ﻝﺪﻣ ﻭ ﻱﺯﺎﺳ ﺶﻴﭘ
ﻲﻨﻴﺑ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎﻌﻣ ﺱﺎﺳﺍ ﺮﺑ ﺯﺭﺍ ﺥﺮﻧ
ﻲﻓﺩﺎﺼﺗ
ﺴﻳﻭﺍﺪﺧ ﻦﺴﺣ ﻲ
١
*
ﺩﺎﺼﺘﻗﺍ ﻩﻭﺮﮔ ﺭﺎﻳﺩﺎﺘﺳﺍ ﻩﺪﻜﺸﻧﺍﺩ
ﻱ ﻪﻴﻣﻭﺭﺍ ﻩﺎﮕﺸﻧﺍﺩ ﺖﻳﺮﻳﺪﻣ ﻭ ﺩﺎﺼﺘﻗﺍ
H.khodavaisi@mail.urmia.ac.ir
ﻲﻣﺍﺮﻬﺑﻼﻣ ﺪﻤﺣﺍ
ﻪﻴﻣﻭﺭﺍ ﻩﺎﮕﺸﻧﺍﺩ ﺩﺎﺼﺘﻗﺍ ﺪﺷﺭﺍ ﺱﺎﻨﺷﺭﺎﻛ A.molabahrami@mail.urmia.ac.ir
ﺖﻓﺎﻳﺭﺩ ﺦﻳﺭﺎﺗ :
3 / 7 / 89 ﺵﺮﻳﺬﭘ ﺦﻳﺭﺎﺗ :
1 / 12 / 90
ﻩﺪﻴﻜﭼ ﺶﻴﭘ ﺍ ﺥﺮﻧ ﻲﺗﺁ ﺪﻧﻭﺭ ﻲﻨﻴﺑ ﺖـﻴﻤﻫﺍ ﺮﭘ ﺯﺍ ﻲﻜﻳ ﻥﺍﻮﻨﻋ ﻪﺑ ﺯﺭ
ﻱﺎـﻫﺮﻴﻐﺘﻣ ﻦﻳﺮﺗﺭﺍﺬـﮔﺮﻴﺛﺄﺗ ﻭ ﻦﻳﺮـﺗ
ﺶﻫﻭﮋﭘ ﺯﺍ ﻱﺭﺎﻴﺴﺑ ﻪﺟﻮﺗ ﺩﺭﻮﻣ ﻩﺭﺍﻮﻤﻫ ،ﻥﻼﻛ ﺩﺎﺼﺘﻗﺍ ﺖـﺳﺍ ﻩﺩﻮﺑ ﻥﺍﺮﮔ
. ﺭﻮـﻈﻨﻣ ﻪـﺑ ﻪـﻟﺎﻘﻣ ﻦـﻳﺍ ﺭﺩ
ﻝﺪﻣ ﺶﻴﭘ ﻭ ﻱﺯﺎﺳ ﻝﺪـﻣ ﻥﺍﺮـﻳﺍ ﺯﺭﺍ ﻲﻤﺳﺭ ﺭﺍﺯﺎﺑ ﺭﺩ ﺯﺭﺍ ﺥﺮﻧ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺪﻧﻭﺭ ﻲﻨﻴﺑ
ﺕﻻﺩﺎـﻌﻣ ﻱﺎـﻫ
ﻮﺋژ ﻲﻧﻭﺁﺮﺑ ﺖﻛﺮﺣ ﻲﻓﺩﺎﺼﺗ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺭﺎﺸﺘﻧﺍ ﻭ ﻱﺮﺘﻣ
- ﻩﺪـﺷ ﻪـﺘﻓﺮﮔﺭﺎﻛ ﻪـﺑ ﻦﺗﺮـﻣ ﺵﺮـﭘ
ﺖـﺳﺍ .
ﻪﺑ ﻝﺪﻣ ﻦﻳﺍ ﺩﺮﻜﻠﻤﻋ ﻲﺳﺭﺮﺑ ﺭﻮﻈﻨﻣ ﺶﻴﭘ ﺭﺩ ﺎﻫ
ﻪﻧﻮﻤﻧ ﺯﺍ ﺝﺭﺎﺧ ﻲﻨﻴﺑ ﻪﺴﻳﺎﻘﻣ ،ﺯﺭﺍ ﺥﺮﻧ ﻱ
ﻦـﻳﺍ ﻦﻴﺑ ﻱﺍ
ﻝﺪﻣ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﻲﺠﻨﺳﺩﺎﺼﺘﻗﺍ ﻝﺪﻣ ﺎﺑ ﺎﻫ
ARIMA
ﺖﺳﺍ ﻪﺘﻓﺮﮔ ﻡﺎﺠﻧﺍ .
ﺯﺍ ﻲﻛﺎـﺣ ﺶﻫﻭﮋـﭘ ﺞﻳﺎـﺘﻧ
ﻝﺪﻣ ﻪﻛ ﺖﺳﺍ ﻥﺁ ﺭﺍﺩ ،ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺭﺩ ﻱﺩﺎﻬﻨﺸﻴﭘ ﻱﺎﻫ
ﻝﺪـﻣ ﻪـﺑ ﺖﺒﺴﻧ ﻱﺮﺘﻬﺑ ﺩﺮﻜﻠﻤﻋ ﻱﺍ
ARIMA
ﺶﻴﭘ ﺭﺩ ﻪﻧﻮﻤﻧ ﺯﺍ ﺝﺭﺎﺧ ﻭ ﻞﺧﺍﺩ ﻲﻨﻴﺑ ﺭﺎﻴﻌﻣ ﺱﺎﺳﺍ ﺮﺑ ﺯﺭﺍ ﺥﺮﻧ ﻱ
ﻲﻣRMSE
ﺪﻨﺷﺎﺑ .
ﻪﻘﺒﻃ ﻱﺪﻨﺑ :JEL C53 , F47
ﻩژﺍﻭ ﺪﻴﻠﻛ :
ﺶﻴﭘ ﻲﻨﻴﺑ ،ﻱﺮﺘﻣﻮـﺋژ ﻲﻧﻭﺁﺮﺑ ﺖﻛﺮﺣ ﻝﺪﻣ ،ﻲﻓﺩﺎﺼﺗ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎﻌﻣ ،ﺯﺭﺍ ﺥﺮﻧ
ﺭﺎﺸﺘﻧﺍ ﻝﺪﻣ ﺵﺮﭘ
* - ﻩﺪﻨﺴﻳﻮﻧ ﻱ ﻝﻮﺌﺴﻣ .
1 - ﻪﻣﺪﻘﻣ
ﺶﻴــﭘ ﻲــﻨﻴﺑ ﻲــﻜﻳ ﻭ ﺖﻳﺮﻳﺪــﻣ ﺭﺩ ﻱﺪــﻴﻠﻛ ﺮــﺼﻨﻋ ﻭ ﻖــﻓﺆﻣ ﺖﻳﺮﻳﺪــﻣ ﻱﺎــﻫﺭﺍﺰﺑﺍ ﺯﺍ
ﻪﻣﺎﻧﺮﺑ ﻱﺰﻳﺭ ﻲﻣ ﺏﻮﺴﺤﻣ ﻱﺩﺎﺼﺘﻗﺍ ﻱﺎﻫ ﺩﻮﺷ
. ﻱﺩﺎـﺼﺘﻗﺍ ﻥﻼـﻛ ﺮﻴﻐﺘﻣ ﻚﻳ ﻥﺍﻮﻨﻋ ﻪﺑ ﺯﺭﺍ ﺥﺮﻧ
ﺶﺨﺑ ﺮﺑ ﺭﺍﺬﮔﺮﻴﺛﺄﺗ ﻭ ﺖﻴﻤﻫﺍﺮﭘ ﺭﺎﻴﺴﺑ ،ﺭﻮـﺸﻛ ﻚﻳ ﻱﺩﺎﺼﺘﻗﺍ ﻲﺟﺭﺎﺧ ﻭ ﻲﻠﺧﺍﺩ ﻒﻠﺘﺨﻣ ﻱﺎﻫ
ﻢﻫ ﺖﺧﺍﺩﺮﭘ ﺯﺍﺮﺗ ﺖﻴﻌﺿﻭ ﻥﻮﭼ ﻦﻴﺑ ﺖﺑﺎﻗﺭ ﺕﺭﺪﻗ ﻭ ﺎﻫ
ـﻘﻧ ،ﻲـﻠﻠﻤﻟﺍ ﻩﺪـﻨﻨﻛ ﻦﻴـﻴﻌﺗ ﺶ
ﺭﺩ ﻱﺍ
ﺖﺳﺎﻴﺳ ﻱﺭﺍﺬﮔ ﻲﻣ ﺎﻔﻳﺍ ﻱﺩﺎﺼﺘﻗﺍ ﻱﺎﻫ ﺪﻨﻛ
. ﺶﺨﺑ ﺯﺭﺍ ﺥﺮﻧ ﺕﺍﺮﻴﻴﻐﺗ ﻚﻳ ﺩﺎﺼﺘﻗﺍ ﻒﻠﺘﺨﻣ ﻱﺎﻫ
ﻲﻣ ﺭﺍﺮﻗ ﺮﻴﺛﺄﺗ ﺖﺤﺗ ﺍﺭ ﺭﻮﺸﻛ ﻝﺪﻣ ﻦﻳﺍﺮﺑﺎﻨﺑ ،ﺪﻫﺩ
ﺶﻴﭘ ﻭ ﻱﺯﺎﺳ ﺮـﻴﻐﺘﻣ ﻦـﻳﺍ ﻲـﺗﺁ ﺪﻧﻭﺭ ﻲﻨﻴﺑ
ﻪﺋﺍﺭﺍ ﻱﺍﺮﺑ ﻱ
ﺖﺳﺎﻴﺳ ﺩﻮﻤﻨﻫﺭ ﻭ ﺎﻫ ﻲﻣ ﺮﻈﻧ ﻪﺑ ﻱﺭﻭﺮﺿ ﻱﺮﻣﺍ ﻱﺩﺎﺼﺘﻗﺍ ﻱﺎﻫ
ﺪﺳﺭ . ﺕﺎـﻴﺑﺩﺍ ﺭﺩ
ﺍ ﻱﺮﺳ ﻲﺠﻨﺳﺩﺎﺼﺘﻗ ﻝﺪـﻣ ﻲﻧﺎـﻣﺯ ﻱﺎﻫ
ﻥﻮـﭼ ﻲﻳﺎـﻫ ARIMA
، GARCH ﻭ
ﺖـﻬﺟVAR
ﻝﺪﻣ ﺶﻴﭘ ﻭ ﻱﺯﺎﺳ ﻲـﻣ ﻪـﺘﻓﺮﮔ ﺭﺎـﻛ ﻪـﺑ ﻱﺩﺎﺼﺘﻗﺍ ﻱﺎﻫﺮﻴﻐﺘﻣ ﻲﻨﻴﺑ
ﺩﻮـﺷ . ﻝﺪـﻣ ﻦـﻳﺍ ﺎـﺑ ﺎـﻫ
ﺖﻳﺩﻭﺪﺤﻣ ﻪﺟﺍﻮﻣ ﻲﻳﺎﻫ
ﺪﻧﺍ . ﻝﺪﻣ ﻦﻳﺍ ﺭﺩ ﻲﺳﺭﺮﺑ ﺖﺤﺗ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺪـﺷﺎﺑ ﺎـﻧﺎﻣ ﺪـﻳﺎﺑ ﺎـﻫ
. ﺭﺩ
ﻲﻣ ﻝﺎﻤﻋﺍ ﻒﻠﺘﺨﻣ ﺐﺗﺍﺮﻣ ﺕﻼﺿﺎﻔﺗ ﻲﻳﺎﻧﺎﻣﺎﻧ ﺕﺭﻮﺻ ﻮﺷ
،ﺩ ﻦﺘـﻓﺭ ﺖـﺳﺩ ﺯﺍ ﺐـﺟﻮﻣ ﺮﻣﺍ ﻦﻳﺍ
ﺪﻨﻤﺷﺯﺭﺍ ﺕﺎﻋﻼﻃﺍ ﺕﺪﻣﺪﻨﻠﺑ
ﻲﻣ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺭﺩ ﺩﻮﺟﻮﻣ ﺩﻮﺷ
. ﻢﻫ ﻝﺪﻣ ﻦﻳﺍ ﻦﻴﻨﭼ ﻪﺑ ﺭﺩﺎﻗ ﺎﻫ
ﺵﺮﭘ ﺵﺯﺍﺮﺑ ﻱﺎﻫ
ﺩﻮﺟﻮﻣ ﻱﺮﺳ ﺪﻧﻭﺭ ﺭﺩ ﺪﻨﺘﺴﻴﻧ ﻲﻧﺎﻣﺯ ﻱﺎﻫ
. ﻒﻌـﺿ ﺩﻮـﺟﻭ ﻩﺪـﺷ ﺩﺎـﻳ ﻱﺎـﻫ
ﻲﻣ ﺐﺒﺳ ﺶﻴﭘ ﺯﺍ ﻞﺻﺎﺣ ﺞﻳﺎﺘﻧ ﻪﺑ ﻥﺍﻮﺘﻧ ﻪﻛ ﺩﻮﺷ
ﻝﺪﻣ ﻦﻳﺍ ﻲﻨﻴﺑ ﺩﻮﺑ ﺭﺍﻭﺪﻴﻣﺍ ﺎﻫ
.
