RANKBASED INFERENCE FOR MULTIVARIATE NONLINEAR AND LONGMEMORY TIME SERIES MODELS

 Hirukawa Junichi HIRUKAWA Junichi
 Department of Mathematics, Faculty of Science, Niigata University

 Taniai Hiroyuki TANIAI Hiroyuki
 School of International Liberal Studies, Waseda University

 Hallin Marc [他] HALLIN Marc
 Institut de Recherche en Statistique, ECARES, Universite libre de Bruxelles

 TANIGUCHI Masanobu
 Department of Applied Mathematics, School of Fundamental Science and Science and Engineering, Waseda University
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Author(s)

 Hirukawa Junichi HIRUKAWA Junichi
 Department of Mathematics, Faculty of Science, Niigata University

 Taniai Hiroyuki TANIAI Hiroyuki
 School of International Liberal Studies, Waseda University

 Hallin Marc [他] HALLIN Marc
 Institut de Recherche en Statistique, ECARES, Universite libre de Bruxelles

 TANIGUCHI Masanobu
 Department of Applied Mathematics, School of Fundamental Science and Science and Engineering, Waseda University
Abstract
The portfolio of the Japanese Government Pension Investment Fund (GPIF) consists of a linear combination of five benchmarks of financial assets. Some of these exhibit longmemory and nonlinear behavior. Their analysis therefore requires multivariate nonlinear and longmemory time series models. Moreover, the assumption that the innovation densities underlying those models are known seems quite unrealistic. If those densities remain unspecified, the model becomes a semiparametric one, and rankbased inference methods naturally come into the picture. Rankbased inference methods under very general conditions are known to achieve the semiparametric efficiency bounds. % through the maximum invariant property of ranks. Defining ranks in the context of multivariate time series models, however, is not obvious. We propose two distinct definitions. The first one relies on the assumption that the innovation density is some unspecified elliptical density. The second one relies on the assumption that the innovation process is described by some unspecified independent component analysis model. Applications to portfolio management problems are discussed.
Journal

 JOURNAL OF THE JAPAN STATISTICAL SOCIETY

JOURNAL OF THE JAPAN STATISTICAL SOCIETY 40(1), 167187, 20100601
THE JAPAN STATISTICAL SOCIETY
References: 24

1
 Expected shortfall : A natural coherent alternative to value at risk

ACERBI C.
Economic Notes 31(2), 379388, 2002
Cited by (1)

2
 Pessimistic portfolio allocation and Choquet expected utility

BASSETT G. W. J.
J. Financ. Econom. 2(4), 477492, 2004
Cited by (1)

3
 Adaptive estimation in timeseries models

DROST F. C.
Ann. Stat. 25(2), 786817, 1997
Cited by (1)

4
 <no title>

HAJEK J.
Theory of Rank Tests, 1967
Cited by (1)

5
 Optimal tests for multivariate location based on interdirections and pseudoMahalanobis ranks

HALLIN M.
Ann. Stat. 30(4), 11031133, 2002
Cited by (1)

6
 Affineinvariant aligned rank tests for the multivariate general linear model with VARMA errors

HALLIN M.
J. Multivariate Anal. 93(1), 122163, 2005
Cited by (1)

7
 Time series analysis via rank order theory : signedrank tests for ARMA models

HALLIN M.
J. Multivariate Anal. 39(1), 129, 1991
Cited by (1)

8
 Semiparametric efficiency, distributionfreeness and invariance

HALLIN M.
Bernoulli 9(1), 137165, 2003
Cited by (1)

9
 Multiplicatively modulated nonlinear autoregressive model and its applications to biomedical signal analysis

KATO H.
Waseda Univ. Time Series Discussion Paper, 2003
Cited by (1)

10
 <no title>

KOENKER R.
Quantile regression, 2005
Cited by (1)

11
 Quantile autoregression

KOENKER R.
J. Amer. Stat. Assoc. 101(475), 980990, 2006
Cited by (1)

12
 Conditional quantile estimation and inference for ARCH models

KOENKER R.
Econom. Theory 12(5), 793813, 1996
Cited by (1)

13
 Modeling Multivariate Volatilities via Independent Components

MATTESON D. S.
http://www.rmi.nus.edu.sg/events/files/PAPER/Multivariate%20Volatility%20Modeling%20p1.pdf, 2010
Cited by (1)

14
 Optimization of conditional valueatrisk

ROCKAFELLAR R. T.
J. Risk 2(3), 2141, 2000
Cited by (1)

15
 <no title>

SCHMETTERER L.
Introduction to Mathematical Statistics, 1974
Cited by (1)

16
 <no title>

TANIAI H.
Semiparametric efficiency of quantile regression in an ARCH context, 2009
Cited by (1)

17
 Coherent measures of risk

ARTZNER P.
Mathematical Finance 9, 203228, 1999
DOI Cited by (11)

18
 Stationary ARCH models : dependence structure and central limit theorem

GIRAITIS L.
Econometric Theory 16, 322, 2000
DOI Cited by (7)

19
 A model for long memory conditional heteroscedasticity

GIRAITIS L.
Ann. Appl. Probab. 10(3), 10021024, 2000
DOI Cited by (2)

20
 Nonparametric vector autoregression

HARDLE W.
J. Statist. Plan. Infer. 68, 221245, 1998
DOI Cited by (4)

21
 Statistical analysis for multiplicatively modulated nonlinear autoregressive model and its applications to electrophysiological signal analysis in humans

KATO H.
IEEE Transactions on Signal Processing 54(9), 34143425, 2006
Cited by (2)

22
 Regression Quantiles

KOENKER R.
Econometrica 46, 3350, 1978
Cited by (13)

23
 Integral representation without additivity

SCHMEIDLER D.
Proceedings of the American Mathematical Society 97, 253261, 1986
DOI Cited by (2)

24
 Subjective probability and expected utility without additivity

SCHMEIDLER D.
Econometrica 57(3), 571587, 1989
DOI Cited by (7)