BibTex RIS Cite

Detection of Whether The Autocorrelated Meteorological Time Series Have Stationarity by Using Unit Root Approach: The Case of Tokat

Year 2005, Volume: 2005 Issue: 1, 45 - 53, 01.06.2005

Abstract

This paper presents methodologies on detecting nonstationarity and removing nonstationarity by differencing for the autocorrelated time series. For this purpose, 5-year daily temperature, light intensity and relative humidity data from weather station in Tokat were used as materials. Since 5-year daily data sequences include many records, the new data sequences were constituted by averaging daily average temperature and relative humidity (average of records at 7.00, 14.00 and 21.00 in a day) and daily light intensity of five years. The existence of serial correlation between the averages from the mentioned climatic components was examined by using graphical approach, Ljung-Box Q and Runs tests. These three approaches imply that the averages have serial correlation. Unit root test (augmented Dickey and Fuller, ADF) was applied to test whether the averaged daily data sequences are nonstationary. The results of ADF emphasis the existence of nonstationarity in the daily data sequences. Similarly, the autocorrelation function graphs (correlogram) show nonstationarty, because of slowly decay in the autocorrelation functions for the daily data sequences. The first differencing was applied to remove nonstationary. After taking the first differencing, the ADF test results and the correlograms of the daily data sequences showed stationary.

References

  • Bayazıt, M., 1981.Hidrolojide İstatistik Yöntemler. İstanbul Teknik Üniversitesi, Yayın No : 1197, 223 s., İstanbul.
  • Box, G.E.P., and Jenkins, G.M., 1976. Time Series Analysis Forecasting and Control. Holden-Day, 575 p., San Francisco-USA.
  • Chow, V.T. 1964. Handbook of Applied Hydrology. McGraw-Hill Book Company, New York.
  • Cromwell, J.B., Labys, W.C. and Terraza, M., 1994. Univariate Tests for Time Series Models. A Sage Publications, Series/number: 07-99, 96 p., London.
  • Dickey, D.A. and Fuller, W.A., 1981. Likelihood Ratio Statistics for Autoregressive Time Series With A Unit Root. Econometrica, 49, 1057-1072.
  • Enders, W., 1995. Applied Econometric Time Series. John Wiley and Sons, Inc., 435 p., New York.
  • Ferguson T.S., Genest, C. and Hallin, M., 2000. Kendal’s Tau for Serial Dependence. The Canadian Journal of Statistics, 28, 587-604.
  • Gibbons, J.D., 1997. Nonparametric Methods for Quantitative Analysis. American Sciences Press, Inc.,537 p., Ohio-USA.
  • Greene, W.H., 2000. Econometric Analysis. Prentice Hall International, Inc., 1004 p., New Jersey-USA.
  • Gujarati, D.N., 2002. Basic Econometrics. McGraw-Hill, N.Y., Fourth Edition, 912 p., New York-USA.
  • Hipel, K.W., McLeod, A.I. and Lennox, W.C., 1977. Advances in Box-Jenkins Modeling 1. Model Construction. Water Resources Research, 13, 567- 575.
  • Huff, F.A. and Changnon, S.A., 1973. Precipitation Modification by Major Urban Areas. Bulletin American Meteorological Society, 54, 1220-1232.
  • Janacek, G., and Swift, L., 1993. Time Series Forecasting, Simulation, Application. Ellis Horwood, 331 p., New York-USA.
  • Ljung, G.M. and Box, G.E.P., 1978. On a Measure of Lack of Fit in Time Series Models. Biometrika, 65, 297-303.
  • McKinnon, J.G., 1990. Critical Values for Co-Integration Tests. UC San Diego Discussion Paper, 90-4.
  • Salas, J.D., Delleur, J.W., Yevjevich, V.M. and Lane, W.L., 1980. Applied Modeling of Hydrologic Time Series. Water Resources Publications, 484 p, Littleton, Colarado.
  • Wei, W.W.S., 1990. Time Series Analysis. Addison- Wesley Publishing Company, Inc., 478 P., New York-USA.
  • Wilson, E.M., 1990. Engineering Hydrology. Macmillan Press Ltd., 348 P., London.

