental designp. 366
Looking aheadp. 367
The linear regression model I--specification, estimation and testingp. 369
Introductionp. 369
Specificationp. 370
Discussion of the assumptionsp. 375
Estimationp. 378
Specification testingp. 392
Predictionp. 402
The residualsp. 405
Summary and conclusionp. 408
A note on measurement systemsp. 409
The linear regression model II--departures from the assumptions underlying the statistical GMp. 412
The stochastic linear regression modelp. 413
The statistical parameters of interestp. 418
Weak exogeneityp. 421
Restrictions on the statistical parameters of interestp. 422
Collinearityp. 432
'Near' collinearityp. 434
The linear regression model III--departures from the assumptions underlying the probability modelp. 443
Misspecification testing and auxiliary regressionsp. 443
Normalityp. 447
Linearityp. 457
Homoskedasticityp. 463
Parameter time invariancep. 472
Parameter structural changep. 481
Variance stabilising transformationsp. 487
The linear regression model IV--departures from the sampling model assumptionp. 493
Implications of a non-random samplep. 494
Tackling temporal dependencep. 503
Testing the independent sample assumptionp. 511
Looking backp. 521
Deriving the conditional expectationp. 523
The dynamic linear regression modelp. 526
Specificationp. 527
Estimationp. 533
Misspecification testingp. 539
Specification testingp. 548
Predictionp. 562
Looking backp. 567
The multivariate linear regression modelp. 571
Introductionp. 571
Specification and estimationp. 574
A priori informationp. 579
The Zellner and Malinvaud formulationsp. 585
Specification testingp. 589
Misspecification testingp. 596
Predictionp. 599
The multivariate dynamic linear regression (MDLR) modelp. 599
The Wishart distributionp. 602
Kronecker products and matrix differentiationp. 603
The simultaneous equations modelp. 608
Introductionp. 608
The multivariate linear regression and simultaneous equations modelsp. 610
Identification using linear homogeneous restrictionsp. 614
Specificationp. 619
Maximum likelihood estimationp. 621
Least-squares estimationp. 626
Instrumental variablesp. 637
Misspecification testingp. 644
Specification testingp. 649
Predictionp. 654
Epilogue: towards a methodology of econometric modellingp. 659
A methodologist's critical eyep. 659
Econometric modelling, formalising a methodologyp. 661
Conclusionp. 671
Referencesp. 673
Indexp. 689
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521269124
ISBN-10: 0521269121
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 720
Published: 29th December 1986
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.88  x 3.81
Weight (kg): 0.98

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