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Time Series Seasonal Adjustment Using Regularized Singular Value Decomposition

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  • Wei Lin
  • Jianhua Z. Huang
  • Tucker McElroy

Abstract

We propose a new seasonal adjustment method based on the Regularized Singular Value Decomposition (RSVD) of the matrix obtained by reshaping the seasonal time series data. The method is flexible enough to capture two kinds of seasonality: the fixed seasonality that does not change over time and the time-varying seasonality that varies from one season to another. RSVD represents the time-varying seasonality by a linear combination of several seasonal patterns. The right singular vectors capture multiple seasonal patterns, and the corresponding left singular vectors capture the magnitudes of those seasonal patterns and how they change over time. By assuming the time-varying seasonal patterns change smoothly over time, the RSVD uses penalized least squares with a roughness penalty to effectively extract the left singular vectors. The proposed method applies to seasonal time-series data with a stationary or nonstationary nonseasonal component. The method also has a variant that can handle the case that an abrupt change (i.e., break) may occur in the magnitudes of seasonal patterns. Our proposed method compares favorably with the state-of-art X-13ARIMA-SEATS program on both simulated and real data examples.

Suggested Citation

  • Wei Lin & Jianhua Z. Huang & Tucker McElroy, 2020. "Time Series Seasonal Adjustment Using Regularized Singular Value Decomposition," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 487-501, July.
    • Handle: RePEc:taf:jnlbes:v:38:y:2020:i:3:p:487-501
    DOI: 10.1080/07350015.2018.1515081
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    Cited by:

    1. In Choi, 2023. "Does climate change affect economic data?," Empirical Economics, Springer, vol. 64(6), pages 2939-2956, June.
    2. Tucker McElroy & Anindya Roy, 2022. "A Review of Seasonal Adjustment Diagnostics," International Statistical Review, International Statistical Institute, vol. 90(2), pages 259-284, August.
    3. Webel, Karsten, 2022. "A review of some recent developments in the modelling and seasonal adjustment of infra-monthly time series," Discussion Papers 31/2022, Deutsche Bundesbank.
    4. Malgorzata Grzywinska-Rapca & Aleksandra A. Olejarz, 2021. "The Level of Economic Development and the Savings Rate of Households," European Research Studies Journal, European Research Studies Journal, vol. 0(2B), pages 430-442.
    5. McElroy, Tucker S. & Jach, Agnieszka, 2023. "Identification of the differencing operator of a non-stationary time series via testing for zeroes in the spectral density," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).

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