The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Banded vector heterogeneous autoregression models

밴드구조 VHAR 모형

  • Sangtae Kim (Department of Statistics, Sungkyunkwan University) ;
  • Changryong Baek (Department of Statistics, Sungkyunkwan University)
  • 김상태 (성균관대학교 통계학과) ;
  • 백창룡 (성균관대학교 통계학과)
  • Received : 2023.04.11
  • Accepted : 2023.06.21
  • Published : 2023.12.31
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Abstract

This paper introduces the Banded-VHAR model suitable for high-dimensional long-memory time series with band structure. The Banded-VHAR model has nonignorable correlations only with adjacent dimensions due to data features, for example, geographical information. Row-wise estimation method is adapted for fast computation. Also, two estimation methods, namely BIC and ratio methods, are proposed to estimate the width of band. We demonstrate asymptotic consistency of our proposed estimation methods through simulation study. Real data applications to pm2.5 and apartment trading volume substantiate that our Banded-VHAR model outperforms traditional sparse VHAR model in forecasting and easy to interpret model coefficients.

본 논문에서는 장기 기억성을 가지는 고차원 시계열 데이터 분석에 유용한, 밴드 구조의 계수행렬들을 가지는 밴드구조 VHAR (Banded-VHAR) 모형을 제안한다. 밴드구조 VHAR 모형은 인접한 차원의 시계열에서만 상관구조를 가지는 성근 고차원 시계열 모형으로 밴드구조에 영향을 주는 요인으로는 대표적으로 지리적 특성이 있다. 밴드구조 VHAR 모형의 빠른 추정을 위해 본 논문은 행별추정방법을 사용하고 또 밴드의 크기를 추정하기 위해 BIC와 잔차제곱합의 비율을 이용한 추정 방법을 소개하였다. 더불어 모의 실험을 통해서 제안한 추정 방법의 점근적 일치성을 확인하였다. 실증자료 분석으로 지역별 초미세먼지 및 아파트 거래량 자료를 활용하여 모형을 적용한 결과 밴드구조 VHAR 모형이 표본외예측 능력의 우수하고, 지리적정보에 기반하여 모형의 해석이 용이하다는 큰 장점이 있음을 살펴보았다.

Keywords

Acknowledgement

이 논문은 한국연구재단의 지원을 받아 수행된 기초연구 사업임 (NRF-2022R1F1A1066209).

References

  1. Baek C and Park M (2021). Sparse vector heterogeneous autoregressive modeling for realized volatility, Journal of the Korean Statistical Society, 50, 495-510. https://doi.org/10.1007/s42952-020-00090-5
  2. Cavalcante L, Bessa RJ, Reis M, and Browell J (2017). Lasso vector autoregression structures for very short-term wind power forecasting, Wind Energy, 20, 657-675. https://doi.org/10.1002/we.2029
  3. Corsi F (2009). A simple approximate long-memory model of realized volatility, Journal of Financial Econometrics, 7, 174-196. https://doi.org/10.1093/jjfinec/nbp001
  4. Cubadda G, Guardabascio B, and Hecq A (2017). A vector heterogeneous autoregressive index model for realized volatility measures, International Journal of Forecasting, 33, 337-344. https://doi.org/10.1016/j.ijforecast.2016.09.002
  5. Engle RF and Marcucci J (2006). A long-run pure variance common features model for the common volatilities of the Dow Jones, Journal of Econometrics, 132, 7-42. https://doi.org/10.1016/j.jeconom.2005.01.021
  6. Gao Z, Ma Y, Wang H, and Yao Q (2019). Banded spatio-temporal autoregressions, Journal of Econometrics, 208, 211-230. https://doi.org/10.1016/j.jeconom.2018.09.012
  7. Guo S, Wang Y, and Yao Q (2016). High-dimensional and banded vector autoregressions, Biometrika, 103, 889-903. https://doi.org/10.1093/biomet/asw046
  8. Hyndman RJ and Khandakar Y (2008). Automatic time series forecasting: The forecast package for R, Journal of Statistical Software, 27, 1-22. https://doi.org/10.18637/jss.v027.i03
  9. Lam C and Yao Q (2012). Factor modeling for high-dimensional time series: Inference for the number of factors, The Annals of Statistics, 40, 694-726. https://doi.org/10.1214/12-AOS970
  10. Lutkepohl H (2005). New Introduction to Multiple Time Series Analysis, Springer Science & Business Media, Berlin.
  11. Ray BK and Tsay RS (2000). Long-range dependence in daily stock volatilities, Journal of Business & Economic Statistics, 18, 254-262.
  12. Wang H, Luo X, and Ling L (2021). Semiparametric spatio-temporal models with unknown and banded autoregressive coefficient matrices, Mathematical Methods in the Applied Sciences, 30 December 2021, 1-31. https://doi.org/10.1002/mma.8053
  13. Zheng Y and Cheng G (2020). Finite-time analysis of vector autoregressive models under linear restrictions, Biometrika, 108, 469-489. https://doi.org/10.1093/biomet/asaa065