ﺯﺍ ﺮﮕﻳﺩ ﻲﻜﻳ ﺵﻭﺭ
ﻝﺪﻣ ﺭﺩ ﺩﻮﺟﻮﻣ ﻱﺎﻫ ﺶﻴﭘ ﻭ ﻱﺯﺎﺳ
ﻱﺮﺳ ﻲﻨﻴﺑ ﻱﺩﺎـﺼﺘﻗﺍ ﻲﻧﺎـﻣﺯ ﻱﺎﻫ
ﻲﻓﺩﺎﺼﺗ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎﻌﻣ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﺖﺳﺍ١
. ﻝﺪﻣ ﻦﻳﺍ ﺰﻟﻮـﺷ ﻭ ﻚﻠﺑ ﺭﺎﻛ ﺎﺑ ﺎﻫ )٢
1973 (
ﻦﺗﺮﻣ ﻭ )٣
1973 ( ﻪﻨﻴﻣﺯ ﺭﺩ ﻱ
ﻝﺪﻣ ﻪﻟﺩﺎﻌﻣ ﻚﻳ ﺐﻟﺎﻗ ﺭﺩ ﻡﺎﻬﺳ ﺖﻤﻴﻗ ﻱﺯﺎﺳ ﻞﻴـﺴﻧﺍﺮﻔﻳﺩ ﻱ
ﻱﺮﺘﻣﻮﺋژ ﻲﻧﻭﺁﺮﺑ ﺖﻛﺮﺣ ﻲﻓﺩﺎﺼﺗ ﺘﻗﺍ ﺕﺎﻴﺑﺩﺍ ﺩﺭﺍﻭ٤
ﻩﺪـﺷ ﻱﺩﺎﺼ ﺪـﻧﺍ
. ﻪـﻟﺩﺎﻌﻣ ﻱ ﺰـﺟGBM
ﺮﻨﻳﻭ ﻲﻓﺩﺎﺼﺗ ﺪﻨﻳﺁﺮﻓ ﺐﻟﺎﻗ ﺭﺩ ﺍﺭ ﻮﮕﻟﺍ ﺭﺩ ﻝﻼﺧﺍ ﻲﻣ ﺵﺯﺍﺮﺑ٥
ﺪﻨﻛ . ﻪـﻟﺩﺎﻌﻣ ﻝﺪﻣ ﻦﻳﺍ ﺎـﻳﻮﭘ ﻱﺍ
ﻲﻣ ﺩﺭﻭﺁﺮﺑ ﻲﺳﺭﺮﺑ ﺖﺤﺗ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺭﺎﺘﻓﺭ ﺵﺯﺍﺮﺑ ﺖﻬﺟ ﺍﺭ ﺪﻨﻛ
. ﻪـﻛ ﻲﻔﻌـﺿ ﺩﻮـﺟﻭ ﻦﻳﺍ ﺎﺑ
ﻧﺎـﻣﺯ ﻱﺮـﺳ ﺪـﻧﻭﺭ ﺭﺩ ﺩﻮـﺟﻮﻣ ﻲـﺷﺮﭘ ﺭﺎـﺘﻓﺭ ﺵﺯﺍﺮـﺑ ﻪﺑ ﺭﺩﺎﻗ ﻪﻛ ﺖﺳﺍ ﻥﺁ ﺩﺭﺍﺩ ﻝﺪﻣ ﻦﻳﺍ ﻲ
ﺖﺴﻴﻧ . ﻦﺗﺮﻣ ) 1976 ( ﻦﺳﺍﻮﭘ ﺶﺨﺑ ﻥﺩﻭﺰﻓﺍ ﺎﺑ ، ﻝﺪـﻣ ﻪﺑ٦
ﻞـﺣ ﺍﺭ ﺭﻮﻛﺬـﻣ ﺶﻟﺎـﭼ ،GBM
ﺖﺳﺍ ﻩﺩﺮﻛ .
ﻪﺑ ﻝﺪﻣ ﺭﺎﺸﺘﻧﺍ ﻝﺪﻣ ﻩﺪﻣﺁ ﺖﺳﺩ -
ﻦﺗﺮـﻣ ﺵﺮـﭘ ﻲـﻣ ﻩﺪـﻴﻣﺎﻧ ٧
ﺩﻮـﺷ .٨
ﺕﺎـﻴﺋﺰﺟ
1- Stochastic Differential Equations ( SDE).
2- Black, F and Scholes, M.
3- Merton, R.C.
4- Geometric Brownian Motion (GBM).
5- Wiener Process.
6- Poisson process.
7- Merton- Jump- Diffusion model (MJD).
8 - ﻱﺍﺮﺑ ﺶﻴﺑ ﻲﻳﺎﻨﺷﺁ ﺮﺗ
ﺭﺎﺸﺘﻧﺍ ﻱﺎﻫ ﻝﺪﻣ ﺎﺑ -
ﻪﺑ ﺵﺮﭘ ) Hanson, F.B
، (2006 ﻮﺷ ﻪﻌﺟﺍﺮﻣ ﺩ .
ﺶﻴﺑ ﻲﻣ ﺍﺭ ﻝﺪﻣ ﻦﻳﺍ ﺩﺭﻮﻣ ﺭﺩ ﺮﺗ ﻱﺎـﻫﺭﺎﻛ ﺭﺩ ﻥﺍﻮـﺗ
ﺱﻭﺭﻮـﺗ ﻭ ﻝﺎـﺑ )١
1985 ( ﻪـﻨﻴﻣﺯ ﺭﺩ ﻱ
ﺵﺮﭘ ﺎﻫ ﻡﺎﻬﺳ ﻲﺘﻤﻴﻗ ﻱ ،
ﻥﻮﻳﺭﻮﺟ )٢
1989 ( ﺯ ﺭﺩ ﻪﻨﻴﻣ ﻱ ﺯﺭﺍ ﺥﺮﻧ ﻭ ﻡﺎﻬﺳ ﺖﻤﻴﻗ ﻭ
ﻢﻫ ﻦﻴﻨﭼ
ﻭﺯ ﺕﺎﻌﻟﺎﻄﻣ )٣
2005 ( ﻭﺯ ﻭ ﻦﺴﻨﻫ ﻭ )٤
2005 ( ﺩﺮﻛ ﻩﺪﻫﺎﺸﻣ .
ﻥﺁ ﻲﻣ ﻝﺎﺒﻧﺩ ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺭﺩ ﻪﭼ ﻪﺋﺍﺭﺍ ﺩﻮﺷ
ﻱ ﻞﻴـﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎـﻌﻣ ﺱﺎـﺳﺍ ﺮـﺑ ﻝﺪـﻣ ﻭﺩ
ﻲﻓﺩﺎﺼﺗ ﻭGBM
ﺶﻴﭘ ﻭ ﺵﺯﺍﺮﺑ ﺖﻬﺟMJD ﺭﺍﺯﺎـﺑ ﺯﺭﺍ ﺥﺮـﻧ ﻲﻧﺎـﻣﺯ ﻱﺮـﺳ ﻲﺗﺁ ﺪﻧﻭﺭ ﻲﻨﻴﺑ
ﻦﻴﺑ ﻪﺴﻳﺎﻘﻣ ﻭ ﻥﺍﺮﻳﺍ ﻲﻤﺳﺭ ﻝﺪﻣ ﻦﻳﺍ
ﻲﺠﻨﺳﺩﺎﺼﺘﻗﺍ ﻝﺪﻣ ﻭ ﺎﻫ ARIMA
ﻲـﻣ ﺪـﺷﺎﺑ . ﺞﻳﺎـﺘﻧ
ﻝﺪﻣ ﻱﺮﺗﺮﺑ ﺯﺍ ﻥﺎﺸﻧ ﺶﻫﻭﮋﭘ ﻝﺪﻣ ﺮﺑMJD
ﻱﺎﻫ ﻭGBM ARIMA ﺶﻴﭘ ﺭﺩ
ﺝﺭﺎـﺧ ﻲﻨﻴﺑ
ﻪﻧﻮﻤﻧ ﺯﺍ ﺭﻭﺎﺘﺸﮔ ﺱﺎﺳﺍ ﺮﺑ ﺯﺭﺍ ﺥﺮﻧ ﻱ
٥RMSE ﺩﺭﺍﺩ .
ﻪﻟﺎﻘﻣ ﺪﻧﻭﺭ ﺕﺎـﻴﺑﺩﺍ ﻭ ﻱﺮﻈﻧ ﻲﻧﺎﺒﻣ ﻡﻭﺩ ﺶﺨﺑ ﺭﺩ ﺍﺪﺘﺑﺍ ﻪﻛ ﺖﺳﺍ ﺐﻴﺗﺮﺗ ﻦﻳﺍ ﻪﺑ ﺮﺿﺎﺣ ﻱ
ﺖﺳﺍ ﻩﺪﻣﺁ ﻉﻮﺿﻮﻣ .
ﻪـﻨﻴﻣﺯ ﺭﺩ ﻪـﺘﻓﺮﮔ ﻡﺎـﺠﻧﺍ ﻲﺟﺭﺎـﺧ ﻭ ﻲﻠﺧﺍﺩ ﺕﺎﻌﻟﺎﻄﻣ ﻪﺑ ﻡﻮﺳ ﺶﺨﺑ ﻱ
ﺶﻴﭘ ﺖـﺳﺍ ﻪـﺘﻓﺎﻳ ﺹﺎﺼﺘﺧﺍ ﺯﺭﺍ ﺥﺮﻧ ﻲﻨﻴﺑ .
ﻩﺩﺍﺩ ﻡﺭﺎـﻬﭼ ﺶـﺨﺑ ﺭﺩ ﻩﺩﺎﻔﺘـﺳﺍ ﺩﺭﻮـﻣ ﻱﺎـﻫ
ﻱ
ﻩﺪﺷ ﻦﻴﻴﺒﺗ ﻖﻴﻘﺤﺗ ﻪﻴﺿﺮﻓ ﻢﺠﻨﭘ ﺶﺨﺑ ﺭﺩ ﻭ ﺪﻧﺍ
ﺖﺳﺍ ﻩﺪﺷ ﺮﻛﺫ ﻖﻴﻘﺤﺗ ﻱ .
ﻢﺸﺷ ﺶﺨﺑ ﺭﺩ
ﺖﺳﺍ ﻩﺪﻣﺁ ﻖﻴﻘﺤﺗ ﺞﻳﺎﺘﻧ .
ﻪﺠﻴﺘﻧ ﻭ ﻪﺻﻼﺧ ﻪﺑ ﻢﺘﻔﻫ ﺶﺨﺑ ﺖﻳﺎﻬﻧ ﺭﺩ ﺹﺎـﺼﺘﺧﺍ ﺚﺤﺑ ﻱﺮﻴﮔ
ﺩﺭﺍﺩ .
2 - ﻖﻴﻘﺤﺗ ﺕﺎﻴﺑﺩﺍ ﻭ ﻱﺮﻈﻧ ﻲﻧﺎﺒﻣ
ﻚﻠﺑ - ﺰﻟﻮﺷ ) 1973 ( ﻦﺗﺮﻣ ﻭ ) 1973 ( ﻪﺋﺍﺭﺍ ﺎﺑ ، ﻱ ﺖﻤﻴﻗ ﻱﺭﻮﺌﺗ ﻪـﻠﻣﺎﻌﻣ ﺭﺎـﻴﺘﺧﺍ ﻱﺭﺍﺬﮔ
٦
ﻪﻨﻴﻣﺯ ﺭﺩ ﺍﺭ ﻲﮔﺭﺰﺑ ﻱ
ﻝﺪﻣ ﺪﻨﺘﺷﺍﺩﺮﺑ ﻲﻟﺎﻣ ﺩﺎﺼﺘﻗﺍ ﺕﺎﻴﺑﺩﺍ ﻭ ﻡﺎﻬﺳ ﺭﺍﺯﺎﺑ ﻱﺎﻫ .
ﻝﺪﻣ ﺱﺎﺳﺍ ﺮﺑ
ﻚﻠﺑ - ﺰﻟﻮﺷ - ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻦﺗﺮﻣ ﻭ m
ﻲﻫﺩﺯﺎـﺑ ﺭﺎـﻈﺘﻧﺍ ﺩﺭﻮـﻣ ﺭﺍﺪـﻘﻣ ﻥﺍﻮﻨﻋ ﻪﺑ ﺐﻴﺗﺮﺗ ﻪﺑ s
ﻲﻣ ﻲﻓﺮﻌﻣ ﺮﻳﺯ ﻂﺑﺍﻭﺭ ﺐﻟﺎﻗ ﺭﺩ ﻭ ﻡﺎﻬﺳ ﺖﻤﻴﻗ ﻲﻫﺩﺯﺎﺑ ﺭﺎﻴﻌﻣ ﻑﺍﺮﺤﻧﺍ ﻭ ﻡﺎﻬﺳ ﺖﻤﻴﻗ ﺪﻧﻮﺷ
:
) 1 x(t h) x(t) (
lim E { ( )}
t h x(t)
h o
+ - m = ®
1
) 2 x(t h) x(t) (
lim E { (t h) }
h x(t)
h
+ -
s = - m
®
2 1 2
0
ﻥﺁ ﻪﻟﺩﺎﻌﻣ ﺭﺩ ﻡﺎﻬﺳ ﺖﻤﻴﻗ ﻩﺎﮔ ﻴﺴﻧﺍﺮﻔﻳﺩ ﻱ
ﻪﺑ ﻱﺮﺘﻣﻮﺋژ ﻲﻧﻭﺁﺮﺑ ﺖﻛﺮﺣ ﻲﻓﺩﺎﺼﺗ ﻞ
ﻲﻣ ﻕﺪﺻ ﺮﻳﺯ ﺕﺭﻮﺻ ﺪﻨﻛ
:
) 3 ( dx(t)= mx(t)dt+ sx(t)dw(t)
1- Ball and Torous.
2- Jorion.
3- Zhu, Z.
4- Hanson, F.B and Zhu, Z.
5- Root Mean Square Error.
6- Theory of option pricing.
