Statistical foundations of econometric modelling:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u.a.
Cambridge Univ. Pr.
1987
|
| Ausgabe: | Repr. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXIII, 695 S. graph. Darst. |
| ISBN: | 0521262852 0521269121 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804119556183031808 |
|---|---|
| adam_text | Statistical foundations
of econometric modelling
•ARIS SPANOS
Birkbeck College
(LONDONUNIVERSITY)
i
~V
Thr right of the
University qf Cambridge
to print end sell
all maimer of books
was granted by
Henry VIII in 1534
The Unirersity has printed
and published continuously
since 1584
CAMBRIDGE UNIVERSITY PRESS
Cambridge
London New York New Rochelle
Melbourne Sydney
Contents
Foreword by David Hendry xi
Preface • xv
Acknowledgements xx
List of symbols and abbreviations xxi
Part I Introduction
1 Econometric modelling, a preliminary view 3
1 1 Econometrics - a brief historical overview 3
1 2 Econometric modelling r- a sketch of a
methodology 15
1 3 Looking ahead 22
2 Descriptive study of data 23
2 1 Histograms and their numerical characteristics 23
2 2 Frequency curves 27
2 3 Looking ahead 29
Part II Probability theory
3 Probability 33
3 1 TKe notion of probability 34
3 2 The axiomatic approach 37
3 3 Conditional probability 43
vi Contents
4 -Random variables and probability distributions 47
4 1 The concept of a random variable 48
4 2 The distribution and density functions 55
4 3 The notion of a probability model 60
4 4 Some univariate distributions 62
4 5 Numerical characteristics of random variables - 68
5 Random vectors and their distributions 78
5 1 Joint distribution and density functions 78
5 2 Some bivariate distributions 83
5 3 Marginal distributions 85
5 4 Conditional distributions 89
6 Functions of random variables 96
6 1 Functions of one random variable 96
6 2* Functions, of several random variables 99
6 3 Functions of normally distributed random variables,
a summary 108
6 4 Looking ahead 109
Appendix 61- The normal and related
distributions 110
7 The general notion of expectation 116
7 1 Expectation of a function of random variables 116
7 2 Conditional expectation 121
7 3 Looking ahead 127
Appendix 7 1- Inequalities 129
8* Stochastic processes 130
8 1 The concept of a stochastic process 131
8 2 Restricting the time-heterogeneity of a stochastic
process 137
8 3 Restricting the memory of a stochastic process 140
8 4 Some special stochastic processes 144
8 5 Summary 162
9 Limit theorems - 165
9 1 The early limit theorems 165
9 2 The law of large numbers 168
9 3 The central limit theorem 173
9 4* Limit theorems for stochastic processes 178
9 5 Summary 180
Contents vii
10* • Introduction to asymptotic theory 183
10 1 Introduction • 183
10 2 Modes of convergence 185
10 3 Convergence of moments 192
10 4 The big O and little o notation 194
10 5 Extending the limit theorems 198
10 6 Error bounds and asymptotic expansions 202
Part III Statistical inference
11 The nature of statistical inference 213
11 1 Introduction 213
11:2 The sampling model 215
11 3 The frequency approach 219
11 4 An overview of statistical inference 221
11 5 Statistics and their distributions 223
Appendix 11 1 - The empirical distribution
function 228
12 Estimation I - properties of estimators 231
12 1 Finite sample properties 232
-12 2 Asymptotic properties 244
12 3 Predictors and their properties 247
13 Estimation II - methods 252
13 1 The method of least-squares 253
13 2 The method of moments 256
13 3 The maximum likelihood method 257
14 Hypothesis testing and confidence regions 285
14 1 Testing, definitions and concepts • 285
14 2 Optimal tests 290
14 3 Constructing optimal tests 296
14 4 The likelihood ratio test procedure 299
14 5 Confidence estimation 303
14 6 Prediction 306
IS* The multivariate normal distribution 312
15 1 Multivariate distributions 312
15 2 The multivariate normal distribution 315
15 3 Quadratic forms related to the normal distribution 319
