Statistical foundations of econometric modelling

Title:

Author:

Spanos, Aris, 1952-

ISBN:

9780521262859

9780521269124

Personal Author:

Spanos, Aris, 1952-

Publication Information:

Cambridge ; New York : Cambridge University Press, 1986.

Physical Description:

xxiii, 695 pages : illustrations ; 24 cm

Subject Term:

Econometrics.

Ekonometri.

Available:*

Library	Material Type	Item Barcode	Shelf Number	Status
Searching... Pamukkale Central Library	Book	0104236	HB141 S64 1986	Searching... Unknown

This textbook provides an introduction to econometrics through a 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. It encourages the mastering of fundamental concepts and theoretical perspectives which guide the formulation and solution of problems in econometric modelling. This makes it an ideal introduction to empirical econometric modelling and the more advanced econometric literature. It is recommended for use on courses giving students a thorough grounding in econometrics at undergraduate or graduate level.

David Hendry

Foreword	p. xi
Preface	p. xv
Acknowledgements	p. xx
List of symbols and abbreviations	p. xxi
Part I Introduction
1 Econometric modelling, a preliminary view	p. 3
1.1 Econometrics--a brief historical overview	p. 3
1.2 Econometric modelling--a sketch of a methodology	p. 15
1.3 Looking ahead	p. 22
2 Descriptive study of data	p. 23
2.1 Histograms and their numerical characteristics	p. 23
2.2 Frequency curves	p. 27
2.3 Looking ahead	p. 29
Part II Probability theory
3 Probability	p. 33
3.1 The notion of probability	p. 34
3.2 The axiomatic approach	p. 37
3.3 Conditional probability	p. 43
4 Random variables and probability distributions	p. 47
4.1 The concept of a random variable	p. 48
4.2 The distribution and density functions	p. 55
4.3 The notion of a probability model	p. 60
4.4 Some univariate distributions	p. 62
4.5 Numerical characteristics of random variables	p. 68
5 Random vectors and their distributions	p. 78
5.1 Joint distribution and density functions	p. 78
5.2 Some bivariate distributions	p. 83
5.3 Marginal distributions	p. 85
5.4 Conditional distributions	p. 89
6 Functions of random variables	p. 96
6.1 Functions of one random variable	p. 96
6.2 Functions of several random variables	p. 99
6.3 Functions of normally distributed random variables, a summary	p. 108
6.4 Looking ahead	p. 109
Appendix 6.1 The normal and related distributions	p. 110
7 The general notion of expectation	p. 116
7.1 Expectation of a function of random variables	p. 116
7.2 Conditional expectation	p. 121
7.3 Looking ahead	p. 127
Appendix 7.1 Inequalities	p. 129
8 Stochastic processes	p. 130
8.1 The concept of a stochastic process	p. 131
8.2 Restricting the time-heterogeneity of a stochastic process	p. 137
8.3 Restricting the memory of a stochastic process	p. 140
8.4 Some special stochastic processes	p. 144
8.5 Summary	p. 162
9 Limit theorems	p. 165
9.1 The early limit theorems	p. 165
9.2 The law of large numbers	p. 168
9.3 The central limit theorem	p. 173
9.4 Limit theorems for stochastic processes	p. 178
9.5 Summary	p. 180
10 Introduction to asymptotic theory	p. 183
10.1 Introduction	p. 183
10.2 Modes of convergence	p. 185
10.3 Convergence of moments	p. 192
10.4 The 'big O' and 'little o' notation	p. 194
10.5 Extending the limit theorems	p. 198
10.6 Error bounds and asymptotic expansions	p. 202
Part III Statistical inference
11 The nature of statistical inference	p. 213
11.1 Introduction	p. 213
11.2 The sampling model	p. 215
11.3 The frequency approach	p. 219
11.4 An overview of statistical inference	p. 221
11.5 Statistics and their distributions	p. 223
Appendix 11.1 The empirical distribution function	p. 228
12 Estimation I--properties of estimators	p. 231
12.1 Finite sample properties	p. 232
12.2 Asymptotic properties	p. 244
12.3 Predictors and their properties	p. 247
13 Estimation II--methods	p. 252
13.1 The method of least-squares	p. 253
13.2 The method of moments	p. 256
13.3 The maximum likelihood method	p. 257
14 Hypothesis testing and confidence regions	p. 285