ﻂﺑﺍﻭﺭ ﺭﺩ )
1 ( ﻭ ) 2 (
t ، ﺭﻭﺩ ﻲﺿﺎﻳﺭ ﺪﻴﻣﺍ ﺭﺍﺪﻘﻣ E ﻩ
ﻱ ﺖﺳﺍ ﻡﺍt
. ﺕﺎﺒﺛﺍ ﺭﻮﻈﻨﻣ ﻪﺑ
ﻲﻣ ﻞﻤﻋ ﻦﻴﻨﭼ ﻻﺎﺑ ﻱﺎﻋﺩﺍ ﺩﻮﺷ
:
ﺑﺎﺛ ﻻﺎﺑ ﻒﻳﺭﺎﻌﺗ ﺱﺎﺳﺍﺮﺑ ﺖ
ﻲﻣ ﻪﻛ ﺩﻮﺷ ﻭ m
ﻟﺩﺎﻌﻣ ﺭﺩ s
ﻪ ﻱ ﺮﻳﺯ ﻲﻓﺩﺎﺼﺗ ﻲﻠﺿﺎﻔﺗ
ﻕﺪﺻ ﻲﻣ ﺪﻨﻨﻛ )
،ﻦﺗﺮﻣ 1973 ﻙﺍﺮﺑ ﻭ ﺯﺮﻠﻳﺎﻣ ، ،١
1991 (:
) 4 ( x(t+h) x(t)- = mx(t)h+ sy(t)h x(t)
1 2
ﻛ ﻥﺁ ﺭﺩ ﻪ y(t)
ﺎﺘـﺳﺍ ﻝﺎـﻣﺮﻧ ﻊـﻳﺯﻮﺗ ﻱﺍﺭﺍﺩ ﻪـﻛ ﺖـﺳﺍ ﻲﻓﺩﺎﺼﺗ ﺮﻴﻐﺘﻣ ﺖـﺳﺍ ﺩﺭﺍﺪﻧ
.
ﻪﻟﺩﺎﻌﻣ ﻱ ) 4 ( ﻪﺘﺴﺴﮔ ﺕﺭﻮﺻ -
ﻪﻟﺩﺎﻌﻣ ﻥﺎﻣﺯ ﻱ
ـﻄﺑﺍﺭ ﺭﺩ ﻩﺪـﺷ ﻲـﻓﺮﻌﻣ ﻪ
ﻱ ) 3 ( ﻲـﻣ ﺪـﺷﺎﺑ .
ﺭﺩ ﺖــﻘﻴﻘﺣ ﻲﻧﺎــﻣﺯ
ﻪــﻛ h®0 ﻥﺁ ﻩﺎــﮔ y(t)h = Dw(t)@dw(t)
1
ﻭ 2
h=dt ﻭ
ﻦﻳﺍﺮﺑﺎﻨﺑ x(t+h) x(t)- =dx(t) ﻲﻣ
ﺩﻮﺷ .
ﻴﺒﺷ ﺭﻮﻈﻨﻣ ﻪﺑ ﻪ
ﻥﺁ ﻲﻓﺩﺎـﺼﺗ ﻞﻴـﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎـﻌﻣ ﺖـﺤﺗ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﻚﻳ ﻱﺯﺎﺳ ﻪـﭼ
ﻲﻣ ﺮﻈﻧ ﻪﺑ ﻲﺳﺎﺳﺍ ﺖـﺳﺍ ﻪـﻟﺩﺎﻌﻣ ﻥﺁ ﻱﺎـﻫﺮﺘﻣﺍﺭﺎﭘ ﻦﻴـﻤﺨﺗ ﻭ ﻲﻠﻴﻠﺤﺗ ﻞﺣ ،ﺪﺳﺭ
. ﺰﻴﻟﺎـﻧﺁ ﺭﺩ
ﻮﺘﻳﺍ ﻢﻟ ﺯﺍ ﻲﻓﺩﺎﺼﺗ ﻪـﻟﺩﺎﻌﻣ ﻚـﻳ ﻲﻠﻴﻠﺤﺗ ﻞﺣ ﺭﻮﻈﻨﻣ ﻪﺑ٢
ﻩﺩﺎﻔﺘـﺳﺍ ﻲﻓﺩﺎـﺼﺗ ﻞﻴـﺴﻧﺍﺮﻔﻳﺩ ﻱ
ﻲﻣ ﺩﻮﺷ )
٣ﻦﻟﺁ
، 2007 .(
ﻲﻣ ﻥﺎﻴﺑ ﺮﻳﺯ ﺕﺭﻮﺻ ﻪﺑ ﻮﺘﻳﺍ ﻢﻟ ﺩﻮﺷ
.
ﻮﺘﻳﺍ ﻢﻟ ﺮﮔﺍ
:
ـﻟﺩﺎﻌﻣ ﺭﺩ ﻪـﻛ ﺪﺷﺎﺑ ﻲﻓﺩﺎﺼﺗ ﺪﻨﻳﺁﺮﻓ x(t) ﻪ
ﻱ ﻲﻓﺩﺎـﺼﺗ ﻞﻴـﺴﻧﺍﺮﻔﻳﺩ ﺮـﻳﺯ
ﻕﺪﺻ ﺪﻨﻛ :
) 5 ( dx(t)=f (t, x(t))dt g(t, x(t))dw(t)+
ﻭ ﻢﻫ ﻦﻴﻨﭼ ﺭﺩ ﻲﺗﺭﻮﺻ ﻪﻛ F(t, x(t))
ﺮـﻴﻐﺘﻣ ﻭﺩ ﻊﺑﺎﺗ ﻩ
ﻱﺍ ﺕﺎﻘﺘـﺸﻣ ﻱﺍﺭﺍﺩ ﻪـﻛ ﺪـﺷﺎﺑ
ﺒﺗﺮﻣ ﻲﺋﺰﺟ ﻪ
ﻱ ﺘﺳﻮﻴﭘ ﻡﻭﺩ ﻭ ﻝﻭﺍ ﻱﺎﻫﺮﻴﻐﺘﻣ ﻪﺑ ﺖﺒﺴﻧ ﻪ
ﻭ t x
،ﺪﺷﺎﺑ ﻥﺁ ﻩﺎـﮔ F(t, x(t))
ﻟﺩﺎﻌﻣ ﺭﺩ ﻪ ﻱ ﻕﺪﺻ ﺮﻳﺯ ﻲﻓﺩﺎﺼﺗ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﻲﻣ
ﺪﻨﻛ :
) 6
ˆ ˆ (
dF(t, x(t))=f (t, x(t))dt+g(t, x(t))dw(t)
ﻛ ﻥﺁ ﺭﺩ ﻪ :
) 7 ( F(t, x(t)) F(t, x(t))
f (t, x(t))ˆ f (t, x(t))
t x(t)
F(t, x(t)) g (t, x(t))
x(t)
¶ ¶
= +
¶ ¶
+ ¶
¶
2 2
2
1 2
F(t, x(t)) ˆ
g(t, x(t)) g(t, x(t))
x(t)
= ¶
¶
1- Malliaris, A.G and Brock, W.A . 2- Ito Lemma.
3- Allen, E.
ﻥﺩﺍﺩ ﺭﺍﺮﻗ ﺎﺑ F(t, x(t))=ln(x(t))
ﻪﻄﺑﺍﺭ ﺱﺎﺳﺍ ﺮﺑ ﻭ ﻮﺘﻳﺍ ﻢﻟ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﻭ ﻱﺎـﻫ
) 6 ( ﻭ
) 7 ( ﻪﻟﺩﺎﻌﻣ ، ﻱ ﻲﻣ ﻞﺣ ﺮﻳﺯ ﺕﺭﻮﺻ ﻪﺑGBM
ﺩﻮﺷ .
) 8 ( d ln(x(t))= m - s( 1 2)dt+ sdw(t)
2
ﻝﺍﺮﮕﺘﻧﺍ ﺎﺑ ﻩﺯﺎﺑ ﻱﻭﺭ ﻦﻴﻓﺮﻃ ﺯﺍ ﻱﺮﻴﮔ
[0, ]t ﻲﻣ ﺖﺷﻮﻧ ﻥﺍﻮﺗ :
) 9 (
t t t
d ln(x(t))= m - s( )dt+ sdw(t)
ò ò
2ò
0 0 0
1 2
) 10 ( x(t)=x( ) exp((m - s1 2)t+ sw(t))
0
2
ﻪﻟﺩﺎﻌﻣ ﻱ ) 10 ( ﻲﻣ ﻥﺎﺸﻧ ﻥﺎﻣﺯ ﻝﻮﻃ ﺭﺩ ﺍﺭ ﻡﺎﻬﺳ ﺖﻤﻴﻗ ﻱﺎﻳﻮﭘ ﺭﺎﺘﻓﺭ ﺪﻫﺩ
. ﻝﺪﻣ GBM
ﺖﺳﺍ ﻩﺪﺷ ﻞﻴﻜﺸﺗ ﺶﺨﺑ ﻭﺩ ﺯﺍ .
ﺭﺩ ﺩﻮـﺟﻮﻣ ﺕﺎﻧﺎـﺳﻮﻧ ﻡﻭﺩ ﺶـﺨﺑ ﻭ ﻲﻧﺎﻣﺯ ﺪﻧﻭﺭ ﻝﻭﺍ ﺶﺨﺑ
ﻲﻣ ﺵﺯﺍﺮﺑ ﺍﺭ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺪﻨﻛ
.
ﺎﺣ ﻝﺪﻣ ﺭﻮﻈﻨﻣ ﻪﺑ ﻝ ﻪـﻟﺩﺎﻌﻣ ﺐـﻟﺎﻗ ﺭﺩ ﺯﺭﺍ ﺥﺮﻧ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﻱﺯﺎﺳ
ﻱ ﺱﺎـﺳﺍ ﺮـﺑGBM
ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻒﻳﺮﻌﺗ ﻭ ﻩﺪﻳﺍ ﻦﻳﺍ ﻱﺮﻴﮔﺭﺎﻛ ﻪﺑ ﺎﺑ ﻭ ﻦﺗﺮﻣ ﻝﻻﺪﺘﺳﺍ ﻭ m
ﻪﺑ s
ﻥﺍﻮﻨﻋ ﻪﺑ ﺐﻴﺗﺮﺗ
ﺭﺍﺪﻘﻣ ﺭﻮﻣ ﻲﻫﺩﺯﺎﺑ ﺭﺎﻴﻌﻣ ﻑﺍﺮﺤﻧﺍ ﻭ ﺯﺭﺍ ﺥﺮﻧ ﻲﻫﺩﺯﺎﺑ ﺭﺎﻈﺘﻧﺍ ﺩﺭﻮﻣ ﻲـﻣ ،ﺯﺭﺍ ﺥﺮﻧ ﺭﺎﻈﺘﻧﺍ ﺩ
ﻥﺍﻮـﺗ
ﻪـﻟﺩﺎﻌﻣ ﺭﺩ ﺯﺭﺍ ﺥﺮﻧ ﻪﻛ ﺩﺮﻛ ﺎﻋﺩﺍ ﻱ
ﻲـﻣ ﻕﺪـﺻGBM ﺪـﻨﻛ
. ﺮـﮔﺍ ،ﺱﺎـﺳﺍ ﻦـﻳﺍ ﺮـﺑ e(t)
ﻥﺎﺸﻧ ﻩﺪﻨﻫﺩ ﻱ ﻪﻈﺤﻟ ﺭﺩ ﺯﺭﺍ ﺥﺮﻧ ﺮﻴﻐﺘﻣ ﺭﺍﺪﻘﻣ ﻱ
ﻪـﻟﺩﺎﻌﻣ ﻲـﻠﻴﻠﺤﺗ ﺏﺍﻮـﺟ ،ﺪﺷﺎﺑ t ﻱ
GBM
ﻪﺑ ﺮﻳﺯ ﺕﺭﻮﺻ ﻪﺑ ﺯﺭﺍ ﺥﺮﻧ ﻱﺍﺮﺑ ﻲﻣ ﺖﺳﺩ
ﺪﻳﺁ :
) 11 (
e(t)=e( ) exp((m - s1 2)t+ sw(t)) 0
2
ﻪﻴﺒﺷ ﺭﻮﻈﻨﻣ ﻪﺑ ﻪـﻟﺩﺎﻌﻣ ﻱﺯﺎـﺳ
ﻱ ) 11 ( ﻩﺩﺍﺩ ﻱﺍﺮـﺑ ﺪـﻳﺎﺑ ﻖـﻴﻘﺤﺗ ﻲـﺳﺭﺮﺑ ﺩﺭﻮـﻣ ﻱﺎـﻫ
ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻭ m
ﺪﻧﻮﺷ ﻩﺩﺯ ﻦﻴﻤﺨﺗ s
. ﻪﺑ ﺎﺑ ﻚـﻳﺮﺘﻣﺍﺭﺎﭘﺎﻧ ﺵﻭﺭ ﻱﺮﻴﮔﺭﺎـﻛ )١
،ﻦـﻟﺁ 2007 (
ﻲﻣ ﺩﺯ ﻦﻴﻤﺨﺗ ﺍﺭ ﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻦﻳﺍ ﻥﺍﻮﺗ .
ﻪـﻟﺩﺎﻌﻣ ﺱﺎﺳﺍ ﺮﺑ ﻱ
) 11 ( ﻱﻮـﮕﻟﺍ ﺭﺩ ﻲﻓﺩﺎـﺼﺗ ﺪـﻧﻭﺭ ،
ﺖﺳﺍ ﻩﺪﺷ ﻆﻔﺣ ﺮﻨﻳﻭ ﺪﻨﻳﺁﺮﻓ ﺐﻟﺎﻗ ﺭﺩGBM .
