Skip to main content
SpringerLink
Log in
Book cover

Data Analysis and Classification pp 435–443Cite as

Temporal Aggregation and Closure of VARMA Models: Some New Results

  • Conference paper
  • First Online:

Abstract

In this paper we examine the effects of temporal aggregation on Vector AutoRegressive Moving Average (VARMA) models. It has relevant implications both in theoretical and empirical domain. Among them we focus the attention on the main consequences of the aggregation (obtained from point in time sampling) on the model identification. Further, under well defined conditions on the model parameters, we explore the closure of the VARMA class (with respect to the temporal aggregation) through theoretical results discussed in proper examples.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    In the following the adjective “markovian” is only related to the form of the model equation (that looks like a Markov process) and not to the stochastic properties of the generating process.

References

  • Breitung, J., & Swanson, N. (2002). Temporal aggregation and spurious instantaneous causality in multiple time series models. Journal of Time Series Analysis, 23, 651–665

    Article  MATH  MathSciNet  Google Scholar 

  • Brewer, K. (1973). Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models. Journal of Econometrics, 1, 133–154

    Article  MATH  Google Scholar 

  • Granger, C., & Siklos, P. (1995). Systematic sampling temporal aggregation, seasonal adjustment and cointegration theory and evidence. Journal of Econometrics, 66, 357–369

    Article  MATH  Google Scholar 

  • Jordà, O., & Marcellino, M. (2004). Time-scale transformations of discrete time processes. Journal of Time Series Analysis, 25, 873–894

    Article  MATH  MathSciNet  Google Scholar 

  • Lütkephol, H. (1987). Forecasting aggregated vector ARMA processes. Berlin: Springer

    Google Scholar 

  • Marcellino, M. (1999). Some consequences of temporal aggregation in empirical analysis. Journal of Business and Economic Statistics, 17, 129–136

    Article  MathSciNet  Google Scholar 

  • McCrorie, J., & Chambers, M. (2006). Granger causality and sampling of economic processes. Journal of Econometrics, 132, 311–336

    Article  MathSciNet  Google Scholar 

  • Reinsel, G. C. (1993). Elements of multivariate time series analysis. New York: Springer

    MATH  Google Scholar 

  • Stram, M., & Wei, W. (1986). Temporal aggregation on ARIMA models. Journal of Time Series Analysis, 7, 279–292

    Article  MATH  MathSciNet  Google Scholar 

  • Tiao, G. C. (1972). Asymptotic behaviour of temporal aggregates of time series. Biometrika, 59, 525–531

    Article  MATH  MathSciNet  Google Scholar 

  • Wei, W. (1981). Effects of systematic sampling on ARIMA models. Communications in Statistics: Theory and Methods, 10, 2389–2398

    Article  Google Scholar 

  • Weiss, A. (1984). Systematic sampling and temporal aggregation in time series models. Journal of Econometrics, 26, 271–281

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Di.S.E.S. Università degli Studi di Salerno, Via Ponte Don Melillo, 84084, Fisciano, SA, Italy

    Marcella Niglio

Authors
  1. Alessandra Amendola
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marcella Niglio
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cosimo Vitale
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marcella Niglio .

Editor information

Editors and Affiliations

  1. Fac. Economia, Università Macerata, Via Crescimbeni 20, Macerata, 62100, Italy

    Francesco Palumbo

  2. Dipto. Matematica e Statistica, Università Federico II di Napoli, Via Cinthia (Monte S. Angelo), Napoli, 80126, Italy

    Carlo Natale Lauro

  3. Depto. Economía y Empresa, Universitat Pompeu Fabra, Ramon Trias Fargas 25-27, Barcelona, 08005, Spain

    Michael J. Greenacre

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Amendola, A., Niglio, M., Vitale, C. (2010). Temporal Aggregation and Closure of VARMA Models: Some New Results. In: Palumbo, F., Lauro, C., Greenacre, M. (eds) Data Analysis and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03739-9_49

Download citation

Publish with us

Policies and ethics

Search

Navigation