Time Series Models: In econometrics, finance and other fields

234 Pages·1996·7.894 MB·English

by  Neil Shephard (auth.), D. R. Cox, D. V. Hinkley, O. E. Barndorff-Nielsen (eds.)

MONOGRAPHSON
STA TISTICS AND APPLIED PROBABILITY
General Editors
D.R. Cox, D.V. Hinkley, N. Keiding, N. Reid,
D.B. Rubin and B.W. Silverman
Stochastic Population Models in Ecology and Epidemiology
M8. Bartlett (1960)
2 Queues D.R Cox and WL. Smith (1961)
3 Monte Carlo Methods J.M Hammersley and D.C. Handscomb (1964)
4 The Statistical Analysis ofSeries ofEvents D.R. Cox and
P.A. W Lewis (1966)
5 Population Genetics WJ. Ewens (1969)
6 Probability, Statistics and Time M8. Bart/ett (1975)
7 Statistical Inference S.D. Silvey (1975)
8 The Analysis ofContingency Tables B.8. Everitt (1977)
9 Multivariate Analysis in Behavioural Research A.E. Maxwell (1977)
10 Stochastic Abundance Models S. Engen (1978)
11 Some Basic Theory for Statistical Inference E.J.G. Pitman (1979)
12 Point Processes D.R. Cox and V. Isham (1980)
13 Identification of Outliers D.M Hawkins (1980)
14 Optimal Design S.D. Silvey (1980)
15 Finite Mixture Distributions B.S. Everitt and D.J. Hand (1981)
16 ClassificationA.D. Gordon (1981)
17 Distribution-free Statistical Methods, 2nd edition J.8. Maritz (1995)
18 Residuals and Influence in Regression R.D. Cook
and S. Weisberg (1982)
19 Applications ofQueueing Theory, 2nd edition G.F. Newell (1982)
20 Risk Theory, 3rd edition R.E. Beard, T Pentikainen and
E. Pesonen (1984)
21 Analysis ofSurvival DataD.R Cox and D. Oakes (1984)
22 An Introduction to Latent Variable Models B.S. Everitt (1984)
23 Bandit Problems D.A. Berry and B. Fristedt (1985)
24 Stochastic Modelling and Control MHA. Davis and R. Vinter (1985)
25 The Statistical Analysis ofCompositional DataJ. Aitchison (1986)
26 Density Estimation for Statistics and Data Analysis
B. W Silverman (1986)
27 Regression Analysis with Applications G.B. Wetherill (1986)
28 Sequential Methods in Statistics, 3rd edition
G.B. Wetherill and K.D. Glazebrook (1986)
29 Tensor Methods in Statisties P. McCullagh (1987)
30 Transformation and Weighting in Regression R.J. Carroll and
D. Ruppert (1988)
31 Asymptotie Teehniques for Use in Statisties O.E. Barndorff-Nielsen
and D.R. Cox (1989)
32 Analysis ofBinary Data, 2nd edition D.R. Cox and E.J. Snell (1989)
33 Analysis ofInfeetious Disease DataNG. Beclcer (1989)
34 Design and Analysis of Cross-Over Trials B. Jones and
MG. Kenward (1989)
35 Empirieal Bayes Methods, 2nd edition J.s. Maritz and T. Lwin (1989)
36 Symmetrie Multivariate and Related Distributions K-T. Fang
S. Kotz and K W. Ng (1990)
37 Generalized Linear Models, 2nd edition P. McCullagh and
J.A. Neider (1989)
38 Cyclie and Computer Generated Designs, 2nd edition
J.A. John and E.R. Williams (1995)
39 Analog Estimation Methods in Eeonometries C.F Manski (1988)
40 Subset Seleetion in Regression A.J. Miller (1990)
41 Analysis ofRepeated Measures MJ. Crowder and D.J. Hand (1990)
42 Statistieal Reasoning with Impreeise Probabilities P. Walley (1991)
43 Generalized Additive Models T.J. Hastie and R.J. Tibshirani (1990)
44 Inspeetion Errors for Attributes in Quality Control
NL. Johnson, S. KotzandX Wu (1991)
45 The Analysis of Contingency Tables, 2nd edition B.S. Everitt (1992)
46 The Analysis ofQuantal Response DataB.J.T. Morgan (1993)
47 Longitudinal Data with Serial Correlation: A State-space Approach
R.H Jones (1993)
48 Differential Geometry and Statistics MK Murray
andJ.W. Rice (1993)
49 Markov Models and Optimization MHA. Davis (1993)
50 Networks and Chaos -Statistical and Probabilistic Aspects
o.E. Barndorff-Nielsen,
J.L. Jemen and W.S. Kendall (1993)
51 Number-theoretic Methods in Statistics K -T. Fang
and Y. Wang (1994)
52 Inference and Asymptotics o.E. Barndorff-Nielsen
and D.R. Cox (1994)
53 Practical Risk Theory for Actuaries C.D. Daykin, T. Pentikäinen
and M Pesonen (1994)
54 Biplots J. C. Gower and D.J. Hand (1996)
55 Predictive Inference: An Introduction S. Geisser (1993)
56 Model-Free Curve Estimation ME. Tarter and MD. Lock (1993)
57 An Introduction to the Bootstrap B. Efron and R.J. Tibshirani (1993)
58 Nonparametrie Regression and Generalized Linear Models
P.J Green and B. W Silverman (1994)
59 Multidimensional ScaJing T.F. Cox and MA.A. Cox (1994)
60 Kemel Smoothing MP. Wand and MC, Jones (1995)