ﺮـﺑ ﺍﺭ ﻝﺪـﻣ ﻦـﻳﺍ ﻱﺮـﺗﺮﺑ ﻪﭼﺮﮔﺍ ﻪﻠﺌﺴﻣ ﻦﻳﺍ
ﻝﺪﻣ ARIMA ﻲﻣ ﻥﺎﻳﺎﻤﻧ
ﻲﻣ ﺐﺒﺳ ﻝﺎﺣ ﻦﻳﺍ ﺎﺑ ،ﺪﻨﻛ ﻪﻴﺒـﺷ ﺞﻳﺎـﺘﻧ ﻪﻛ ﺩﻮﺷ
ﺭﺍﺪـﻳﺎﭘ ﻱﺯﺎـﺳ
ﺪﺷﺎﺒﻧ . ﻪﺑ ﻪﻴﺒﺷ ﺪﻨﻳﺁﺮﻓ ﺭﻮﻛﺬﻣ ﺶﻟﺎﭼ ﻞﺣ ﺭﻮﻈﻨﻣ ﺭﺍﺮﻜﺗ ﻚﻳ ﻱﺍﺮﺑ ﻱﺯﺎﺳ
5000 ﻡﺎـﺠﻧﺍ ﻲﻳﺎﺗ
ﻲﻣ ﺩﺮﻳﺬﭘ . ﻪـﺠﻴﺘﻧ ﻥﺍﻮـﻨﻋ ﻪـﺑ ﻱﺭﺍﺮـﻜﺗ ﻥﺁ ،ﺭﺍﺮﻜﺗ ﺩﺍﺪﻌﺗ ﻦﻳﺍ ﻦﻴﺑ ﺭﺩ ﺲﭙﺳ ﻱ
ﻪﻴﺒـﺷ ﻱﺯﺎـﺳ
ﻲﻣ ﻲﻓﺮﻌﻣ ﻢﻛ ﻱﺍﺭﺍﺩ ﻪﻛ ﺩﻮﺷ
ﺭﺍﺪﻘﻣ ﻦﻳﺮﺗ ﻪـﻧﻮﻤﻧ ﻞﺧﺍﺩ ﺵﺯﺍﺮﺑ ﺭﺩRMSE
ﻱ ﻲﻧﺎـﻣﺯ ﻱﺮـﺳ
ﺪﺷﺎﺑ ) ﻚﻴﻨﺳﻼﭘ
،٢
2010 .(
ﻲﻣ ﻪﻛ ﺖﺳﺍ ﻦﺷﻭﺭ ﺶﻴـﭘ ﺯﺍ ﻞـﺻﺎﺣ ﺞﻳﺎـﺘﻧ ﻪـﺑ ﻥﺍﻮﺗ
ﻪـﻛ ﻲـﻨﻴﺑ
1 Nonparametric method.
2 Pluciennik, P.
ﻪﺑ ﻦﻳﺍ ﻪﺑ ﺐﻴﺗﺮﺗ ﻲﻣ ﺖﺳﺩ ﻭ ﺪﻳﺁ
ﻢﻫ ﻦﻴﻨﭼ ﺩ ﻢﻛ ﻱﺍﺭﺍ ﻪـﻧﻮﻤﻧ ﻞـﺧﺍﺩ ﺵﺯﺍﺮـﺑ ﺭﺩ ﺎﻄﺧ ﻦﻳﺮﺗ ﻱ
ﺩﺮﻛ ﺩﺎﻤﺘﻋﺍ ،ﺖﺳﺍ ﺯﺭﺍ ﺥﺮﻧ .
ﻝﺪﻣ ﻱﺮﺳ ﻱﺍﺮﺑGBM
ﻥﺁ ﻲﻧﺎـﻣﺯ ﺪـﻧﻭﺭ ﺭﺩ ﺵﺮـﭘ ﺩﻮـﺟﻭ ﺎـﺑ ﻲﻧﺎـﻣﺯ ﻱﺎﻫ ﺐـﺳﺎﻨﻣ ﺎـﻫ
ﻲﻤﻧ ﺪﺷﺎﺑ . ﺖـﺴﻴﻧ ﻲﻧﺎـﻣﺯ ﻱﺮﺳ ﺪﻧﻭﺭ ﺭﺩ ﺵﺮﭘ ﺵﺯﺍﺮﺑ ﻪﺑ ﺭﺩﺎﻗ ﻝﺪﻣ ﻦﻳﺍ ﺖﻘﻴﻘﺣ ﺭﺩ .
ﻦﺗﺮـﻣ
) 1976 ( ﻪﻟﺩﺎﻌﻣ ﻪﺑ ﻦﺳﺍﻮﭘ ﺶﺨﺑ ﻥﺩﻭﺰﻓﺍ ﺎﺑ ﻱ
ﺭﺎﺸﺘﻧﺍ ﻝﺪﻣGBM -
ﺮـﻳﺯ ﺕﺭﻮـﺻ ﻪﺑ ﺍﺭ ﺵﺮﭘ
ﺩﺮﻛ ﻲﻓﺮﻌﻣ :
) 12 ( dx(t)= mx(t)dt+ sx(t)dw(t) kx(t)dN(t)+
ﻛ ﻥﺁ ﺭﺩ ﻪ ﺪﻨﻳﺁﺮﻓ N(t)
ﻧﺎﻴﺑ ﺖﻘﻴﻘﺣ ﺭﺩ ﻭ ﻦﺳﺍﻮﭘ ﻲﻓﺩﺎﺼﺗ ﺵﺮﭘ ﺩﺍﺪﻌﺗ ﺮﮕ
ﺎﻫ ﺩﻮـﺟﻮﻣ ﻱ
ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺭﺩ ﻲﻣ
ﺪﺷﺎﺑ . ﺭﺩ ﻪﻛ ﺖﺳﺍ ﺮﻛﺫ ﻪﺑ ﻡﺯﻻ ﻪﻟﺩﺎﻌﻣ
ﻱ ) 12 ( m ، ﻲﻫﺩﺯﺎﺑ ﺩﺭﻮﻣ ﺭﺎﻈﺘﻧﺍ
،ﺯﺭﺍ ﺥﺮﻧ ﺭﺎﻴﻌﻣ ﻑﺍﺮﺤﻧﺍ s
ﻲﻫﺩﺯﺎﺑ ﻭ ﺯﺭﺍ ﺥﺮﻧ ﻱﺭﺎﻈﺘﻧﺍ ﻩﺯﺍﺪـﻧﺍ k
ﻱ ﺵﺮـﭘ ﺪـﻧﻭﺭ ﺭﺩ ﺩﻮـﺟﻮﻣ
ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﻥﺎﺸﻧ ﺍﺭ
ﻲﻣ ﺪﻫﺩ . ﺪـﻨﻳﺁﺮﻓ ﻝﺎـﻤﺘﺣﺍ ﻲﻟﺎﮕﭼ ﻊﺑﺎﺗ ﻒـﻳﺮﻌﺗ ﺮـﻳﺯ ﻞﻜـﺷ ﻪـﺑ N(t)
ﻲﻣ ﺩﻮﺷ .
) 13
n (
t ( t) P(N(t) n) e
n!
-l l
= =
ﻝﺪﻣ ﻞﺣ ﺭﻮﻈﻨﻣ ﻪﺑ ﻲﻣMJD
ﻥﺩﺍﺩ ﺭﺍﺮـﻗ ﺎـﺑ ﻮـﺘﻳﺍ ﻢـﻟ ﺯﺍ ﻥﺍﻮـﺗ ( , ( )) ln( ( ))
F t x t = x t
ﺩﺮﻛ ﻩﺩﺎﻔﺘﺳﺍ .
ﻦﻳﺍ ﺭﺩ ﺕﺭﻮﺻ :
) 14
n ( d ln(x(t)) ( s )dt dw(t) ln( k )dN(t)
= m - + s + +
2
1 2
ﺑ ﻦﻴﻓﺮﻃ ﺯﺍ ﻱﺮﻴﮔ ﻝﺍﺮﮕﺘﻧﺍ ﺎ ﻪﻟﺩﺎﻌﻣ
ﻱ ﻻﺎﺑ ﻩﺯﺎﺑ ﺭﺩ ﻱ [0, ]t ﻲﻠﻴﻠﺤﺗ ﺏﺍﻮﺟ ﻪﻟﺩﺎﻌﻣ
ﻱ ﺩﺎـﻳ
ﺪﺷ ﻩ ﺮﻳﺯ ﻞﻜﺷ ﻪﺑ ﻪﺑ
ﻲﻣ ﺖﺳﺩ ﺪﻳﺁ
. ﻪﺠﻴﺘﻧ ﺭﺩ ﻲﻣ
ﺖﺷﻮﻧ ﻥﺍﻮﺗ :
) 15 (
N(t)
n n
x(t) x( ) exp{( )t w(t) ln( k )}
=
= m -s2 + s +
å
+1
0 1
2
ﻪﻟﺩﺎﻌﻣ ﻱ ) 15 ( ﻝﺪﻣ ﻲﻠﻴﻠﺤﺗ ﺏﺍﻮﺟ ﻲﻣMJD
ﺪﺷﺎﺑ . ﻪﻟﺩﺎﻌﻣ ﻦﻳﺍ ﺭﺩ kn
ﻩﺯﺍﺪـﻧﺍ ﺮﮕﻧﺎﻴﺑ ﻱ
ﺖﺳﺍ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺭﺩ ﺩﻮﺟﻮﻣ ﺵﺮﭘ ﻦﻴﻣﺍn .
ﻩﺪﻳﺍ ﻱﺮﻴﮔﺭﺎﻛ ﻪﺑ ﺎﺑ ﻝﺎﺣ ﻱ
ﻣ ﻱﺍﺮـﺑ ﻦﺗﺮﻣ ﺮـﻴﻐﺘ
ﻲﺗﺭﻮﺻ ﺭﺩ ﺯﺭﺍ ﺥﺮﻧ ﻪﻛ
ﻩﺪﻨﻫﺩ ﻥﺎﺸﻧ e(t) ﻱ
ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻭ ﺪﺷﺎﺑ ﻥﺎﻣﺯ ﺭﺩ ﺯﺭﺍ ﺥﺮﻧ ،m
ﻭ s
kn
ﻪﺑ ﺮﺗ ﺐﻴﺗ ﺯﺭﺍ ﺥﺮـﻧ ﺭﺎـﻈﺘﻧﺍ ﺩﺭﻮـﻣ ﻲﻫﺩﺯﺎـﺑ ﺭﺎـﻴﻌﻣ ﻑﺍﺮـﺤﻧﺍ ،ﺯﺭﺍ ﺥﺮﻧ ﻲﻫﺩﺯﺎﺑ ﻦﻴﮕﻧﺎﻴﻣ ﻭ
ﻩﺯﺍﺪﻧﺍ ﻱ ﻲﻣ ﺕﺭﻮﺻ ﻦﻳﺍ ﺭﺩ ،ﺪﺷﺎﺑ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺪﻧﻭﺭ ﺭﺩ ﺩﻮﺟﻮﻣ ﺵﺮﭘ ﻦﻴﻣﺍ n ﺩﺮﻛ ﺎﻋﺩﺍ ﻥﺍﻮﺗ
ﻝﺪﻣ ﺭﺩ ﺯﺭﺍ ﺥﺮﻧ ﻪﻛ MJD
ﻲﻣ ﻕﺪﺻ ﺪﻨﻛ
. ﻪﻟﺩﺎﻌﻣ ﺱﺎﺳﺍ ﺮﺑ ﻱ
) 15 ( ﻝﺪـﻣ ﻲـﻠﻴﻠﺤﺗ ﺏﺍﻮﺟ
ﻪﺑ ﺮﻳﺯ ﺕﺭﻮﺻ ﻪﺑ ﺯﺭﺍ ﺥﺮﻧ ﺮﻴﻐﺘﻣ ﻱﺍﺮﺑMJD ﻲﻣ ﺖﺳﺩ
ﺪﻳﺁ :
) 16 (
N(t)
n n
e(t) e( ) exp{( )t w(t) ln( k )}
=
= m -s2 + s +
å
+1
0 1
2
ﻢﻫ ﻥﺎﻨﭼ ﻪﻛ ﻩﺪﻳﺩ ﻣ ﻲ ﺩﻮﺷ ﻪﻟﺩﺎﻌﻣ ﻱ ) 16 ( ﻪﺳ ﺯﺍ ﺶﺨﺑ ﺖﺳﺍ ﻩﺪﺷ ﻞﻴﻜﺸﺗ .
ﺖﻤـﺴﻗ ﻝﻭﺍ
،ﻲﻧﺎﻣﺯ ﺪﻧﻭﺭ ﺶﺨﺑ
ﻭ ﺕﺎﻧﺎﺳﻮﻧ ﻡﻭﺩ ﺖﻤﺴﻗ ﺖﻳﺎﻬﻧ ﺭﺩ
ﺵﺮـﭘ ﻡﻮـﺳ ﺎـﻫ
ﻱﺮـﺳ ﺭﺩ ﺩﻮـﺟﻮﻣ ﻱ
ﺵﺯﺍﺮﺑ ﺍﺭ ﻲﻧﺎﻣﺯ ﻲﻣ
ﺪﻨﻛ . ﻪﻟﺩﺎﻌﻣ ﺪﻨﻧﺎﻤﻫ ﻱ
ﺪـﻨﻳﺁﺮﻓ ﺩﻮـﺟﻭ ﻞﻴﻟﺩ ﻪﺑ ﺰﻴﻧ ﻝﺪﻣ ﻦﻳﺍ ﺭﺩGBM
ﻪﺠﻴﺘﻧ ،ﻮﮕﻟﺍ ﺭﺩ ﺮﻨﻳﻭ ﻱ
ﻪﻴﺒﺷ ﻪﻟﺩﺎﻌﻣ ﻱﺯﺎﺳ ﺪﻫﺍﻮﺨﻧ ﺭﺍﺪﻳﺎﭘ ﻱ
ﺩﻮﺑ . ﻥﺩﺮـﻛ ﻑﺮـﻃﺮﺑ ﺭﻮـﻈﻨﻣ ﻪﺑ
ﻪﻴﺒﺷ ﺵﻭﺭ ﺎﺑ ﻪﺑﺎﺸﻣ ﺰﻴﻧ ﻪﻠﺌﺴﻣ ﻦﻳﺍ ﻝﺪﻣ ﻱﺯﺎﺳ
ﺪﺷ ﺪﻫﺍﻮﺧ ﻞﻤﻋGBM .
