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Forecasting pollen concentration by a two-step functional model. (English) Zbl 1192.62254
Summary: A functional regression model to forecast the cypress pollen concentration during a given time interval, considering the air temperature in a previous interval as the input, is derived by means of a two-step procedure. This estimation is carried out by functional principal component (FPC) analysis and the residual noise is also modeled by FPC regression, taking as the explicative process the pollen concentration during the earlier interval. The prediction performance is then tested on pollen data series recorded in Granada (Spain) over a period of 10 years.

62P12 Applications of statistics to environmental and related topics
62H25 Factor analysis and principal components; correspondence analysis
62N02 Estimation in survival analysis and censored data
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[1] Aguilera, Forecasting binary longitudinal data by a functional PC-ARIMA model, Computational Statistics and Data Analysis 52 pp 3187– (2008) · Zbl 1452.62691
[2] Aguilera, An approximated principal component prediction model for continuous-time stochastic processes, Applied Stochastic Models and Data Analysis 13 pp 61– (1997) · Zbl 0885.62109
[3] Aguilera, Forecasting time series by functional PCA. Discussion of several weighted approaches, Computational Statistics 14 pp 443– (1999a) · Zbl 0941.62102
[4] Aguilera, Forecasting with unequally spaced data by a functional principal component approach, Test 8 pp 233– (1999b) · Zbl 0945.62095
[5] Brockwell, ITSM 2000 Professional Version 6.0 (1999)
[6] Brumback, Smothing spline models for the analysis of nested and crossed samples of curves, Journal of the American Statistical Association 93 pp 961– (1998) · Zbl 1064.62515
[7] Brumback, Transitional regression models, with application to environmental time series, Journal of the American Statistical Association 95 pp 16– (2000)
[8] Chen, Bayesian predictive inference for time series count data, Biometrics 56 pp 678– (2000) · Zbl 1060.62508
[9] Coull, Simple incorporation of interactions into additive models, Biometrics 57 pp 539– (2001) · Zbl 1209.62352
[10] Fornaciari, A regression model for the start of the pollen season in Olea europaea, Grana 37 pp 110– (1998)
[11] Galán, The role of temperature in the onset of the Olea europaea l. pollen season in southwestern Spain, International Journal of Biometeorology 45 pp 8– (2001)
[12] Galán, Model for forecasting Olea europaea l. airborne pollen in south-west Andalusia, Spain, International Journal of Biometeorology 45 pp 59– (2001)
[13] Hall, On properties of functional principal component analysis, Journal of the Royal Statistical Society, Series B 68 pp 109– (2006) · Zbl 1141.62048
[14] He, Functional canonical analysis for square integrable stochastic processes, Journal of Multivariate Analysis 85 pp 54– (2003) · Zbl 1014.62070
[15] Müller, Time-varying functional regression for predicting remaining lifetime distributions from longitudinal trajectories, Biometrics 61 pp 1064– (2005) · Zbl 1087.62129
[16] Ocaña, Functional principal component analysis by choice of norm, Journal of Multivariate Analysis 71 pp 262– (1999) · Zbl 0944.62059
[17] Ramsay, Functional Data Analysis (2005) · Zbl 1079.62006
[18] Smith, Constructing a 7-day ahead forecast model for grass pollen at north London, United Kingdom, Clinical and Experimental Allergy 35 pp 1400– (2005)
[19] Stark, Using meteorologic data to predict daily ragweed pollen levels, Aerobiologia 13 pp 177– (1997)
[20] Valderrama , M. J. Ocaña , F. A. Aguilera , A. M. 2002 Forecasting PC-ARIMA models for functional data Proceedings in Computational Statistics W. Härdle B. Rönz 25 36 International Association for Statistical Computing, Physica-Verlag
[21] Yao, Functional data analysis for sparse longitudinal data, Journal of the American Statistical Association 100 pp 577– (2005a) · Zbl 1117.62451
[22] Yao, Functional linear regression analysis for longitudinal data, Annals of Statistics 33 pp 2873– (2005b) · Zbl 1084.62096
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