14.1 Testing, definitions and concepts	p. 285
14.2 Optimal tests	p. 290
14.3 Constructing optimal tests	p. 296
14.4 The likelihood ratio test procedure	p. 299
14.5 Confidence estimation	p. 303
14.6 Prediction	p. 306
15 The multivariate normal distribution	p. 312
15.1 Multivariate distributions	p. 312
15.2 The multivariate normal distribution	p. 315
15.3 Quadratic forms related to the normal distribution	p. 319
15.4 Estimation	p. 320
15.5 Hypothesis testing and confidence regions	p. 323
16 Asymptotic test procedures	p. 326
16.1 Asymptotic properties	p. 326
16.2 The likelihood ratio and related test procedures	p. 328
Part IV The linear regression and related statistical models
17 Statistical models in econometrics	p. 339
17.1 Simple statistical models	p. 339
17.2 Economic data and the sampling model	p. 342
17.3 Economic data and the probability model	p. 346
17.4 The statistical generating mechanism	p. 349
17.5 Looking ahead	p. 352
Appendix 17.1 Data	p. 355
18 The Gauss linear model	p. 357
18.1 Specification	p. 357
18.2 Estimation	p. 359
18.3 Hypothesis testing and confidence intervals	p. 363
18.4 Experimental design	p. 366
18.5 Looking ahead	p. 367
19 The linear regression model I--specification, estimation and testing	p. 369
19.1 Introduction	p. 369
19.2 Specification	p. 370
19.3 Discussion of the assumptions	p. 375
19.4 Estimation	p. 378
19.5 Specification testing	p. 392
19.6 Prediction	p. 402
19.7 The residuals	p. 405
19.8 Summary and conclusion	p. 408
Appendix 19.1 A note on measurement systems	p. 409
20 The linear regression model II--departures from the assumptions underlying the statistical GM	p. 412
20.1 The stochastic linear regression model	p. 413
20.2 The statistical parameters of interest	p. 418
20.3 Weak exogeneity	p. 421
20.4 Restrictions on the statistical parameters of interest	p. 422
20.5 Collinearity	p. 432
20.6 'Near' collinearity	p. 434
21 The linear regression model III--departures from the assumptions underlying the probability model	p. 443
21.1 Misspecification testing and auxiliary regressions	p. 443
21.2 Normality	p. 447
21.3 Linearity	p. 457
21.4 Homoskedasticity	p. 463
21.5 Parameter time invariance	p. 472
21.6 Parameter structural change	p. 481
Appendix 21.1 Variance stabilising transformations	p. 487
22 The linear regression model IV--departures from the sampling model assumption	p. 493
22.1 Implications of a non-random sample	p. 494
22.2 Tackling temporal dependence	p. 503
22.3 Testing the independent sample assumption	p. 511
22.4 Looking back	p. 521
Appendix 22.1 Deriving the conditional expectation	p. 523
23 The dynamic linear regression model	p. 526
23.1 Specification	p. 527
23.2 Estimation	p. 533
23.3 Misspecification testing	p. 539
23.4 Specification testing	p. 548
23.5 Prediction	p. 562
23.6 Looking back	p. 567
24 The multivariate linear regression model	p. 571
24.1 Introduction	p. 571
24.2 Specification and estimation	p. 574
24.3 A priori information	p. 579
24.4 The Zellner and Malinvaud formulations	p. 585
24.5 Specification testing	p. 589
24.6 Misspecification testing	p. 596
24.7 Prediction	p. 599
24.8 The multivariate dynamic linear regression (MDLR) model	p. 599
Appendix 24.1 The Wishart distribution	p. 602
Appendix 24.2 Kronecker products and matrix differentiation	p. 603
25 The simultaneous equations model	p. 608
25.1 Introduction	p. 608
25.2 The multivariate linear regression and simultaneous equations models	p. 610
25.3 Identification using linear homogeneous restrictions	p. 614
25.4 Specification	p. 619
25.5 Maximum likelihood estimation	p. 621
25.6 Least-squares estimation	p. 626
25.7 Instrumental variables	p. 637
25.8 Misspecification testing	p. 644
25.9 Specification testing	p. 649
25.10 Prediction	p. 654
26 Epilogue: towards a methodology of econometric modelling	p. 659
26.1 A methodologist's critical eye	p. 659
26.2 Econometric modelling, formalising a methodology	p. 661
26.3 Conclusion	p. 671
References	p. 673
Index	p. 689

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