3 - ﻲﺑﺮﺠﺗ ﺕﺎﻌﻟﺎﻄﻣ
3 - 1 - ﻲﻠﺧﺍﺩ ﺕﺎﻌﻟﺎﻄﻣ ﻱﺭﺎﺼﻧﺍ ﺎﺿﺭ ﻭ ﻲﻫﺎﮔﺭﺩ ﻦﺴﺣ )
1386 (
، ﻪﻜﺒﺷ ﻝﺪﻣ ﺎﻫ
ﻱﺍﺮﺑ ﺍﺭ ﻲﺒﺼﻋ ﻱ ﺶﻴﭘ
ﻲﻨﻴﺑ ﺥﺮﻧ
ﺪﻴﺸﺨﺑ ﺩﻮﺒﻬﺑ ﺲﻧﺎﻳﺭﺍﻭ ﻢﻃﻼﺗ ﺺﺧﺎﺷ ﺱﺎﺳﺍ ﺮﺑ ﺯﺭﺍ ﻩ
ﻧﺍ ﺪ . ﻦﻳﺪـﺑ ﺭﻮـﻈﻨﻣ ﻥﺁ ﺎـﻫ ﻭﺩ ﺺﺧﺎـﺷ
ﺲﻧﺎﻳﺭﺍﻭ ﻭ چﺭﺎﮔ ﺍﺭ ﻪﺑ ﻥﺍﻮﻨﻋ ﺺﺧﺎﺷ ﺎﻫ ﻱ ﻢﻃﻼﺗ ﺥﺮﻧ ﺯﺭﺍ ﻪﺑ ﻚﻴﻜﻔﺗ ﺭﺩ ﺮﻈﻧ ﻪـﺘﻓﺮﮔ ﻭ ﻪـﺑ ﻭﺩ
ﻖﻳﺮﻃ ﺭﺩ ﻝﺪﻣ ﺩﺭﻮﻣ ﻩﺩﺎﻔﺘﺳﺍ ﺭﺍﺮﻗ ﺩﺍﺩ ﻩ ﺪﻧﺍ . ﺭﺎﺑ ﻝﻭﺍ ﻔﻗﻭ ﻪ ﻱ ﻥﺁ ﺍﺭ ﻪﺑ ﻪﻔﻗﻭ ﺎﻫ ﻱ ﺥﺮﻧ ﺯﺭﺍ ﻪﻓﺎـﺿﺍ
ﺩﺮﻛ ﻩ ﻭ ﺮﮕﻳﺩ ﺭﺎﺑ ﺺﺧﺎﺷ ﻢﻃﻼﺗ ﺍﺭ ﺢﻄﺳ ﻱﺪﻨﺑ ﻩﺩﺮﻛ ﻭ ﺎﺑ ﻪﺘﺳﺩ ﻱﺪﻨﺑ ـﺸﻣ ﺕﺍﺪﻫﺎ ﺱﺎـﺳﺍﺮﺑ
،ﻢﻃﻼﺗ ﺢﻄﺳ ﻝﺪﻣ
ﺶﻴﭘ ﻲﻨﻴﺑ ﮋﻳﻭ ﻩ ﻱﺍ ﺍﺭ ﻱﺍﺮﺑ ﺮﻫ ﻪﺘﺳﺩ ﺯﺍ ﺕﺍﺪﻫﺎﺸﻣ ﻪﺑ
ﺭﺎﻛ ﺩﺮﺑ ﻩ ﺪﻧﺍ ﺞﻳﺎـﺘﻧ.
ﻥﺎﺸﻧ ﻲﻣ ﺪﻫﺩ ﻪﻛ ﻝﺪﻣ ﺎﻫ ﻱ ﺡﻮﻄﺳ ﻱﻻﺎﺑ
،ﻢﻃﻼﺗ ﺭﺩ ﻪﺴﻳﺎﻘﻣ ﺎﺑ ﻝﺪﻣ ﺎﻨﺒﻣ ، ﺶﻴﭘ ﺕﺭﺪﻗ ﻲﻨﻴﺑ
ﺥﺮﻧ ﺯﺭﺍ ﻲﺗﺁ ﺍﺭ ﺩﻮﺒﻬﺑ ﻲﻣ ﺪﻨﻫﺩ .
ﺎﻴﻧﺪﺣﻮﻣ ﺮﺻﺎﻧ ﻭ ﻲﺒﻴﻃ ﻞﻴﻤﻛ ﺪﻴﺳ )
1387 (
، ﻪﻌﻟﺎﻄﻣ ﺭﺩ ﻱﺍ
ﻪﻜﺒﺷ ﺱﺎﺳﺍﺮﺑ ﺎﻫ
ﻲﺒـﺼﻋ ﻱ
ﺴﻳﺎﻘﻣ ﻭ ﻪ ﻱ ﺵﻭﺭ ﺎـﺑ ﺵﻭﺭ ﻦـﻳﺍ ﺎـﻫ
ﻱ ﻨـﺳﺩﺎﺼﺘﻗﺍ ﻪـﺑ ﻱﺭﺎﺘﺧﺎـﺳ ﻲﺠ
ﺶﻴـﭘ ﻲـﻨﻴﺑ ﺯﺭﺍ ﺥﺮـﻧ
ﺘﺧﺍﺩﺮﭘ ﻪ ﺪﻧﺍ . ﻥﺁ ﺎﻫ ﻜﺒﺷ ﻝﺪﻣ ﻪﻛ ﺍﺭ ﻪﻴﺿﺮﻓ ﻦﻳﺍ ﻪ
ﻱ ﻝﺪﻣ ﺮﮕﻳﺩ ﻪﺑ ﺖﺒﺴﻧ ﻲﺒﺼﻋ ﺎـﻫ
ﺩﺮـﻜﻠﻤﻋ
ﻪﺘﺷﺍﺩ ﻱﺮﺘﻬﺑ ﺖﺳﺍ
ﺩﺍﺩ ﺭﺍﺮﻗ ﻲﺳﺭﺮﺑ ﺩﺭﻮﻣ ﺍﺭ ﻩ
ﺪﻧﺍ ﻳﺎﺘﻧ ﻪﻛ ـﺿﺮﻓ ﻦـﻳﺍ ﻲﺘـﺳﺭﺩ ﺯﺍ ﻲﻛﺎـﺣ ﺞ ﻪﻴ
ﻩﺩﻮﺑ ﺖﺳﺍ .
ﺴﺣ ﻥﺎﻳﺮﺒﻛﺍ ﺎﺿﺭ ﻭ ﻥﺎﺑﺯﺮﻣ ﻦﻴ )
1384 (
، ـﺴﻳﺎﻘﻣ ﻪﺑ ﻪ
ﻱ ﻝﺪـﻣ ﻦﻴـﺑ ﺎـﻫ
ﻱ ﻨـﺳﺩﺎﺼﺘﻗﺍ ﻲﺠ
ﻭ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﻭ ﻱﺭﺎﺘﺧﺎﺳ ﻪﻜﺒﺷ
ﻱ ﺭﺩ ﻲﺒﺼﻋ ﺶﻴﭘ
ﻲﻨﻴﺑ ﺘﺧﺍﺩﺮﭘ ﺯﺭﺍ ﺥﺮﻧ ﻪ
ﺪﻧﺍ . ﻲﻠـﺻﺍ ﻑﺪﻫ
ﻥﺁ ﺎﻫ ﻩﺩﻮﺑ ﻪﻴﺿﺮﻓ ﻦﻳﺍ ﻥﻮﻣﺯﺁ ﺖﺳﺍ
ﻪﻜﺒﺷ ﺵﻭﺭ ﺎﻳﺁ ﻪﻛ ﻲﺒﺼﻋ ﻱﺎﻫ
) ﻲﻄﺧﺮﻴﻏ (
ﺞﻳﺎﺘﻧ ﻱﺍﺭﺍﺩ
ﺮﺘﻬﺑ ﺭﺩ ﻪﺴﻳﺎﻘﻣ ﻞﺑﺎﻗ ﻭ ﺶﻴﭘ
ﻲﻨﻴﺑ ﻱﻮـﮕﻟﺍ ﺹﻮـﺼﺧ ﻪـﺑ ﻲﺘﻨـﺳ ﻱﺎﻫﻮﮕﻟﺍ ﻪﺑ ﺖﺒﺴﻧ ﺯﺭﺍ ﺥﺮﻧ
ﺏﺍﻮﺟ ؟ﺮﻴﺧ ﺎﻳ ﺖﺳﺍ ﻲﻓﺩﺎﺼﺗ ﻡﺎﮔ ﺶﻫﻭﮋﭘ
ﺮﮔ ﻥﺍ ﻪﺑ ﻝﺍﻮﺌﺳ ﺖﺳﺍ ﺖﺒﺜﻣ ﺭﻮﻛﺬﻣ .
ﻥﺍﺭﺎﻜﻤﻫ ﻭ ﻩﺪﻨﻓﺎﺑ )
1388 ( ﻲﺸﻫﻭﮋﭘ ﺭﺩ ﻪﺑ
ﺶﻴـﭘ ﻲـﻨﻴﺑ ﺭﻭﺩ ﻱﺍﺮـﺑ ﺯﺭﺍ ﺥﺮـﻧ ﻩ
ﻱ ﻲﻧﺎـﻣﺯ
1381 - 1387 ﺱﺎﺳﺍ ﺮﺑ ﻝﺪﻣ
ﺎﻫ ﻱ ARIMA ﻪﻜﺒﺷ ،
ﻱ ﻱﺯﺎـﻓ ﻲﺒﺼﻋ ANFIS
ﻭ ﻪﻜﺒـﺷ ﻱ
ﻲﻧﻮﻴﺳﺮﮔﺭ ﺩﻮﺧ ﻲﺒﺼﻋ NNARX
ﺘﺧﺍﺩﺮﭘ ﻪ ﺍ ﺪﻧ . ﺴﻳﺎﻘﻣ ﺯﺍ ﻞﺻﺎﺣ ﺞﻳﺎﺘﻧ ﻪ
ﻱ ﺭﻮﻛﺬـﻣ ﻝﺪﻣ ﻪﺳ
ﺭﺎﻴﻌﻣ ﺱﺎﺳﺍﺮﺑ ﺎﻫ
ﻒﻠﺘﺨﻣ ﻱ ﺶﻴﭘ
ﻲﻨﻴﺑ ﻥﺎﺸﻧ ﻲﻣ ﺭﺩ ﻪـﻛ ﺪـﻫﺩ ﺶﻴـﭘ
ﻲـﻨﻴﺑ ﺯﺭﺍ ﺥﺮـﻧ ، ﻝﺪـﻣ
ﻜﺒﺷ ﻪ ﻱ ﻱﺯﺎﻓ ﻲﺒﺼﻋ ANFIS
ﺮﺑ ﻝﺪﻣ ﺎﻫ ﻴﻗﺭ ﻱ ﺐ ﺩﺭﺍﺩ ﻱﺮﺗﺮﺑ .
ﺪﻨﺴﻳﻮﻧ ﺕﺎﻋﻼﻃﺍ ﺱﺎﺳﺍﺮﺑ ﻪﻛ ﺖﺳﺍ ﺮﻛﺫ ﻪﺑ ﻡﺯﻻ ﺭﻮـﻈﻨﻣ ﻪـﺑ ﻲـﻠﺧﺍﺩ ﺕﺎـﻌﻟﺎﻄﻣ ﺭﺩ ،ﻥﺎﮔ
ﻝﺪﻣ ﺶﻴﭘ ﻭ ﻱﺯﺎﺳ ﻝﺎـﺣ ﻪـﺑ ﺎـﺗ ﻲﻓﺩﺎـﺼﺗ ﻞﻴـﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎـﻌﻣ ﺱﺎـﺳﺍ ﺮـﺑ ﺯﺭﺍ ﺥﺮـﻧ ﻲﻨﻴﺑ
ﻪﻌﻟﺎﻄﻣ ﺖﺳﺍ ﻪﺘﻓﺮﮕﻧ ﻡﺎﺠﻧﺍ ﻱﺍ .١
3 - 2 - ﻲﺟﺭﺎﺧ ﺕﺎﻌﻟﺎﻄﻣ
ﻥﺍﺮﮕﻳﺩ ﻭ ﻦﻳﺍﺮﻛ )٢
2000 ( ﻝﺪﻣ ﺭﻮﻈﻨﻣ ﻪﺑ ، ﻩﺩﺍﺩ ﻱﺍﺮﺑ ﺯﺭﺍ ﺥﺮﻧ ﻱﺯﺎﺳ
ﺪـﻧﻮﭘ ﻪـﻧﺍﺯﻭﺭ ﻱﺎـﻫ
ﻪﻠﺻﺎﻓ ﺭﺩ ﺲﻴﻠﮕﻧﺍ ﻱ
ﻲﻧﺎﻣﺯ 1990 ﺎﺗ 1998 ﺭﺎﺸﺘﻧﺍ ﻲﻓﺩﺎﺼﺗ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎﻌﻣ ﻝﺪﻣ ﺯﺍ -
ﻩﺩﺮﻛ ﻩﺩﺎﻔﺘﺳﺍ ﺵﺮﭘ ﺪﻧﺍ
. ﻥﺁ ﺭﺎﺸﺘﻧﺍ ﻝﺪﻣ ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻦﻴﻤﺨﺗ ﻱﺍﺮﺑ ﺎﻫ -
ﻦﻴـﻤﺨﺗ ﺵﻭﺭ ﺵﺮـﭘ
ﻪﺘﻓﺮﮔ ﺭﺎﻛ ﻪﺑ ﺍﺭ ﻲﻳﺎﻤﻨﺘﺳﺍﺭ ﺮﺜﻛﺍﺪﺣ ﺪﻧﺍ
. ﻪﻴﺒﺷ ﺞﻳﺎﺘﻧ ﻥﺎـﺸﻧ ﻩﺪـﺷ ﻩﺩﺯ ﻦﻴـﻤﺨﺗ ﻝﺪـﻣ ﻱﺯﺎﺳ
ﻲﻣ ﻪﺳﻭﺮﭘ ﺭﺩ ﻪﻛ ﺪﻫﺩ ﻱ
ﻥﺁ ﻱﺩﺎﻬﻨﺸﻴﭘ ﻝﺪﻣ ،ﻩﺩﺍﺩ ﻖﻠﺧ ﺎﺳﻮﻧ ﺎﻫ
ﺵﺮﭘ ﻭ ﺕﺎﻧ ﺭﺩ ﺩﻮﺟﻮﻣ ﻱﺎﻫ
ﻩﺩﺍﺩ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﻲﻣ ﺵﺯﺍﺮﺑ ﻲﺑﻮﺧ ﻪﺑ ﺍﺭ ﺯﺭﺍ ﺥﺮﻧ ﻲﻌﻗﺍﻭ ﻱﺎﻫ
ﺪﻨﻛ .
