The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Time Series Modelling of Air Quality in Korea: Long Range Dependence or Changes in Mean?

한국의 미세먼지 시계열 분석: 장기종속 시계열 혹은 비정상 평균변화모형?

  • 백창룡 (성균관대학교 통계학과)
  • Received : 2013.10.03
  • Accepted : 2013.11.14
  • Published : 2013.12.31
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Abstract

This paper considers the statistical characteristics on the air quality (PM10) of Korea collected hourly in 2011. PM10 in Korea exhibits very strong correlations even for higher lags, namely, long range dependence. It is power-law tailed in marginal distribution, and generalized Pareto distribution successfully captures the thicker tail than log-normal distribution. However, slowly decaying autocorrelations may confuse practitioners since a non-stationary model (such as changes in mean) can produce spurious long term correlations for finite samples. We conduct a statistical testing procedure to distinguish two models and argue that the high persistency can be explained by non-stationary changes in mean model rather than long range dependent time series models.

이 논문에서는 한국의 대기질을 결정하는 중요한 수치인 미세먼지(PM10)에 대한 통계적 고찰을 한다. 2011년 매시 관찰된 자료 분석을 토대로 미세먼지가 매우 높은 시차에서도 강한 양의 상관관계를 가지는 장기 종속 시계열의 특징을 보임을 밝힌다. 또한 주변분포는 꼬리가 두터운 모형으로서 로그-정규분포보다는 일반화 파레토 분포가 훨씬 더 자료를 잘 적합함을 보인다. 하지만 이러한 높은 상관관계는 종종 단순한 평균변화 모형에 의한 그럴듯싸한 가짜 효과에 기인하기도 하여 통계모형을 세우는데 많은 혼동을 준다. 따라서 이 논문에서는 강한 종속성이 장기 종속 시계열에 의한 것인지 아니면 비정상 평균변화에 의한 것인지 근본적인 물리적 모형에 대한 논의를 통계적인 가설 검정을 통해 살펴본다. 그 결과 미세먼지의 강한 종속성은 구조변화에의한 착시 효과임을 밝힌다.

Keywords

References

  1. Baek, C. and Pipiras, V. (2010). Estimation of parameters in heavy-tailed distribution when its second order tail exponent is known, Journal of Statistical Planning and Inference, 140, 1957-1967. https://doi.org/10.1016/j.jspi.2010.01.046
  2. Baek, C. and Pipiras, V. (2012). Statistical tests for a single change in mean against long-range dependence, Journal of Time Series Analysis, 33, 131-151. https://doi.org/10.1111/j.1467-9892.2011.00747.x
  3. Baek, C. and Pipiras, V. (2013). On distinguishing multiple changes in mean and long-range dependence using local Whittle estimation, submitted, Available from: http://web.skku.edu/crbaek.
  4. Csorgo, L. and Horvath, L. (1997). Limit Theorems in Change-point Analysis, Wiley & Sons Ltd., Chichester.
  5. Doukhan, P., Oppenheim, G. and Taqqu, M. (2003). Theory and Applications of Long-Range Dependence, Birkhauser Boston Inc., Boston.
  6. Diebold, F. and Inoue, A. (2001). Long memory and regime switching, Journal of Econometrics, 105, 131-159. https://doi.org/10.1016/S0304-4076(01)00073-2
  7. Geweke, J. and Porter-Hudak, S. (1983). The estimation and application of long memory time series models, Journal of Time Series Analysis, 4, 221-238. https://doi.org/10.1111/j.1467-9892.1983.tb00371.x
  8. Hurvich, C., Deo, R. and Brodsky, J. (1998). The mean squared error of Geweke and Porter-Hudak's estimator of the memory parameter, Journal of Time Series Analysis, 19, 19-46. https://doi.org/10.1111/1467-9892.00075
  9. Mandelbrot, B. (1997). A case against the lognormal distribution, In Fractals and Scaling in Finance, Springer, New York.
  10. Pan, J. and Chen, S. (2008). Monitoring long-memory air quality data using ARFIMA model, Environmetrics, 19, 209-219. https://doi.org/10.1002/env.882
  11. Robinson, P. M. (1995a). Gaussian semiparametric estimation of long range dependence, The Annals of Statistics, 23, 1630-1661. https://doi.org/10.1214/aos/1176324317
  12. Robinson, P. M. (1995b). Log-periodogram regression of time series with long range dependence, The Annals of Statistics, 23, 1048-1072. https://doi.org/10.1214/aos/1176324636
  13. Varotsos, C., Ondov, J. and Efstathiou, M. (2005). Scaling properties of air pollution in Athens, Greece and Baltimore, Maryland, Atmospheric Environment, 39, 1352-2310.
  14. Yang, K.-L. (2002). Spatial and seasonal variation of PM10 mass concentrations in Taiwan, Atmospheric Environment, 36, 3403-3411. https://doi.org/10.1016/S1352-2310(02)00312-6
  15. Windsor, H. and Toumi, R. (2001). Scaling and persistence of UK pollution, Atmospheric Environment, 35, 4545-4556. https://doi.org/10.1016/S1352-2310(01)00208-4

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