Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T13:36:18.313Z Has data issue: false hasContentIssue false

Comovements Between Diffusion Processes

Characterization, Estimation, and Testing

Published online by Cambridge University Press:  11 February 2009

Valentina Corradi
Affiliation:
University of Pennsylvania

Abstract

The aim of this paper is to characterize and analyze long-run comovements among diffusion processes. Broadly speaking, if X = (X1,,X2,;t ≥ 0) is a nonergodic diffusion in R2, but there exists a linear combination, say, γ′X, that is instead ergodic in R, then we say there exists a linear stochastic comovement between the components of X. Linear diffusions exhibiting stochastic comovements admit an error correction representation. Estimation of γ and hypothesis testing, under different sampling schemes, are considered.

Type
Articles
Copyright
Copyright © Cambridge University Press 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Arnold, L. (1974) Stochastic Differential Equations: Theory and Applications. New York: Wiley.Google Scholar
Athreya, K.B. & Pantula, S.G. (1986) Mixing properties of Harris chains and autoregressive processes. Journal of Applied Probability 23, 880892.CrossRefGoogle Scholar
Bhattacharya, R.N. (1982) On the functional central limit theorem and the law of iterated logarithm for Markov processes. Zeitschriftfiir Wahrscheinuchkeitstheorie und Verwandte Cebiete 60, 185201.CrossRefGoogle Scholar
Comte, F. (1996) Discrete and Continuous Time Cointegration. Mimeo, Universite Paris 6.Google Scholar
Corradi, V. & H. White (1995) Specification Tests for the Variance of a Diffusion. Manuscript, University of Pennsylvania.Google Scholar
Dachuna-Castelle, D. & D. Florens-Zmirou (1986) Estimation of the coefficient of a diffusion from discretely sampled observations. Stochastics 19, 263284.CrossRefGoogle Scholar
Eberlain, E. (1986) On strong invariance principles under dependence assumptions. Annals of Probability 14, 260270.Google Scholar
Hansen, B.E. (1992) Convergence to stochastic integrals for dependent heterogeneous processes. Econometric Theory 8, 489500.Google Scholar
Harrison, J.M., R. Pitbladdo, & Schaefer, S.M. (1984) Continuous price processes in frictionless markets have infinite variation. Journal of Business 57, 353365.CrossRefGoogle Scholar
Ichihara, H. & K. Kunita (1974) A classification of second order degenerate elliptic operators and its probabilistic characterization. Zeitschriftfiir Wahrscheinuchkeitstheorie und Verwandte Cebiete 30, 235254.CrossRefGoogle Scholar
Ikeda, N. & S. Watanabe (1989) Stochastic Differential Equations and Diffusion Processes, 2nd ed.Amsterdam: North-Holland.Google Scholar
Johansen, S. (1988) Statistical analysis of c ointegrating vectors. Journal of Economics and Dynamics Control 12, 231254.Google Scholar
Karatzas, I. & Shreve, S.E. (1991) Brownian Motion and Stochastic Calculus, 2nd ed.New York: Springer-Verlag.Google Scholar
Kurtz, T.G. & P. Protter (1991) Weak limi t theorems for stochastic integrals and stochastic differential equations. Annals of Probabitity 19, 10351070.Google Scholar
McLeisch, D.L. (1975) Invariance principles for dependent variables. Zeitschriftfiir Wahrscheinuchkeitstheorie und Verwandte Cebiete 32, 165178.CrossRefGoogle Scholar
Meyn, S.P. & Tweedie, R.L. (1993) Stability of Markovian processes III: Lyapunov criteria for continuous time processes. Advances in Applied Probability 25, 518548.CrossRefGoogle Scholar
Oksendal, B. (1985) Stochastic Differential Equations: An Introduction with Applications. New York: Springer-Verlag.CrossRefGoogle Scholar
Perron, P. (1991) A continuous time approximation to the unstable first-order autoregressive process: The case without intercept. Econometrica 59, 211236.CrossRefGoogle Scholar
Phillips, P.C.B. (1987) Towards a unified asymptotic theory for autoregression. Biometrika 74, 533547.CrossRefGoogle Scholar
Phillips, P.C.B. (1991a) Optimal inference in cointegrated systems. Econometrica 59, 283306.CrossRefGoogle Scholar
Phillips, P.C.B. (1991b) Error correction and long-run equilibrium in continuous time. Econometrica 59, 967980.Google Scholar
Phillips, P.C.B. (1991c) Spectral regression for cointegrated time series. In Bamett, W.A., Powell, J., & Tauchen, G. (eds.), Nonparametric and Semiparametric Methods in Econometrics and Statistics, pp. 413435. New York: Cambridge University Press.Google Scholar
Phillips, P.C.B. & S. Ouliaris (1990) Asymptotic properties of residual based tests for cointegration. Econometrica 58, 165193.CrossRefGoogle Scholar
Sorensen, B.E. (1992) Continuous record asymptotics in systems of stochastic differential equations. Econometric Theory 8, 2851.CrossRefGoogle Scholar
Strook, D.W. &Varadhan, S.R.S. (1979) Multidimensional Diffusion Processes. Berlin: Springer-Verlag.Google Scholar