ﻥﺍﺮﮕﻳﺩ ﻭ ﻞﺳﺎﺑ )٣
2004 (
، ﺪـﻨﻳﺁﺮﻓ ﺯﺍ ﻩﺩﺎﻔﺘـﺳﺍ ﺎـﺑ ﺍﺭ ﻩﺪـﻨﻨﻛ ﻑﺮـﺼﻣ ﺖـﻤﻴﻗ ﺺﺧﺎـﺷ
ﻱﺮﺘﻣﻮﺋژ ﻲﻧﻭﺁﺮﺑ ﺖﻛﺮﺣ ﻝﺪﻣ
ﺎﺳ ﺩﺮﻛ ﻱﺯ ﻩ ﻪﺑ ﺭﻮﻛﺬﻣ ﻝﺪﻣ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﺎﺑ ﻭ ﺶﻴﭘ
ﻲـﻨﻴﺑ ﻡﺭﻮـﺗ
ﺘﺧﺍﺩﺮﭘ ﻪ ﺍ ﺪﻧ . ﻥﺁ ﻢﻫ ﺎﻫ ﻦﻴـﻨﭼ ﺲـﭘ ﻪـﺴﻳﺎﻘﻣ ﺯﺍ ﻱ
ﺎـﺑ ﻲﻓﺩﺎـﺼﺗ ﻞﻴـﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎـﻌﻣ ﻝﺪـﻣ
ﻝﺪﻣ ﺎﻫ ﻭ ﻲﻓﺩﺎﺼﺗ ﻡﺎﮔ ﻱ GARCH-M
ﺪﻴﺳﺭ ﻪﺠﻴﺘﻧ ﻦﻳﺍ ﻪﺑ ﻩ ﺍ
ﻞﻴـﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎـﻌﻣ ﻪـﻛ ﺪﻧ
ﺭﺩ ﻲﻓﺩﺎﺼﺗ ﺶﻴﭘ
ﻲﻨﻴﺑ ﻥﺎﺸﻧ ﺩﻮﺧ ﺯﺍ ﻱﺮﺘﻬﺑ ﺩﺮﻜﻠﻤﻋ ،ﻡﺭﻮﺗ ﻲﻣ
ﺪﻫﺩ .
ﻦﻴﭽﻳﺮــﻛ ﻭ ﻱﺮﮕــﺴﻋ )٤
2008 ( ﺕﻻﺩﺎــﻌﻣ ﻝﺪــﻣ ﻚــﻳ ﺖــﺤﺗ ﺍﺭ ﺖــﻔﻧ ﺖــﻤﻴﻗ ﻲﻳﺎــﻳﻮﭘ
ﺘﻧﺍ ﻲﻓﺩﺎﺼﺗ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺭﺎﺸ
- ﺵﺮﭘ ﻝﺪﻣ ﺯﺎﺳ ﺩﺮﻛ ﻱ ﻩ ﺪﻧﺍ . ﻥﺁ ﻱﺍﺮـﺑ ﺎـﻫ ﻱﺎـﻫﺮﺘﻣﺍﺭﺎﭘ ﻦﻴـﻤﺨﺗ
ﺘﻓﺮﮔﺭﺎﻛ ﻪﺑ ﺍﺭ ﻲﻳﺎﻤﻨﺘﺳﺍﺭ ﺮﺜﻛﺍﺪﺣ ﺵﻭﺭ ﺭﻮﻛﺬﻣ ﻝﺪﻣ ﻪ
ﻭ ﺪﻴـﺳﺭ ﻪـﺠﻴﺘﻧ ﻦﻳﺍ ﻪﺑ ﻩ
ﺪـﻧﺍ ﺭﺩ ﻪـﻛ
ﻩﺭﻭﺩ ﻝﻮﻃ ﻱ
ﺮﻈﻧ ﺩﺭﻮﻣ
، ﻭ ﻝﺩﺎﻌﺗ ﺯﺍ ﺝﺭﺎﺧ ﺖﻔﻧ ﺭﺍﺯﺎﺑ ﻢﻫ
ﻦﻴﻨﭼ ﻙﻮﺷ ﻪﺑ ﺖﺒﺴﻧ ﺎـﻫ
ﻑﺮـﻃ ﻱ
ﺖﺳﺍ ﻩﺩﻮﺑ ﺱﺎﺴﺣ ﺎﺿﺎﻘﺗ ﻭ ﻪﺿﺮﻋ .
1 - ﻖﻳﺪﺻ ﻲﻛﺎﺧ ﻭ ﻩﺩﺍﺯﻮﻟﺎﺧ )
1383 ( ﻗ ﺺﺧﺎﺷ ﺮﺑ ﺍﺭ ﻥﺍﺮﻬﺗ ﺱﺭﻮﺑ ﺭﺍﺯﺎﺑ ﻡﺎﻬﺳ ﺖﻤﻴ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎﻌﻣ ﺱﺎﺳﺍ
ﻝﺪﻣ ﻲﻓﺩﺎﺼﺗ ﺶﻴﭘ ﻭ ﻱﺯﺎﺳ
ﻩﺩﺮﻛ ﻲﻨﻴﺑ ﺪﻧﺍ . ﻥﺁ ﻪﺴﻳﺎﻘﻣ ﻪﺑ ﺎﻫ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﻝﺪﻣ ﺎﺑ ﻝﺪﻣ ﻦﻳﺍ ﻱ
ARIMA ﻪﺘﺧﺍﺩﺮﭘ ﺪﻧﺍ .
ﺞﻳﺎﺘﻧ ﺮﮕﻧﺎﻴﺑ ﻥﺁ ﺖﺳﺍ ﺪﻣ ﻪﻛ ﺶﻴﭘ ﺭﺩ ﺍﺭ ﻱﺮﺘﻬﺑ ﺩﺮﻜﻠﻤﻋ ﻲﻓﺩﺎﺼﺗ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎﻌﻣ ﻝ ﻡﺎﻬﺳ ﺖﻤﻴﻗ ﺺﺧﺎﺷ ﻲﻨﻴﺑ
ﻲﻣ ﻥﺎﺸﻧ ﺩﻮﺧ ﺯﺍ ﺪﻫﺩ
. ﻥﺁ ﺖﺳﺍ ﺮﻛﺫ ﻪﺑ ﻡﺯﻻ ﺍﺭ ﻲﺻﺎﺧ ﺵﻭﺭ ﺎﻫ
ﺮﺑ ﻱﺍ ﻪﻟﺩﺎﻌﻣ ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻦﻴﻤﺨﺗ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﻱ
ﻩﺩﺮﻜﻧ ﻪﺋﺍﺭﺍ ﻩﺩﺎﻔﺘﺳﺍ ﺩﺭﻮﻣ ﻲﻓﺩﺎﺼﺗ ﺪﻧﺍ
. ﻢﻫ ﻥﺁ ﻱﺩﺎﻬﻨﺸﻴﭘ ﻝﺪﻣ ﻦﻴﻨﭼ ﺵﺮﭘ ﺵﺯﺍﺮﺑ ﻪﺑ ﺭﺩﺎﻗ ﺎﻫ
ﻲﺘﻤﻴﻗ ﻱﺎﻫ ﻡﺎﻬﺳ
ﺖﺴﻴﻧ . 2- Craine, R and Lochstoer, Lars.A and Syrtveit, K.
3- Basel M. AL.Eidehc, Ahmad S. A. AL.refal and Wafaa M. Sbeiti.
4- Askari.H and Krichene.N.
ﻚﻴﻨــﺳﻼﭘ )١
2010 ( ﺪــﻣ ، ﻝ ﺎــﻫ ﻱﺍﺮــﺑ ﺍﺭ ﻲﻓﺩﺎــﺼﺗ ﻞﻴــﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎــﻌﻣ ﻒــﻠﺘﺨﻣ ﻱ
ﺶﻴﭘ ﻲﻨﻴﺑ ﻱﺮﺳ ﺎﻫ ﺖـﺳﺍ ﻪـﺘﻓﺮﮔﺭﺎﻛ ﻪـﺑ ﻲﻳﺎـﭘﻭﺭﺍ ﻒﻠﺘﺨﻣ ﺭﺍﺯﺎﺑ ﺪﻨﭼ ﻲﻟﺎﻣ ﻲﻧﺎﻣﺯ ﻱ .
ـﺳ ﺲﭙ
ﻪﺴﻳﺎﻘﻣ ﻝﺪﻣ ﻦﻴﺑ ﻱﺍ ﻻﺩﺎﻌﻣ ﻱﺎﻫ
ﻝﺪﻣ ﻭ ﻲﻓﺩﺎﺼﺗ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺕ ﺎﻫ
ﻲﻧﺎـﻣﺯ ﻱﺮﺳ ﻱ ARIMA
ﻭ GARCH ﻡﺎﺠﻧﺍ
ﻩﺩﺍﺩ ﺖﺳﺍ . ﻥﺎـﺸﻧ ﻱﻭ ﺞﻳﺎﺘﻧ ﻲـﻣ
ﻱﺎـﻄﺧ ﻪـﻛ ﺪـﻫﺩ ﺶﻴـﭘ
ﻲـﻨﻴﺑ ﻝﺪـﻣ
ﻝﺪﻣ ﺯﺍ ﻲﻓﺩﺎﺼﺗ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎﻌﻣ ﺎﻫ
ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﻱ ﻢﻛ
ﺮﺗ ﺖﺳﺍ .
4 - ﻩﺩﺍﺩ ﻦﻴﻴﺒﺗ ﻖﻴﻘﺤﺗ ﻭﺮﻤﻠﻗ ﻭ ﺎﻫ
ﻩﺩﺍﺩ ﺎﻫ ﻩﺩﺎﻔﺘﺳﺍ ﺩﺭﻮﻣ ﻱ ﻱ
ﻩﺩﺍﺩ ﺮﺿﺎﺣ ﻖﻴﻘﺤﺗ ﺎﻫ
ﻪﻧﺍﺯﻭﺭ ﻱ ﻱ ﻲﻤـﺳﺭ ﺭﺍﺯﺎﺑ ﺯﺭﺍ ﺥﺮﻧ )
ﻝﺎـﻳﺭ
ﺭﻻﺩ ﻞﺑﺎﻘﻣ ﺭﺩ (
ﺩ ﻩﺯﺎﺑ ﺭ ﻱ ﻲﻧﺎﻣﺯ 23 ﻦﻳﺩﺭﻭﺮﻓ 1380
ﺎﺗ ﻝﻭﺍ ﺩﺍﺩﺮﻣ 1390 ﻲﻣ ﺪﺷﺎﺑ . ﻩﺩﺍﺩ ﺎـﻫ
ﺏﻭ ﺯﺍ ﺪﺷ ﻪﺘﻓﺮﮔ ﻱﺰﻛﺮﻣ ﻚﻧﺎﺑ ﺖﻳﺎﺳ ﻩ
ﺪﻧﺍ . ﻪـﻧﻮﻤﻧ ﺏﺎـﺨﺘﻧﺍ ﺖـﻠﻋ ﻪـﻛ ﺖﺳﺍ ﺮﻛﺫ ﻪﺑ ﻡﺯﻻ ﻱ
ﺯﺍ ﻭ ﺖـﺳﺍ ﻲﻧﺎـﻣﺯ ﻱﺮـﺳ ﻦﻳﺍ ﺪﻧﻭﺭ ﺭﺩ ﺭﻮﺸﻛ ﻱﺯﺭﺍ ﻡﺎﻈﻧ ﺮﻴﻴﻐﺗ ﻞﻴﻟﺩ ﻪﺑ ﺵﺮﭘ ﺩﻮﺟﻭ ﺭﻮﻛﺬﻣ ﺭﺩ ﺵﺮـﭘ ﺵﺯﺍﺮـﺑ ﻱﺍﺮـﺑ ﻲﻟﺪـﻣ ﻦﻴـﻤﺨﺗ ﻭ ﺩﺭﻭﺁﺮـﺑ ﻪـﻛ ﻖـﻴﻘﺤﺗ ﻲﻠـﺻﺍ ﻑﺪﻫ ﺮﺑﺎﻨﺑ ﻲﻳﻮﺳ ﻱﺮﺳ ﻪﻧﻮﻤﻧ ﺏﺎﺨﺘﻧﺍ ،ﺖﺳﺍ ﻲﻧﺎﻣﺯ ﻱﺎﻫ ﻮﻣ ﺮﻈﻧ ﺩﺭﻮﻣ ﻱ
ﻲﻣ ﺮﻈﻧ ﻪﺑ ﻪﺟ ﺪﺳﺭ
. ﺭﺍﺩﻮـﻤﻧ 1 ﺪـﻧﻭﺭ ،
ﻩﺩﺍﺩ ﻲﻧﺎﻣﺯ ﺯﺭﺍ ﺥﺮﻧ ﻱﺎﻫ
ﻲﻣ ﻥﺎﺸﻧ ﺍﺭ ﺪﻫﺩ
.
ﺭﺍﺩﻮﻤﻧ 1 - ﻩﺩﺍﺩ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺪﻧﻭﺭ ﺎﻫ
ﻲﻤﺳﺭ ﺭﺍﺯﺎﺑ ﺯﺭﺍ ﺥﺮﻧ ﻱ )
ﺭﻻﺩ ﺮﺑﺍﺮﺑ ﺭﺩ ﻝﺎﻳﺭ (
5 - ﻖﻴﻘﺤﺗ ﺕﺎﻴﺿﺮﻓ
ﻪﻴﺿﺮﻓ ﻱ ﻦﻴﻴﺒﺗ ﺮﻳﺯ ﺕﺭﻮﺻ ﻪﺑ ﺮﺿﺎﺣ ﻖﻴﻘﺤﺗ ﻲﻣ
ﺩﻮﺷ :
ﻝﺪﻣ ﻱﺎﻫ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎﻌﻣ ﻲﻓﺩﺎﺼﺗ
GBM ﻭ ﻝﺪﻣ ﻪﺑ ﺖﺒﺴﻧ ﻱﺮﺘﻬﺑ ﺩﺮﻜﻠﻤﻋMJD
ARIMA ﺭﺩ
ﺶﻴﭘ ﻲﻨﻴﺑ ﺭﺍﺩ ﺯﺭﺍ ﺥﺮﻧ ﻧ
ﺪ .
1- Pluciennik, P.