Bağımlı Meteorolojik Zaman Serilerinde Durağanlığın Birim Kök Yaklaşımı ile Belirlenmesi: Tokat Örneği

Year 2005, Volume: 2005 Issue: 1, 45 - 53, 01.06.2005

Abstract

Bu çalışmanın amacı, bağımlı zaman serilerindeki değişimin saptanması ve bu değişimin fark dönüşümüyle giderilmesi ile ilgili metodolojileri sunmaktadır. Bu amaçla, Tokat meteoroloji istasyonunda ölçülen 5 yıllık günlük sıcaklık, güneşlenme şiddeti ve bağıl nem verisi materyal olarak kullanıldı. 5 yıllık ölçümler çok fazla veri içerdiğinden, günlük ortalama sıcaklık ve bağıl nem (7.00, 14.00 ve 21.00 ölçümlerinden elde edilen) ve 5 yıllık günlük güneşlenme şiddetinin ortalamaları alınarak yeni veri serileri oluşturuldu. Adı geçen bu iklim elemanlarından elde edilen ortalamalar arasındaki otokorelasyonun varlığı grafiksel yaklaşım, Ljung-Box Q istatistiği ve Runs test ile incelendi. Bu üç yaklaşım, ortalamaların otokorelasyona sahip olduğunu göstermektedir. Ortalama günlük veri serilerindeki değişimi test etmek için Birim kök testi (augmented Dickey and Fuller, ADF) uygulanmıştır. ADF test sonuçları günlük veri serilerinde değişimin olduğunu belirtmektedir. Benzer şekilde, günlük veri serileri için elde edilen otokorelasyon fonksiyonları yavaş azalım gösterdiğinden dolayı, otokorelasyon grafikleri (korrelogram) değişimi belirtiyor. Günlük veri serilerindeki değişimi gidermek için birinci fark dönüşümü uygulandı. Birinci fark dönüşümünden sonra, günlük veri serilerinin ADF test sonuçları ve korrelogramları durağanlığı göstermiştir.

References

  • Bayazıt, M., 1981.Hidrolojide İstatistik Yöntemler. İstanbul Teknik Üniversitesi, Yayın No : 1197, 223 s., İstanbul.
  • Box, G.E.P., and Jenkins, G.M., 1976. Time Series Analysis Forecasting and Control. Holden-Day, 575 p., San Francisco-USA.
  • Chow, V.T. 1964. Handbook of Applied Hydrology. McGraw-Hill Book Company, New York.
  • Cromwell, J.B., Labys, W.C. and Terraza, M., 1994. Univariate Tests for Time Series Models. A Sage Publications, Series/number: 07-99, 96 p., London.
  • Dickey, D.A. and Fuller, W.A., 1981. Likelihood Ratio Statistics for Autoregressive Time Series With A Unit Root. Econometrica, 49, 1057-1072.
  • Enders, W., 1995. Applied Econometric Time Series. John Wiley and Sons, Inc., 435 p., New York.
  • Ferguson T.S., Genest, C. and Hallin, M., 2000. Kendal’s Tau for Serial Dependence. The Canadian Journal of Statistics, 28, 587-604.
  • Gibbons, J.D., 1997. Nonparametric Methods for Quantitative Analysis. American Sciences Press, Inc.,537 p., Ohio-USA.
  • Greene, W.H., 2000. Econometric Analysis. Prentice Hall International, Inc., 1004 p., New Jersey-USA.
  • Gujarati, D.N., 2002. Basic Econometrics. McGraw-Hill, N.Y., Fourth Edition, 912 p., New York-USA.
  • Hipel, K.W., McLeod, A.I. and Lennox, W.C., 1977. Advances in Box-Jenkins Modeling 1. Model Construction. Water Resources Research, 13, 567- 575.
  • Huff, F.A. and Changnon, S.A., 1973. Precipitation Modification by Major Urban Areas. Bulletin American Meteorological Society, 54, 1220-1232.
  • Janacek, G., and Swift, L., 1993. Time Series Forecasting, Simulation, Application. Ellis Horwood, 331 p., New York-USA.
  • Ljung, G.M. and Box, G.E.P., 1978. On a Measure of Lack of Fit in Time Series Models. Biometrika, 65, 297-303.
  • McKinnon, J.G., 1990. Critical Values for Co-Integration Tests. UC San Diego Discussion Paper, 90-4.
  • Salas, J.D., Delleur, J.W., Yevjevich, V.M. and Lane, W.L., 1980. Applied Modeling of Hydrologic Time Series. Water Resources Publications, 484 p, Littleton, Colarado.
  • Wei, W.W.S., 1990. Time Series Analysis. Addison- Wesley Publishing Company, Inc., 478 P., New York-USA.
  • Wilson, E.M., 1990. Engineering Hydrology. Macmillan Press Ltd., 348 P., London.
There are 18 citations in total.

Details

Primary Language Turkish
Journal Section Research Articles
Authors

Kadri Yürekli This is me

Osman Çevik This is me

Publication Date June 1, 2005
Published in Issue Year 2005 Volume: 2005 Issue: 1

Cite

APA Yürekli, K., & Çevik, O. (2005). Bağımlı Meteorolojik Zaman Serilerinde Durağanlığın Birim Kök Yaklaşımı ile Belirlenmesi: Tokat Örneği. Journal of Agricultural Faculty of Gaziosmanpaşa University (JAFAG), 2005(1), 45-53.