Abstract
The effect of temporal aggregation on several time-series is considered. For several classes of time-series models it is well-known that the classes are closed under temporal aggregation, aggregation of a high frequency process yields a corresponding low frequency process in the same class. Examples are wide stationary ARMA and weak GARCH. We use two simple lemmas to obtain these results in a more direct way. The lemmas allow for generalizations in several directions. Discussed are fractionally differenced time-series, heavy tailed stable type processes, and GARCH-M.
The author would like to thank Theo E. Nijman and Arie L. Rijkeboer for valuable discussions and helpful suggestions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bollerslev T (1986) Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics 31, 307–327
Bollerslev T (1988) On the Correlation Structure for the Generalized Autoregressive Con-ditional Heteroskedastic Process, Journal of Time Series Analysis 9, 121–131
Bollerslev T, Chou R Y and Kroner K F (1992) ARCH Modeling in Finance: a Review of the Theory and Empirical Evidence, Journal of Econometrics 52, 5–60
Brockwell P J and Davis R A (1987) Time Series: Theory and Methods, Springer
Davis R A and Resnick S I (1986) Limit Theory for the Sample Covariance and Correlation Functions of Moving Averages, Annals of Statistics 14, 533–558
De Vries C G (1991) On the Relation between GARCH and Stable Processes, Journal of Econometrics 48, 313–324
Diebold F X and Rudebusch G P (1991) Is Consumption too Smooth? Long Memory andthe Deaton Paradox, The Review of Economics and Statistics 73, 1–9
Diebold F X and Rudebusch G P (1992) On the Power of the Dicky-Fuller Test AgainstFractional Alternatives, Economics Letters 35, 155–160
Drost F C and Nijman T E (1993) Temporal Aggregation of GARCH Processes, Econometrica, to appear
Engle R F (1982) Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation, Econometrica 50, 987–1008
Engwerda J C, Ran A C M and Rijkeboer A L (1991) Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution of the Matrix Equation X+A’X -1 ’A = I, Working Paper FEW 482, Tilburg University
Fama E (1965) Behavior of Stock Market Prices, Journal of Business 38, 34–105
Fox R and Taqqu M S (1986) Large Sample Properties of Parameter Estimates forStrongly Dependent Stationary Gaussian Time Series, Annals of Statistics 14, 517–532
Geweke J and Porter-Hudak S (1983) The Estimation and Application of Long-Memory Time Series Models, Journal of Time Series Analysis 4, 221–238
Granger C W and Joyeux R (1980) An Introduction to Long-Memory Time Series Modelsand Fractionally Differencing, Journal of Time Series Analysis 1, 15–29
Hansen L P and Sargent T J (1983) The Dimensionality of the Aliasing Problem in Mod-els with Rational Spectral Densities, Econometrica 51, 377–388
Nijman T E and Sentana E (1993) Marginalization and Contemporaneous Aggregation in Multivariate GARCH Processes, CentER Discussion Papers 9312, Tilburg Univer-sity
Sentana E (1991) Quadratic ARCH Models: a Potential Re-Interpretation of ARCH Models, Preprint, LSE
Sowell F (1992) Maximum likelihood Estimation of Stationary Univariate Fractionally Integrated Time Series Models, Journal of Econometrics 53, 165–188
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Physica-Verlag Heidelberg
About this paper
Cite this paper
Drost, F.C. (1994). Temporal Aggregation of Time-Series. In: Kaehler, J., Kugler, P. (eds) Econometric Analysis of Financial Markets. Studies in Empirical Economics. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-48666-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-48666-1_2
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-642-48668-5
Online ISBN: 978-3-642-48666-1
eBook Packages: Springer Book Archive