Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지
DOI QR코드

DOI QR Code

The research on daily temperature using continuous AR model

일별 온도의 연속형 자기회귀모형 연구 - 6개 광역시를 중심으로 -

  • Kim, Ji Young (School of Law, Public Administration and Economics, The Catholic University of Korea) ;
  • Jeong, Kiho (School of Economics and Trade, Kyungpook National University)
  • 김지영 (가톨릭대학교 법정경학부 경제학전공) ;
  • 정기호 (경북대학교 경제통상학부)
  • Received : 2013.12.03
  • Accepted : 2014.01.10
  • Published : 2014.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

This study uses a continuous autoregressive (CAR) model to analyze daily average temperature in six Korean metropolitan cities. Data period is Jan. 1, 1954 to Dec. 31, 2010 covering 57 years. Using a relative long time series reveals that the linear time trend components are all statistically significant in the six cities, which was not shown in previous studies. Particularly the plus sign of its coefficient implies the effect on Korea of the global warming. Unit-root test results are that the temperature time series are stationary without unit-root. It turns out that CAR(3) is suitable for stochastic component of the daily temperature. Since developing suitable continuous stochastic model of the underlying weather related variables is crucial in pricing the weather derivatives, the results in this study will likely prove useful in further future studies on pricing weather derivatives.

본 연구는 기후파생상품의 가격결정 연구를 위한 중간과정으로서 우리나라 일별 평균기온에 대한 연속형 시계열 모형을 추정한다. 6개 광역도시를 대상으로 1954년 1월 1일부터 2010년 12월 31일까지의 57년간 일별 기온 시계열을 추세, 계절성, 불규칙 변동으로 구분하여 분석하였다. 특히 불규칙 성분은 연속형 자기회귀모형을 적용하였다. 분석결과, (1) 57년의 비교적 장기간 온도 시계열을 적용함으로써, 우리나라 선행연구의 결과와는 다르게 추세 성분이 통계적 유의성을 갖는 것으로 나타났다. 특히 추세성분의 기울기가 양의 부호를 가짐으로써 지구온난화의 추이가 우리나라에서 진행 중임을 보였다. (2) 추세와 계절성분이 제거된 불규칙성분에 대해 단위근 검정을 적용한 결과, 6개 광역시 모두에 대해 단위근이 없는 안정적인 것으로 나타났다. (3) 불규칙 성분에 대해 연속형 모형인 CAR모형을 적용한 결과, 차수가 3인 CAR(3)가 적합한 것으로 나타났으며 이러한 결과는 국외문헌의 결과와도 일치한다. 파생상품의 가격결정에는 기초자산의 연속형 시계열 모형의 개발이 가장 중요하므로 본 연구의 결과는 기후파생상품의 가격결정 연구에 활용될 수 있을 것이다.