6 - ﻝﺪﻣ ﻦﻴﻤﺨﺗ ﺎﻫ
ﺞﻳﺎﺘﻧ ﺢﻳﺮﺸﺗ ﻭ
ﻝﺪﻣ ﻦﻴﻤﺨﺗ ﺞﻳﺎﺘﻧ ﺶﺨﺑ ﻦﻳﺍ ﺭﺩ ﺎﻫ
ﻭ ﺶﻴﭘ ﻲﻨﻴﺑ ﺯﺍ ﺝﺭﺎﺧ ﻪﻧﻮﻤﻧ ﻱ ﻩﺪﺷ ﺵﺭﺍﺰﮔ ﺯﺭﺍ ﺥﺮﻧ
ﺖﺳﺍ . ﻝﺪﻣ ﻦﻴﻤﺨﺗ ﻱﺍﺮﺑ ﻩﺩﺍﺩ ﻞﻛ ﺯﺍMJD
ﺎﻫ ) ﻪﻧﻮﻤﻧ ﻝﻭﺍ ﻱ ( ﻝﺪﻣ ﺵﺯﺍﺮﺑ ﻱﺍﺮﺑ ﻭ ﺍGBM
ﺯ
ﻩﺩﺍﺩ ﻪﻧﻮﻤﻧ ﻱﺎﻫ ﻪﻠـﺻﺎﻓ ﺭﺩ ﺮﻈﻧ ﺩﺭﻮﻣ ﻱ
ﻱ 5 ﻝﺎـﺳ ﻦﻳﺩﺭﻭﺮـﻓ 1381
ﺩﺍﺩﺮـﻣ ﻝﻭﺍ ﺎـﺗ 1390
) ﻪﻧﻮﻤﻧ ﻡﻭﺩ ﻱ ( ﻲﻣ ﻩﺩﺎﻔﺘﺳﺍ ﺩﻮﺷ
. ﻝﺪـﻣ ﻪـﻛ ﺖـﺳﺍ ﻦـﻳﺍ ﺏﺎﺨﺘﻧﺍ ﻦﻳﺍ ﺖﻠﻋ ﻪـﺑ ﺭﺩﺎـﻗGBM
ﺵﺮﭘ ﺵﺯﺍﺮﺑ ﻪـﻧﻮﻤﻧ ﻦﻳﺍﺮﺑﺎـﻨﺑ ،ﺖـﺴﻴﻧ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺭﺩ ﺩﻮﺟﻮﻣ ﻱﺎﻫ
ﻞـﻛ ﺯﺍ ﻲﺘﻤـﺴﻗ ﻡﻭﺩ ﻱ
ﻩﺩﺍﺩ ﻲﻣ ﺎﻫ ﻲﻧﺎﻬﮔﺎﻧ ﺵﺮﭘ ﻞﻣﺎﺷ ﻪﻛ ﺪﺷﺎﺑ ﺖﺴﻴﻧ ﺭﻮﺸﻛ ﻱﺯﺭﺍ ﻡﺎﻈﻧ ﺮﻴﻴﻐﺗ ﺯﺍ ﻲﺷﺎﻧ
. ﻞﺒﻗ ﺍﺪﺘﺑﺍ
ﺯﺍ ﻝﺪﻣ ﺎﺳ ﻝﺪﻣ ﻦﻴﻤﺨﺗ ﻭ ﻱﺯ
،ﺎﻫ ﻪﻧﻮﻤﻧ ﻱﺎﻫ ﺶﻳﺎـﻣﺯﺁ ﻭ ﺵﺯﻮـﻣﺁ ﺶـﺨﺑ ﻭﺩ ﻪﺑ ﻲﺳﺭﺮﺑ ﺖﺤﺗ
ﻢﻴﺴﻘﺗ ﻲﻣ ﻧﻮﺷ ﺪ . ﺵﺯﻮﻣﺁ ﺶﺨﺑ ﻱﺍﺮﺑ
ﻝﺪﻣ ﺩﺭﻭﺁﺮﺑ ﺎﻫ
ﻱﺎﻄﺧ ﺩﺭﻭﺁﺮﺑ ﺖﻬﺟ ﺶﻳﺎﻣﺯﺁ ﺶﺨﺑ ﻭ
ﺶﻴﭘ ﻲﻨﻴﺑ ﺯﺍ ﺝﺭﺎﺧ ﻪﻧﻮﻤﻧ ﻝﺪﻣ ﻱ ﻪﺴﻳﺎﻘﻣ ﻭ ﺎﻫ ﻱ
ﻥﺁ ﺩﺮﻜﻠﻤﻋ ﺘﺳﺍ ﺩﺭﻮﻣ ﺎﻫ
ﻲﻣ ﺭﺍﺮﻗ ﻩﺩﺎﻔ ﺩﺮﻴﮔ
.
ﻪﻧﻮﻤﻧ ﻱﺍﺮﺑ ﺯﺍ ﻝﻭﺍ ﻱ
23 ﻦﻳﺩﺭﻭﺮﻓ 1380
ﻝﺎـﺳ ﺩﺍﺩﺮﺧ ﺮﺧﺁ ﺎﺗ 1390
ﺯﺍ ﻭ ﺵﺯﻮـﻣﺁ ﺶـﺨﺑ
ﻝﺎﺳ ﺩﺍﺩﺮﻣ ﻝﻭﺍ ﺎﺗ ﺮﻴﺗ ﻝﻭﺍ 1390
ﻪﻧﻮﻤﻧ ﺶﻳﺎﻣﺯﺁ ﺶﺨﺑ ﻲﻣ ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﻝﻭﺍ ﻱ
ﺩﻮﺷ . ﻱﺍﺮﺑ
ﻪﻧﻮﻤﻧ ﺯﺍ ﻡﻭﺩ ﻱ 23
ﻦﻳﺩﺭﻭﺮﻓ 1380
ﺩﺍﺩﺮﺧ ﺮﺧﺁ ﺎﺗ 1390
ﺎـﺗ ﺮـﻴﺗ ﻝﻭﺍ ﺯﺍ ﻭ ﺵﺯﻮـﻣﺁ ﺶﺨﺑ
ﺩﺍﺩﺮﻣ ﻝﻭﺍ 1390
ﻪﻧﻮﻤﻧ ﺶﻳﺎﻣﺯﺁ ﺶﺨﺑ ﺖﺳﺍ ﻩﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﻡﻭﺩ ﻱ
. ﻭﺩ ﺶﻳﺎﻣﺯﺁ ﺶﺨﺑ
ﻪﻧﻮﻤﻧ ﻱ ﻪﻤﻫ ﻥﺍﻮﺘﺑ ﺎﺗ ﺖﺳﺍ ﻩﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﻥﺎﺴﻜﻳ ﻱ
ﻝﺪﻣ ﺍﺭ ﻩﺪـﺷ ﻩﺩﺯ ﻦﻴـﻤﺨﺗ ﻱﺎـﻫ
ﺶﻴﭘ ﺭﺩ ﺩﺮﻛ ﻪﺴﻳﺎﻘﻣ ﺮﮕﻳﺪﻤﻫ ﺎﺑ ﻪﻧﻮﻤﻧ ﺯﺍ ﺝﺭﺎﺧ ﻲﻨﻴﺑ .
ﻪﺑ ﻝﺪﻣ ﺩﺭﻭﺁﺮﺑ ﺭﻮﻈﻨﻣ ARIMA
ﺲﻛﺎﺑ ﻱژﻮﻟﻭﺪﺘﻣ ﺯﺍ -
ﺰﻨﻴﻜﻨﺟ ﻲـﻣ ﻩﺩﺎﻔﺘﺳﺍ ١
ﺩﻮـﺷ . ﺮـﺑ
ﻥﻮﻣﺯﺁ ﻖﻳﺮﻃ ﺯﺍ ﺍﺪﺘﺑﺍ ﺱﺎﺳﺍ ﻦﻳﺍ ﻪﺸﻳﺭ ﻱﺎﻫ
ﺲﭙﻴﻠﻴﻓ ﺪﺣﺍﻭ ﻱ -
٢ﻥﻭﺮﭘ ﻢﻴـﻤﻌﺗ ﺮﻟﻮـﻓ ﻲﻜﻳﺩ ﻭ
ﻪﺘﻓﺎﻳ ﻪﺒﺗﺮﻣ٣
ﻪـﻧﻮﻤﻧ ﻭﺩ ﺮـﻫ ﻱﺍﺮﺑ ﺯﺭﺍ ﺥﺮﻧ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﻲﮕﺘﺷﺎﺒﻧﺍ ﻱ ﺺﺨـﺸﻣ ﻡﻭﺩ ﻭ ﻝﻭﺍ ﻱ
ﻲﻣ ﺩﻮﺷ . ﻲﻣ ﻥﺎﺸﻧ ﻩﺩﺮﺒﻣﺎﻧ ﻥﻮﻣﺯﺁ ﻭﺩ ﺞﻳﺎﺘﻧ ﻪـﻧﻮﻤﻧ ﻪـﻛ ﺪـﻫﺩ
ﻦﻳﺍﺮﺑﺎـﻨﺑ ﻭ ﺎـﻧﺎﻣ ﻝﻭﺍ ﻱ I(0)
ﻭ
ﻪــﻧﻮﻤﻧ ﺘــﺷﺎﺒﻧﺍ ﻡﻭﺩ ﻱ ﻪــﺟﺭﺩ ﺯﺍ ﻪ
ﻲــﻨﻌﻳ ﻚــﻳ ﻱ ﻲــﻣI(1)
ﺪــﺷﺎﺑ . ﻊــﺑﺍﻮﺗ ﻖــﻳﺮﻃ ﺯﺍ ﺲﭙــﺳ
ﻲﮕﺘﺴﺒﻤﻫﺩﻮﺧ ﻲﺋﺰﺟ ﻲﮕﺘﺴﺒﻤﻫﺩﻮﺧ ﻭ٤
ﻢﻫ ﻭ٥
ﻚـﻴﺋﺎﻛﺁ ﺭﺎﻴﻌﻣ ﻦﻴﻨﭼ ﻪـﻔﻗﻭ ،٦
ﻪـﻨﻴﻬﺑ ﻱﺎـﻫ
ﻭAR ﻪﻧﻮﻤﻧ ﻭﺩ ﻱﺍﺮﺑMA
ﻱ ﻲﻣ ﻦﻴﻴﻌﺗ ﻩﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﺩﻮﺷ
. ﻦﻳﺪﺑ ﻪـﻨﻴﻬﺑ ﻝﺪﻣ ﺐﻴﺗﺮﺗ
ARIMA ﺲﻛﺎﺑ ﻱژﻮﻟﻭﺪﺘﻣ ﺱﺎﺳﺍ ﺮﺑ
- ﻪﻧﻮﻤﻧ ﻱﺍﺮﺑ ﺰﻨﻴﻜﻨﺟ ﻝﻭﺍ ﻱ
AR(1) ﻪـﻧﻮﻤﻧ ﻱﺍﺮﺑ ﻭ ﻱ
ﻡﻭﺩ ARIMA(12,1,1) ﻲﻣ
ﺪﺷﺎﺑ .
ﻝﺪﻣ ﺩﺭﻭﺁﺮﺑ ﺭﻮﻈﻨﻣ ﻪﺑ ﻪﻧﻮﻤﻧ ﻱﺍﺮﺑMJD
ﻩﺩﺍﺩ ﻞﻛ ﻞﻣﺎﺷ ﻪﻛ ﻝﻭﺍ ﻱ ﻲـﺳﺭﺮﺑ ﺖـﺤﺗ ﻱﺎﻫ
ﻲـﻣ ﻪﺒـﺳﺎﺤﻣ ﻚﻳﺮﺘﻣﺍﺭﺎﭘﺎﻧ ﺵﻭﺭ ﺯﺍ ﻪﻟﺩﺎﻌﻣ ﻦﻳﺍ ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﺍﺪﺘﺑﺍ ،ﺖﺳﺍ ﺩﻮـﺷ
. ﻝﻭﺪـﺟ ﺭﺩ 1
ﻝﺪﻣ ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻦﻴﻤﺨﺗ ﺞﻳﺎﺘﻧ ﻱﺎﻫ
ﻭGBM ﺖﺳﺍ ﻩﺪﺷ ﺵﺭﺍﺰﮔMJD
.
1- Box-Jenkins methodology.
2- Phillips-Peron unit root test.
3- Augmented Dickey-Fuller unit root test.
4- Auto Correlation Functions (ACF).
5- Partial Autocorrelation Functions (PAF).
6- Akaike Information Criterion (AIC).
ﻝﻭﺪﺟ 1 - ﻝﺪﻣ ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻦﻴﻤﺨﺗ ﺎﻫ
ﻱ ﻭGBM ﻚﻳﺮﺘﻣﺍﺭﺎﭘﺎﻧ ﺵﻭﺭ ﻪﺑMJD
k N(t) m s
ﻝﺪﻣ
GBM
MJD
ﻊﺒﻨﻣ : ﺕﺎﺒﺳﺎﺤﻣ ﺶﻫﻭﮋﭘ ﺮﮔ ﻥﺍ
ﺮﺑﺎﻨﺑ ﻝﻭﺪﺟ ﺞﻳﺎﺘﻧ 1
ﻪﻟﺩﺎﻌﻣ ﻭ ﻱﺎـﻫ ) 11 ( ﻭ ) 16 ( ﻝﺪـﻣ ، ﻱﺎـﻫ ﻭGBM ﻦﻴـﻤﺨﺗMJD
ﻩﺩﺍﺩ ﻱﺍﺮﺑ ﻩﺪﺷ ﻩﺩﺯ ﻲﻣ ﺮﻳﺯ ﺕﺭﻮﺻ ﻪﺑ ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺭﺩ ﻩﺩﺎﻔﺘﺳﺍ ﺩﺭﻮﻣ ﺯﺭﺍ ﺥﺮﻧ ﻱﺎﻫ
ﺪﻨﺷﺎﺑ :
) 17 (
e(t)=7924exp(( .0 3361)t+0 1089. w(t))
) 18 (
e(t)=1755exp{( .0 2732)t+0 1494. w(t)+ln(1+3 5151. )}
ﻥﺁ ﺯﺍ ﻱﺎﻫﻮﮕﻟﺍ ﺭﺩ ﻲﻓﺩﺎﺼﺗ ﺪﻧﻭﺭ ﻪﻛﺎﺟ ﻭGBM
ﻆﻔﺣMJD ﺖﺳﺍ ﻩﺪﺷ )
ﺪـﻨﻳﺁﺮﻓ ﺩﻮﺟﻭ
ﻮﮕﻟﺍ ﺭﺩ ﺮﻨﻳﻭ (
ﻲﻣ ﺐﺒﺳ ﻪﻠﺌﺴﻣ ﻦﻳﺍ ، ﻪﻴﺒﺷ ﺯﺍ ﻞﺻﺎﺣ ﺞﻳﺎﺘﻧ ﻪﻛ ﺩﻮﺷ
ﻱﺯﺎﺳ ) ﻪـﺳﻭﺮﭘ ﻱ ﻖـﻠﺧ
١ﻩﺩﺍﺩ ( ﻝﺪﻣ ﻦﻳﺍ ﺪﺷﺎﺒﻧ ﺭﺍﺪﻳﺎﭘ ﺎﻫ .