viii Contents
15 4 Estimation 320
15 5 Hypothesis testing and confidence regions 323
16* Asymptotic test procedures 326
16 1 Asymptotic properties 326
16 2 The likelihood ratio and related test procedures 328
Part IV The linear regression and related statistical
models
• 17 Statistical models in econometrics 339
17 1 Simple statistical models 339
17 2 • Economic data and the sampling model 342
17 3 Economic data and the probability model 346
17 4 The statistical generating mechanism 349
• 17 5 Looking ahead 352
Appendix 17 1 - Data 355
18 The Gauss linear model 357
18 1 Specification 357
18 2 Estimation 359
18 3 Hypothesis testing and confidence intervals 363
18 4 Experimental design 366
18 5 Looking ahead 367
19 The linear regression model I - specification,
estimation and testing 369
19 1 Introduction 369 j
19 2 Specification 370 j
19 3 Discussion ofthe assumptions 375 j
19 4 Estimation 378
19 5 Specification testing 392
19 6 Prediction 402
19 7 The residuals 405
19 8 Summary and conclusion 408
Appendix 19 1-A note on measurement systems 409
20 The linear regression model II - departures from
the assumptions underlying the statistical GM 412
20 1 The stochastic linear regression model 413
20 2 The statistical parameters of interest 418
Contents ix
20 3 Weak exogeneity 421
20 4 Restrictions on the statistical parameters of
interest 422
20 5 Collinearity 432
20 6 Near collinearity 434
21 The linear regression model III - departures from
the assumptions underlying the probability model 443
21 1 Misspecification testing and auxiliary regressions 443
21 2 Normality 447
21 3 Linearity 457
21 4 Homoskedasticity 463
21 5 Parameter time invariance 472
21 6 Parameter structural change 481
Appendix 21 1 - Variance stabilising
transformations 487
22 The linear regression model IV - departures from
the sampling model assumption 493
22 1 Implications of a non-random sample 494
22 2 Tackling temporal dependence 503
22 3 Testing the independent sample assumption 511
22 4 Looking back 521
Appendix 22 1 - Deriving the conditional
expectation 523
23 The dynamic linear regression model 526
23 1 Specification 527
23 2 Estimation 533
23 3 Misspecification testing 539
23 4 Specification testing 548
23 5 Prediction - 562
23 6 Looking back 567
24 The multivariate linear regression model
24 1 Introduction
24 2 Specification and estimation
24 3- A priori information
24 4 The Zellner and Malinvaud formulations
24 5 Specification testing
24 6 Misspecification testing
x Contents
24 7 Prediction * 599
24 8 The multivariate dynamic linear regression
(MDLR) model 599
Appendix 24 1 - The Wishart distribution 602
Appendix 24 2 - Kronecker products and matrix
differentiation 603
25 The simultaneous equations model 608
25 1 Introduction 608
25 2 The multivariate linear regression and
simultaneous equations models 610
25 3 Identification using linear homogeneous
restrictions 614
25 4 Specification 619
25 5 Maximum likelihood estimation 621
25 6 Least-squares estimation 626
25 7 Instrumental variables 637
25 8 Misspecification testing 644
25 9 Specification testing , 649
25 10 Prediction 654
26 Epilogue: towards a methodology of econometric
modelling 659
26 1 A methodologist s critical eye 659
26 2 Econometric modelling, formalising a
methodology 661
26 3 Conclusion 671
References 673
Index 689
* Starred chapters and/or sections are typically more difficult and
might be avoided at first reading
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| language | English |
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| physical | XXIII, 695 S. graph. Darst. |
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| title | Statistical foundations of econometric modelling |
| title_auth | Statistical foundations of econometric modelling |
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| title_full | Statistical foundations of econometric modelling |
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