Keywords

References

  1. Alaton, P., Djehiche, B. and Stillberger, D. (2002). On modelling and pricing weather derivatives. Applied Mathematical Finance, 9, 1-20. https://doi.org/10.1080/13504860210132897
  2. Bae, G. and Jeong, J. (2009). Model of pricing weather derivatives. Korean Journal of Futures and Options, 17, 49-66.
  3. Benth, F. S. and Saltyte-Benth, J. (2005a). Stochastic modelling of temperature variations with a view towards weather derivatives. Applied Mathematical Finance, 12, 53-85. https://doi.org/10.1080/1350486042000271638
  4. Benth, F. E. (2007). Putting a price on temperature derivatives. Scandinavian Journal of Statistics, 34, 746-767.
  5. Benth, F. E., Saltyte-Benth, J. and Janlinskas, P. (2007). A spiral temporal model for temperature with seasonal variance. Journal of Applied Statistics, 34, 823-841. https://doi.org/10.1080/02664760701511398
  6. Caballero, R., Jewson, S. and A. Brix, A. (2002). Long memory in surface air temperature detection, modeling and application to weather derivative valuation. Climate Research, 21, 127-140. https://doi.org/10.3354/cr021127
  7. Campbell, S. and Diebold, F. (2002). Weather forecasting for weather derivatives, Working paper, Rodney White Center for Financial Research, University of Pennsylvania, U.S.A.
  8. Campbell, S. and Diebold, F. (2005). Weather forecasting for weather derivatives. Journal of the American Statistical Association, 100, 6-16. https://doi.org/10.1198/016214504000001051
  9. Cao, M. and Wei, J. (2000). Equilibrium valuation of weather derivatives, Working paper, University of Toronto.
  10. Chan, K., Karolyi, G., Longstaff, F. and Sanders, B. (1992), An empirical comparison of alternative models of short-term interest rate. Journal of Finance, 47, 1209-1228 https://doi.org/10.1111/j.1540-6261.1992.tb04011.x
  11. Choi, H. and Lim, D. (2013). Bankruptcy prediction using ensemble svm model. Jounal of the Korean Data & Information Science Society, 24, 113-1125. https://doi.org/10.7465/jkdi.2013.24.6.1113
  12. Dischel, B. (1998a). Black-Scholes won't do. Energy and Power Risk Management, 8-9.
  13. Dischel, B. (1998b). At last: A model for weather risk. Energy and Power Risk Management, 20-21.
  14. Dornier, F. and Queruel, M. (2000). Caution to the wind, weather risk special report. Energy and Power Risk Management Risk Magazine, 30-32.
  15. Gillespie, D. (1996). Exact numerical simulation of the Orstein-Uhlenbeck process and its integral. Physical Review, 54, 2084-2091.
  16. Hardle, W. and Osipenko, M. (2011). Spatial risk premium on weather derivatives and hedging weather exposure in electricity. The Energy Journal, 33, 149-170.
  17. Hardle, W. and Cabrera, B. L. (2012). Implied market price of weather risk. Applied Mathematical Finance, 19, 59-95. https://doi.org/10.1080/1350486X.2011.591170
  18. Hull, J. and White, A. (1990). Pricing interest-rate derivative securities. Review of Financial Studies, 3, 573-592. https://doi.org/10.1093/rfs/3.4.573
  19. Hull, J. and White, A. (1996). Using Hull-White interest rate trees. Journal of Derivatives, 3, 26-36. https://doi.org/10.3905/jod.1996.407949
  20. Ichihara, K. and Kunita, H. (1974). A classification of the second order degenerate elliptic operators and its probabilistic characterization. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 30, 235-254. https://doi.org/10.1007/BF00533476
  21. Kim, M. and Kim, J. (2004). Study on pricing weather option. Korea Financial Engineering Society, 1-26.
  22. Kim, H. and Kim, T. (1992). Stochastic model of winter temperature in Seoul. The Korean Journal of Applied Statistics, 5, 59-80.
  23. Kim, H. and Lee, Y. (2013). A study on the density analysis of climatological stations using the correlation integral method in the fractal dimension. Jounal of the Korean Data & Information Science Society, 24, 53-62. https://doi.org/10.7465/jkdi.2013.24.1.53
  24. Lee, J. (2002). A Study on the v aluation of the CDD/HDD weather options. Korean Journal of Financial Studies, 31, 229-255.
  25. Phillips, A. W. (1959). The estimation of parameters in systems of stochastic differential equations. Biometrika, 46, 67-76. https://doi.org/10.1093/biomet/46.1-2.67
  26. Shim, J. and Lee, J. (2009). Kernel method for autoregressive data. Jounal of the Korean Data & Information Science Society, 20, 949-964.
  27. Shim, J. and Hwang, C. (2013). Expected shortfall estimation using kernel machines. Jounal of the Korean Data & Information Science Society, 24, 625-636. https://doi.org/10.7465/jkdi.2013.24.3.625
  28. Syroka, D. J. and Toumi, R. (2001). Scaling and persistence in observed and modelled surface temperature. Geophysical Research Letters, 28, 3255-3259. https://doi.org/10.1029/2000GL012273

Cited by

  1. A study on the slope sign test for explosive autoregressive models vol.26, pp.4, 2015, https://doi.org/10.7465/jkdi.2015.26.4.791
  2. A statistical prediction for concentrations of Manganese in the ambient air vol.27, pp.3, 2016, https://doi.org/10.7465/jkdi.2016.27.3.577
  3. A study on the relationship between the onshore and offshore Chinese Yuan markets vol.26, pp.6, 2015, https://doi.org/10.7465/jkdi.2015.26.6.1387