تحلیل داده های فضایی-زمانی: مطالعه موردی داده های میانگین سرعت باد روزانه استان زنجان

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه آمار، دانشگاه آزاد اسلامی، واحد علوم و تحقیقات

2 گروه آمار، دانشگاه زنجان

چکیده

در این مقاله، ابتدا مبانی نظری مدلسازی نیمه طیفی مطالعه شده و به توصیف چند خاصیت از مدل های نیمه طیفی اخیر پرداخته می شود. سپس یک روش برای برآورد تابع کوواریانس فضایی-زمانی در حالت نیمه-طیفی پیشنهاد شده است. به منظور ارزیابی عملکرد مدل های نیمه طیفی ارائه شده، دو شبیه سازی انجام گرفته که در هرکدام از آنها روش برآورد پیشنهادی با سایر روش ها مقایسه شده است. روش مورد نظر موفقیت زیادی نسبت به سایر روش ها بخصوص برای مجموعه مشاهدات بزرگ داشته است. سرانجام برای داده های واقعی مربوط به متوسط روزانه سرعت باد در استان زنجان از روش پیشنهادی استفاده شده است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Analysis of Spatial-Temporal data: the Case Study of Zanjan Daily mean Wind Speed Data

نویسندگان [English]

  • Ali Shahnavaz 1
  • Ali M. Mosammam 2
  • Mohammad Hassan Behzadi 1
1 Department of Statistics. Science and Research Branch. Islamic Azad University. Tehran. Iran
2 Department of Statistics. University of Zanjan. Zanjan. Iran
چکیده [English]

In this paper, we first study the theory of the spatial-temporal half spectral modelling and describe some properties of recently proposed half spectral models. Next, we propose an estimation method for the estimation of spatial-temporal covariance functions in the half-spectral setting. To assess the performance of the proposed half-spectral models, we conduct two simulations. in which we compare the proposed fitting approach with respect to the other classical estimation methods. The proposed methods have great success in fitting parametric space-time covariance functions specifically for massive data sets. Finally, we apply the proposed methods for a real daily wind speed data in Zanjan, Iran.

کلیدواژه‌ها [English]

  • Space-time model
  • Half-spectral model
  • Whittle likelihood
[1] Shumway, R.H. and Stoffer, D.S. (2017). Time Series Analysis and its Applications with R Examples. 4th ed., Springer Texts in Statistics, Springer, Cham.
[2] Chilès, J.P. and Delfner, P. (2012). Geostatistics: Modeling Spatial Uncertainty. 2nd ed., Wiley, New York.
[3] Cressie, N. and Wikle, C.K. (2013). Statistics for spatio-temporal data, John Wiley and Sons.
[4] Cressie, N. (1993). Statistics for spatial data, New York: John Willey and Sons.
[5] Bochner, S. (1955). Harmonic analysis and the theory of probability. University of California Press, Berkeley and Los Angeles.
[6] Cressie, N. and Huang, H.C. (1999). Classes of nonseparable, spatio-temporal stationary covariance functions. J. Amer. Statist. Assoc., 94, 1330-1340.
[7] Kammler, D.W. (2007). A first course in Fourier analysis. 2nd ed., Cambridge University Press, Cambridge.
[8] Gneiting, T. (2002). Nonseparable stationary covariance functions for space-time data. J. Amer. Statist. Assoc., 97, 590-600.
[9] Kent, J.T., Mohammadzadeh, M. and Mosammam, A.M. (2011). The dimple in Gneiting's spatial-temporal covariance model. Biometrika, 98, 489-494.
[10] Omidi, M. and Mohammadzadeh, M. (2015). A New Method to Build Spatio-Temporal Covariance Functions: Analysis of Ozone Data. Statistical Papers, 57, 689–703.
[11] Horrell, M.T. and Stein, M.L. (2017). Half-spectral space-time covariance models. Spat. Stat., 19, 90-100.
[12] Stein, M.L. (2005). Statistical methods for regular monitoring data. J. R. Stat. Soc. Ser. B Stat.Methodol., 67, 667-687
[13] Rodr'iguez-Iturbe, I. and Meji'a, J.M. (1974). The design of rainfall networks in time and space. WaterResources Research, 10, 713-728.
[14] Stein, M.L. (2011). When does the screening effect not hold?. Ann. Statist., 39, 2795-2819
[15] Journel, A.G. and Huijbregts, C.J. (1978). Mining geostatistics. Academic press.
[16] Mosammam, A.M. and Kent, J.T. (2016). Estimation and testing for covariance-spectral spatial-temporal models. Environ. Ecol. Stat., 23, 43-64.
[17] Mardia, K.V. and Marshall, R.J. (1984). Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika, 71, 135-146.
[18] Cressie, N. (1985). Fitting variogram models by weighted least squares. Journal of the International Association for Mathematical Geology, 17, 563-586.
[19] Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems with discussion. Journal of the Royal Statistical Society, no. Series B, 192-236.
[20] Whittle, P. (1954). On stationary processes in the plane. Biometrika, 41, 434-449.
[21] Whittle, P. (1954). On stationary processes in the plane. Biometrika, 41, 434-449.
[22] Sahu, S.K.G., Gelfand, A.E., Holland, D.M. and Mardia, K. (2006). Spatio-Temporal modeling of fine particulate matter. Journal of Agricultural, Biological and Environmental Statistics, 11, 61-86.
[23] Huang, H.C., Martinez, F., Mateu, J and Montes, F. (2007). Model comparison and selection for stationary space-time models. Computational statistics and data analysis, 51, 4577-4596.
[24] Cleveland, W.S. (1981). LOWESS: A program for smoothing scatterplots by robust locally weighted regression. The American Statistician 35, 54
[25] Hoeting, J.A., Davis, R. A., Merton, A. A., & Thompson, S. E. (2006). Model selection for geostatistical models. Ecological Applications, 16(1), 87-98.
[26] Lee, H., and Ghosh, S.K. (2009). Performance of information criteria for spatial models. Journal of statistical computation and simulation, 79(1), 93-106.
[27] Huang, H.C., Martinez, F., Mateu, J., and Montes, F. (2007). Model comparison and selection for stationary space–time models. Computational Statistics & Data Analysis, 51(9), 4577-4596.
[28] امیدی، مهدی، محمدزاده، محسن (1392). تعیین ساختار همبستگی داده­های فضایی با توابع مفصل، نشریه علوم دانشگاه خوارزمی، 3، شماره 3، صص797-808.