I am reading an article that mentions Periodic Autorregressive Multivariate Models and their noises; however, in no section have the authors explained or shown references to these models.

I looked for references online, but so far I could not find a single reliable source for more information about these models.

Do you know of any site or book with an accurate description of this family of models and their applications?

Thank you.

  • $\begingroup$ It could also be that the authors are referring to periodic multivariate autoregressive model MPAR (p). $\endgroup$
    – Jxson99
    Jun 22, 2016 at 13:40

1 Answer 1


See for instance PARMA Models with Applications in R, Dudek et al (2015), which explains how Periodic autoregressive–moving-average models (periodic ARMA models, PARMA models) are used to model non-stationary time series with periodic structure. The book aims to provide appropriate tools for the complete analysis of periodic time series using PARMA modelling and to popularize this approach among non-specialists.

In addition, there is Periodic Autoregressive Time Series Models in R: The partsm Package by Lopez-Lacalle (2005) that introduces the package and references:

Franses, P. and Paap, R. (2004), Periodic Time Series Models, Advanced Texts in Econometrics. Oxford University Press

See also Chapter 17 'Periodic VAR Processes and Intervention Models' in New Introduction to Multiple Time Series Analysis by Helmut Lutkepohl (2005), which discusses time-varying coefficients for multivariate time series, and co-integrated VAR models in particular.

From an applied perspective, see Forecasting with Prediction Intervals for periodic ARMA Models by Anderson et al (2013) on prediction with further references.

  • 1
    $\begingroup$ Thanks a lot for your answer, Stefan. It truly helped me! $\endgroup$
    – Jxson99
    Jun 22, 2016 at 14:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.