Accounting seasonal nonstationarity in time series models for short-term ozone level forecast (original) (raw)

Abstract

Due to the nonlinear feature of a ozone process, regression based models such as the autoregressive models with an exogenous vector process (ARX) suffer from persistent diurnal behaviors in residuals that cause systematic over-predictions and under-predictions and fail to make accurate multi-step forecasts. In this article we present a simple class of the functional coefficient ARX (FARX) model which allows the regression coefficients to vary as a function of another variable. As a special case of the FARX model, we investigate the threshold ARX (TARX) model of Tong [Lecture notes in Statistics, Springer-Verlag, Berlin, 1983; Nonlinear time series: a dynamics system approach, Oxford University Press, Oxford, 1990] which separates the ARX model in terms of a variable called the threshold variable. In this study we use time of day as the threshold variable. The TARX model can be used directly for ozone forecasts; however, investigation of the estimated coefficients over the threshold regimes suggests polynomial coefficient functions in the FARX model. This provides a parsimonious model without deteriorating the forecast performance and successfully captures the diurnal nonstationarity in ozone data. A general linear _F_-test is used to test varying coefficients and the portmanteau tests, based on the autocorrelation and partial autocorrelation of fitted residuals, are used to test error autocorrelations. The proposed models were applied to a 2 year dataset of hourly ozone concentrations obtained in downtown Cincinnati, OH, USA. For the exogenous processes, outdoor temperature, wind speed, and wind direction were used. The results showed that both TARX and FARX models substantially improve one-day-ahead forecasts and remove the diurnal pattern in residuals for the cases considered.

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References

• Akaike H (1974) A new look at statistical model identification. IEEE Trans Automat Contr AC-19:716–723
  Google Scholar
• Bauer G, Deistler M, Scherrer W (2001) Time series models for short term forecasting of ozone in the eastern part of Austria. Environmetrics 12:117–130
  Google Scholar
• Bloomfield P, Royle JA, Steinberg LJ, Yang Q (1996) Accounting for meteorological effects in measuring urban ozone levels and trends. Atmos Environ 30(17):3067–3077
  Google Scholar
• Box GEP, Jenkins GM (1976) Time series analysis:forecasting and control, revised edn. Holden Day, San Francisco
  Google Scholar
• Cai Z, Fan J, Li R (2000) Efficient estimation and inferences for varying-coefficient models. J Am Stat Assoc 95:888–902
  Google Scholar
• Chen R, Tsay R (1993) Functional-coefficient autoregressive models. J Am Stat Assoc 88:298–308
  Google Scholar
• Cleveland WS, Grosse E, Shyu WM (1991) Local regression models. Statistical Models in S, 309–376, Wadsworth, Pacific Grove
• Damon J, Guillas S (2002) The inclusion of exogeneous variables in functional autoregressive ozone forecasting. Environmetrics 13:759–774
  Google Scholar
• Davis MD, Deistler M (1998) Modeling ozone in the Chicago urban area. In: Nychka D, Piegorsch W, Cox LH (eds) Case Studies in Environmental Statistics, Lecture Notes in Statistics. Springer, Berlin
• Fan J, Zhang W (1999) Statistical estimation in varying coefficient models. Ann Stat 27:1491–1518
  Google Scholar
• Fasso A, Negri I (2002) Non-linear statistical modeling of high frequency ground ozone data. Environmetrics 13:225–241
  Google Scholar
• Fiester U, Balzer K (1991) Surface ozone and meteorological predictors on a subregional scale. Atmos Environ 25:1781–1790
  Google Scholar
• Hastie TJ, Tibshirani RJ (1993) Varying-coefficient models (with discussion). J R Stat Soc B 55:757–796
  Google Scholar
• Hui K-J (1992) Time series of the analysis of the interdependence among air pollutants. Atmos Environ 26:491–503
  Google Scholar
• Kumar A, Bellam N, Sud A (1999) Performance of industrial source complex model in predicting long-term concentrations in an urban area. Environ Prog 18(2):93–100
  Google Scholar
• Ljung GM, Box GEP (1978) On a measure of lack of fit in time series models. Biometrika 65:297–303
  Google Scholar
• Meng Z, Dadub D, Seinfeld JH (1997) Chemical coupling between atmospheric ozone and particulate matter. Science 227:116–119
  Google Scholar
• Merz PH, Painter LG, Ryason PR (1972) Aerometric data analysis. Time series analysis and forecast and an atmospheric smog diagram. Atmos Environ 6:319–342
  Google Scholar
• Millionis M, Davies TD (1994) Regression and stochastic models for air pollution-I. Review, comments and suggestion. Atmos Environ 28(17):2801–2810
  Google Scholar
• Monti AC (1994) A proposal for residual autocorrelation test in linear models. Biometrika 81:776–780
  Google Scholar
• Schwarz F (1978) Estimating the dimension of a model. Ann Stat 6:461–464
  Google Scholar
• Seinfeld JH (1998) Ozone air quality models:a critical review. J Atmos Pollut Control Assoc 38:616–647
  Google Scholar
• Simpson RW, Layton AP (1983) Forecasting peak ozone levels. Atmos Environ 17:1644–1654
  Google Scholar
• Tong H (1983) Threshold models in non-linear time series analysis. In: Brillinger D, Fienberg J, Gani J, Hartigan J, Krickberg K (eds) Lecture Notes in Statistics. Springer-Verlag, Berlin
• Tong H (1990) Nonlinear time series: a dynamic system approach. Oxford University Press, Oxford
  Google Scholar

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Acknowledgements

The authors wish to express thanks to Anna Kelley with HCDOES for providing us with the data. Thanks also to the three reviewers who made very helpful comments on this manuscript.

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Authors and Affiliations

1. Department of Mathematical Sciences, University of Cincinnati, ML 0025, Cincinnati, OH, 45221-0025, USA
   Sung Eun Kim
2. Department of Civil Engineering, University of Toledo, Toledo, OH, 43606-3390, USA
   Ashok Kumar

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1. Sung Eun Kim
2. Ashok Kumar

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Correspondence toSung Eun Kim.

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Kim, S.E., Kumar, A. Accounting seasonal nonstationarity in time series models for short-term ozone level forecast.Stoch Environ Res Ris Assess 19, 241–248 (2005). https://doi.org/10.1007/s00477-004-0228-y

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• Published: 09 February 2005
• Issue date: October 2005
• DOI: https://doi.org/10.1007/s00477-004-0228-y

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