Abstract
Using a simple theoretical model and giving an empirical example it is investigated if it matters whether we use (monthly) averages or end-of-period (month) data in performing Granger-causality tests. It is shown that no major problems are to be expected if the two series are temporally aggregated in the same way, but non-trivial problems can occur if the two series have different kinds of temporal aggregation.
Similar content being viewed by others
References
Brewer, K.R.W., (1973), Some Consequences of Temporal Aggregation and Systematic Sampling for ARMA and ARMAX models, Journal of Econometrics 1, 133–154.
Christiano, L.J. andM. Eichenbaum, (1987), Temporal Aggregation and Structural Inference in Macroeconomics, Carnegie-Rochester Conference Series on Public Policy 26, 63–130.
Engle, R.F. andC.W.J. Granger, (1987), Cointegration and Error Correction: Representation, Estimation and Testing, Econometrica 55, 251–276.
Granger, C.W.J., (1988), Some Recent Developments in a Concept of Causality, Journal of Econometrics 39, 199–211.
Kirchgässner, G., (1981), Einige neuere statistische Verfahren zur Erfassung kausaler Beziehungen zwischen Zeitreihen, Darstellung und Kritik, Vandenhoeck und Ruprecht, Göttingen.
Mundlak, Y., (1961), Aggregation over Time in Distributed Lag Models, International Economic Review 2, 154–163.
Pierce, D.A. andL.D. Haugh, (1977), Causality in Temporal Systems, Characterizations and a Survey, Journal of Econometrics 5, 265–293.
Pierce, D.A. andL.D. Haugh, (1979), The Characterization of Instantaneous Causality, A Comment, Journal of Econometrics 10, 257–259.
Price, J.M., (1979), The Characterization of Instantaneous Causality, A Correction, Journal of Econometrics 10, 253–256.
Sims, C.A., (1971), Discrete Approximations to Continuous Time Distributed Lags in Econometrics, Econometrica 39, 545–563.
Strotz, R.H. andH.O.A. Wold, (1960), Recursive versus Nonrecursive Systems: An Attempt to Synthesis, Econometrica 28, 417–427.
Telser, L.G., (1967), Discrete Samples and Moving Sums in Stationary Stochastic Processes, Journal of the American Statistical Association 62, 484–499.
Tiao, G.C., (1972), Asymptotic Behaviour of Temporal Aggregates of Time Series, Biometrika 59, 525–531.
Tiao, G.C. andW.S. Wei, (1976), Effect of Temporal Aggregation on the Dynamic Relationship of Two Time Series Variables, Biometrika 63, 513–523.
Wei, W.S., (1978), The Effect of Temporal Aggregation on Parameter Estimation in Distributed Lag Models, Journal of Econometrics 8, 237–246.
Weiss, A.A., (1984), Systematic Sampling and Temporal Aggregation in Time Series Models, Journal of Econometrics 26, 271–281.
Working, H., (1960), Note on the Correlation of First Differences of Averages in a Random Chain, Econometrica 28, 916–918.
Author information
Authors and Affiliations
Additional information
We gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft by Grant No. 322 147. We thank Gerd Ronnig and a referee for helpful comments and suggestions, Bärbel Finkenstädt for performing the computations and Anna Rushing-Jungeilges for editing the paper in English.
Rights and permissions
About this article
Cite this article
Kirchgässner, G., Wolters, J. Implications of temporal aggregation on the relation between two time series. Statistical Papers 33, 1–19 (1992). https://doi.org/10.1007/BF02925307
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02925307