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Simultaneous estimation of stable parameters for multiple autoregressive processes from datasets of nonuniform sizes

Author

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  • Lederer, Johannes

    (Universität Hamburg)

  • von Sachs, Rainer

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

We develop a finite-sample theory for estimating the coefficients and for the prediction of multiple stable autoregressive processes that (i) share an unknown lag order but (ii) can differ in their individual sample sizes. Our technique is based on penalisation similar to hierarchical, overlapping group-Lasso but requires a new mathematical set-up to accommodate (i) and (ii). The set-up differs from existing work considerably, for example, in that we estimate the common lag order directly from the data rather than using extrinsic criteria. We prove that the estimated autoregressive processes enjoy stability, and we establish rates for both the estimation and prediction error that can outmatch the known rates in our setting. Our insights on the lag selection and the stability are also of interest for the case of individual autoregressive processes.

Suggested Citation

  • Lederer, Johannes & von Sachs, Rainer, 2024. "Simultaneous estimation of stable parameters for multiple autoregressive processes from datasets of nonuniform sizes," LIDAM Reprints ISBA 2024040, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2024040
    Note: In: Journal of Time Series Analysis, 2025
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