61 Statistics for Long Memory Processes J Beran (1995)
62 Nonlinear Models for Repeated Measurement Data M Davidian
and D.M Giltinan (1995)
63 Measurement Error in Nonlinear Models R.J Carroll. D. Ruppert
and L.A. Stefanski (1995)
64· Analyzing and Modeling Rank Data JI Marden (1995)
65 Time Series Models:ln econometrics, finance and other fields
D.R. Cox. D. V Hinkley and o.E. Barndorff-Nielsen (1996)
(Full details conceming this series are available from the Publishers).
Time Series Models
In econometrics, finance and other fields
Edited by
D.R.Cox
Honorary Fellow
Nuffield College
Oxford, UK
D. V. Hinkley
Professor of Statistics
University 0/ Calijornia
Santa Barbara, USA
and
O.E. Barndorff-Nielsen
Professor of Theoretical Statistics
Aarhus University
Denmark
Springer-Science+Business Media, B.Y.
First edition 1996
© 1996. The copyright for Chapters 1-5 is held by the respective authors.
ISBN 978-0-412-72930-0 ISBN 978-1-4899-2879-5 (eBook)
DOI 10.1007/978-1-4899-2879-5
Softcover reprint of the hardcover 1 st edition 1996
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Contents
List of contributors xi
Preface xiü
1 Statistical aspects of ARCH and stochastic volatility
Neil Shephard 1
1.1 Introduction 1
1.2 ARCH 8
1.3 Stochastic volatility 22
1.4 Multivariate models 41
1.5 Option pricing with changing volatility 46
1.6 Continuous-time models 49
1.7 Conduding remarks 51
1.8 Appendix 52
1.9 Computing and data sources 54
Acknowledgements 54
References 55
2 Likelihood-based inference for cointegration of some nonstationary
time series
S.ren Johansen 69
2.1 Introduction 69
2.2 Granger's representation theorem 75
2.3 Purchasing power parity: an illustrative example 78
2.4 Formulation of the reduced-form error correction model
and various hypotheses on the cointegrating relations 82
2.5 Estimation of cointegrating relations and calculation of
test statistics 86
2.6 The empirical example continued 90
2.7 Asymptotic theory 93
viii CONTENTS
2.8 ConcIusion 97
Acknowledgements 98
References 98
3 Forecasting in macro-economics
Michael P. elements and David F. Hendry 101
3.1 Introduction 101
3.2 A framework for economic forecasting 103
3.3 Alternative methods of forecasting 105
3.4 The economic system and forecasting models 107
3.5 Measuring forecast accuracy 112
3.6 A taxonomy of forecast errors 118
3.7 Parameter constancy 124
3.8 Parameter non-constancy 126
3.9 Intercept corrections 130
3.10 Conclusions 134
Acknowledgements 136
References 136
4 Longitudinal panel data:
an overview of current methodology
NanM. Laird 143
4.1 Introduction 143
4.2 General formulation 143
4.3 The GEE approach to longitudinal data analysis 147
4.4 Likelihood-based approaches to longitudinal data analysis 153
4.5 Estimation with incomplete data 157
4.6 Example: childhood obesity. 161
4.7 Random effects models 164
4.8 Discussion 169
Acknowledgements 172
References 172
5 Pricing by no arbitrage
Bjarne Astrup Jensen and J~rgen Aase Nielsen 177
5.1 Introduction 177
5.2 Notation 180
5.3 The 'no arbitrage' condition 181
5.4 Equivalent martingale measures and risk-neutralized
price processes 185
5.5 Change ofnumeraire 187
5.6 Attainability 187
CONTENTS ix
5.7 Multiperiod model in discrete time 191
5.8 Complete market and splitting index 197
5.9 Complete market and martingale basis 204
5.10 Continuous-time models: basic assumptions 209
5.11 Relative price processes and change of numeraire 212
5.12 Complete market in continuous time 218
5.13 Equivalent martingale measures and absence of
'approximate arbitrage' 221
5.14 Concluding remarks 222
Acknowledgements 223
References 223
Contributors
Neil G. Shephard, Nuffield College., Oxford, OXI INF, UK.
S~ren Johansen, Institute of Mathematical Statistics, University of
Copenhagen 0, Universitetparken 5,2100 Copenhagen, Denmark.
David F. Hendry, Nuffield College, Oxford, OXI INF, UK.
Michael P. Clements, Department ofEconomics, University ofWarwick,
Coventry, UK.
Nan Laird, Department of Biostatistics, Harvard School of Public
Health, 677 Huntington Avenue, Boston, MA 02115-6096, USA.
Bjarne A. Jensen, Institute of Finance, Copenhagen Business School,
Rosen~ms Alle 31, 1970 Frederiksberg C, Denmark.
J~rgen A. Nielsen, Department of Theoretical Statistics and
Operations Research, Institute of Mathematics, Aarhus University,
Ny Muukegade, 8000 Aarhus C, Denmark.