ﻪﻴﺒـﺷ ﺪـﻨﻳﺁﺮﻓ ﻞﻜﺸﻣ ﻦﻳﺍ ﻞﺣ ﻱﺍﺮﺑ ﻱﺍﺮـﺑ ﻱﺯﺎـﺳ
5000
ﻦﻳﺍ ﻦﻴﺑ ﺯﺍ ﻭ ﻪﺘﻓﺮﻳﺬﭘ ﻡﺎﺠﻧﺍ ﺭﺍﺮﻜﺗ 5000
ﻪﻴﺒـﺷ ﺭﺍﺮـﻜﺗ ﺭﺎـﺑ ﻱﺍﺭﺍﺩ ﻪـﻛ ﻱﺭﺍﺮـﻜﺗ ﻥﺁ ،ﻱﺯﺎـﺳ
ﻢﻛ ﺗ ﻦﻳﺮ ﻪﻧﻮﻤﻧ ﻞﺧﺍﺩ ﺵﺯﺍﺮﺑ ﺭﺩRMSE
ﻱ ﻩﺩﺍﺩ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﻪﻨﻴﻬﺑ ﺭﺍﺮﻜﺗ ﻥﺍﻮﻨﻋ ﻪﺑ ﺪﺷﺎﺑ ﺎﻫ
ﺖﺳﺍ ﻩﺪﺷ ﺏﺎﺨﺘﻧﺍ .٢
ﻱﺎﻫﺭﺍﺩﻮﻤﻧ ﺭﺩ 2
ﻭ 3 ﻱﺮـﺳ ﻩﺩﺍﺩ ﻲﻧﺎـﻣﺯ ﻱﺎـﻫ ﺵﺯﺍﺮـﺑ ﻭ ﻲـﻌﻗﺍﻭ ﻱﺎـﻫ
ﻪﻨﻴﻬﺑ ﻱ ﻪﻧﻮﻤﻧ ﻱﺍﺮﺑ ﻪﻧﻮﻤﻧ ﻞﺧﺍﺩ ﻝﺪـﻣ ﺱﺎـﺳﺍ ﺮـﺑ ﻝﻭﺍ ﻱ
ﻱﺎـﻫ ﻪـﻄﺑﺍﺭ ﺭﺩMJD
ﻱ ) 18 ( ﻭ
AR(1) ﻩﺪﺷ ﻪﺴﻳﺎﻘﻣ ﺪﻧﺍ
.
ﺭﺍﺩﻮﻤﻧ 2 - ﻪﺴﻳﺎﻘﻣ ﻱ ﻩﺩﺍﺩ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺎﻫ
ﺱﺎﺳﺍ ﺮﺑ ﻪﻧﻮﻤﻧ ﻞﺧﺍﺩ ﺵﺯﺍﺮﺑ ﻭ ﻲﻌﻗﺍﻭ ﻱ ﻝﺪﻣ MJD
1- Data Generating Process.
2 - ﺪﻨﻳﺁﺮﻓ ﻪﻴﺒﺷ ﻪﻣﺎﻧﺮﺑ ﻚﻳ ﺐﻟﺎﻗ ﺭﺩ ﻱﺯﺎﺳ ﻱ
ﻡﺮﻧ ﻂﻴﺤﻣ ﺭﺩ ﻩﺪﺷ ﻪﺘﺷﻮﻧ ﺭﺍﺰﻓﺍ
MATLAB
ﺍ ،ﺖﺳﺍ ﻪﺘﻓﺮﻳﺬﭘ ﻡﺎﺠﻧ
ﻲﻣ ﻞﻳﺎﻤﺗ ﺕﺭﻮﺻ ﺭﺩ ﻥﺎﮔﺪﻨﻧﺍﻮﺧ ﺖﺳﺍﻮﺧﺭﺩ ﻪﻟﺎﻘﻣ ﻥﺎﮔﺪﻨﺴﻳﻮﻧ ﺯﺍ ﺍﺭ ﺎﻫ ﻪﻣﺎﻧﺮﺑ ﻦﻳﺍ ﻞﻳﺎﻓ ﺪﻨﻧﺍﻮﺗ
ﻛ ﺪﻨﻨ .
ﺭﺍﺩﻮﻤﻧ 3 - ﻪﺴﻳﺎﻘﻣ ﻱ ﻩﺩﺍﺩ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺎﻫ
ﻝﺪﻣ ﺱﺎﺳﺍﺮﺑ ﻪﻧﻮﻤﻧ ﻞﺧﺍﺩ ﺵﺯﺍﺮﺑ ﻭ ﻲﻌﻗﺍﻭ ﻱ AR(1)
ﻱﺎﻫﺭﺍﺩﻮﻤﻧ ﺞﻳﺎﺘﻧ ﺱﺎﺳﺍﺮﺑ 2
ﻭ 3 ﻝﺪـﻣ ﻑﻼﺧﺮـﺑ ، ﻝﺪـﻣ ،AR
ﺵﺯﺍﺮـﺑ ﻪـﺑ ﺭﺩﺎـﻗMJD
ﺳﻮﻧ ﻢﻫ ﻭ ﺕﺎﻧﺎ ﺖﺳﺍ ﺯﺭﺍ ﺥﺮﻧ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺭﺩ ﺩﻮﺟﻮﻣ ﺵﺮﭘ ﻦﻴﻨﭼ
.
ﻱﺎﻫﺭﺍﺩﻮﻤﻧ ﺭﺩ 4
ﻭ 5 ﻱﺮﺳ ، ﻩﺩﺍﺩ ﻲﻧﺎﻣﺯ ﻱﺎﻫ ﻪﻨﻴﻬﺑ ﺵﺯﺍﺮﺑ ﻭ ﻲﻌﻗﺍﻭ ﻱﺎﻫ
ﻱ ﻪـﻧﻮﻤﻧ ﻞﺧﺍﺩ
ﻪـﻧﻮﻤﻧ ﻱﺍﺮﺑ ﻝﺪـﻣ ﺱﺎـﺳﺍ ﺮـﺑ ﻝﻭﺍ ﻱ
ﻱﺎـﻫ ﻪـﻄﺑﺍﺭ ﺭﺩGBM
ﻱ ) 17 ( ﻭ ARIMA()
ﻩﺪﺷ ﻪﺴﻳﺎﻘﻣ ﺪﻧﺍ
.
ﺭﺍﺩﻮﻤﻧ 4 - ﻪﺴﻳﺎﻘﻣ ﻱﺮﺳ ﻱ ﻩﺩﺍﺩ ﻲﻧﺎﻣﺯ ﻝﺪﻣ ﺱﺎﺳﺍﺮﺑ ﻪﻧﻮﻤﻧ ﻞﺧﺍﺩ ﺵﺯﺍﺮﺑ ﻭ ﻲﻌﻗﺍﻭ ﻱﺎﻫ
GBM
ﺭﺍﺩﻮﻤﻧ 5 - ﻪﺴﻳﺎﻘﻣ ﻱ ﻩﺩﺍﺩ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺮﺑ ﻪﻧﻮﻤﻧ ﻞﺧﺍﺩ ﺵﺯﺍﺮﺑ ﻭ ﻲﻌﻗﺍﻭ ﻱﺎﻫ
ﻝﺪﻣ ﺱﺎﺳﺍ
ARIMA()
ﻥﺁ ﻱﺎﻫﺭﺍﺩﻮﻤﻧ ﺯﺍ ﻪﭼ 4
ﻭ 5 ﻲﻣ ﻪﺠﻴﺘﻧ ﻝﺪـﻣ ﻑﻼﺧﺮـﺑ ﻪـﻛ ﺖـﺳﺍ ﻦـﻳﺍ ﺩﻮﺷ
ARIMA ،
ﻱﺩﺎﻬﻨﺸﻴﭘ ﻝﺪﻣ ﻧﺎﺳﻮﻧ GBM
ﺵﺯﺍﺮـﺑ ﻲﺑﻮـﺧ ﻪـﺑ ﺍﺭ ﺯﺭﺍ ﺥﺮـﻧ ﻲﻧﺎـﻣﺯ ﻱﺮـﺳ ﺭﺩ ﺩﻮﺟﻮﻣ ﺕﺎ
ﻲﻣ ﺪﻨﻛ . ﻪﻴﺒﺷ ﻡﺎﺠﻧﺍ ﺯﺍ ﺲﭘ ﻝﺪـﻣ ﻱﺍﺮـﺑ ﻪﻨﻴﻬﺑ ﺭﺍﺮﻜﺗ ﺏﺎﺨﺘﻧﺍ ﻭ ﻱﺯﺎﺳ
ﻱﺎـﻫ ﻭGBM
،MJD
ﻪـﺑ
ﺶﻴﭘ ﻪﻧﻮﻤﻧ ﺶﻳﺎﻣﺯﺁ ﺶﺨﺑ ﺱﺎﺳﺍﺮﺑ ﻪﻧﻮﻤﻧ ﺯﺍ ﺝﺭﺎﺧ ﻲﻨﻴﺑ ﻲﻣ ﻪﺘﺧﺍﺩﺮﭘ ﻡﻭﺩ ﻭ ﻝﻭﺍ ﻱﺎﻫ
ﺩﻮـﺷ .
ﻝﻭﺪﺟ 3 ﺶﻴﭘ ﻱﺎﻄﺧ ﻥﺍﺰﻴﻣ ، ﻪﻧﻮﻤﻧ ﺯﺍ ﺝﺭﺎﺧ ﻲﻨﻴﺑ
ﻱ ﻝﺪـﻣ ﻦـﻳﺍ ﺎـﻫ
ﻲﻧﺎـﻣﺯ ﻱﺮـﺳ ﻝﺪـﻣ ﻭ
ARIMA ﻲﻘﻓﺍ ﻱﺍﺮﺑ ﺍﺭ
1 ﻪﻳﺎﭘ ﺮﺑ ﻭ ﻪﻫﺎﻣ ﻱ
ﺭﻭﺎﺘﺸﮔ ﻲـﻣ ﻥﺎـﺸﻧRMSE
ﺪـﻫﺩ . ﻦـﻳﺍ ﺞﻳﺎـﺘﻧ
ﺶﻴﭘ ﺭﺩ ﻪﻛ ﺖﺳﺍ ﻥﺁ ﺯﺍ ﻲﻛﺎﺣ ﻝﻭﺪﺟ ﻝﺪﻣ ،ﻪﻧﻮﻤﻧ ﺯﺍ ﺝﺭﺎﺧ ﻲﻨﻴﺑ
ﻞﻴـﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎﻌﻣ ﻱﺎﻫ
ﻝﺪﻣ ﻪﺑ ﺖﺒﺴﻧ ﻱﺮﺘﻬﺑ ﺩﺮﻜﻠﻤﻋ ﻲﻓﺩﺎﺼﺗ ﻲﻧﺎـﻣﺯ ﻱﺮﺳ ﻱﺎﻫ
ARIMA ﺪـﻧﺭﺍﺩ
. ﺮـﻛﺫ ﻪـﺑ ﻡﺯﻻ
ﻝﻭﺪﺟ ﺞﻳﺎﺘﻧ ﻪﻛ ﺖﺳﺍ 3
ﻲﻣ ﻥﺎﺸﻧ ﻝﺪﻣ ﺪﻫﺩ MJD
ﻝﺪﻣ ﻪﺑ ﺖﺒﺴﻧ ﻱﺮﺘﻬﺑ ﺩﺮﻜﻠﻤﻋGBM
ﺶﻴﭘ ﺭﺩ ﺍﺭ ﻪﻧﻮﻤﻧ ﺯﺍ ﺝﺭﺎﺧ ﻲﻨﻴﺑ
ﻲﻣ ﻥﺎﺸﻧ ﺩﻮﺧ ﺯﺍ ﺯﺭﺍ ﺥﺮﻧ ﻱ ﺪﻫﺩ
. ﺵﺭﺍﺰـﮔ ﺞﻳﺎـﺘﻧ ﺱﺎـﺳﺍ ﺮﺑ
ﻝﻭﺪﺟ ﺭﺩ ﻩﺪﺷ 3
ﻪﻴﺿﺮﻓ ﻲﻣ ﺭﺍﺮﻗ ﺵﺮﻳﺬﭘ ﺩﺭﻮﻣ ﻖﻴﻘﺤﺗ ﻱ ﺩﺮﻴﮔ
.
ﻝﻭﺪﺟ 3 - ﻱﺎﻄﺧ ﺶﻴﭘ ﻲﻨﻴﺑ ﺯﺍ ﺝﺭﺎﺧ ﻪﻧﻮﻤﻧ ﻱ ﻝﺪﻣ ﺎﻫ ﻒﻠﺘﺨﻣ ﻱ )
ﺭﺍﺪﻘﻣ (RMSE
ﻪﻧﻮﻤﻧ MJD
ﻝﻭﺍ ﻱ AR(1)
ﻪﻧﻮﻤﻧ GBM
ﻡﻭﺩ ﻱ ARIMA(12,1,1)
ﻊﺒﻨﻣ : ﺕﺎﺒﺳﺎﺤﻣ ﺶﻫﻭﮋﭘ ﺮﮔ ﻥﺍ
ﻝﻭﺪﺟ 4 ﺶﻴﭘ ﻞﻣﺎﺷ ، ﻲﻨﻴﺑ
ﻪﻧﻮﻤﻧ ﺯﺍ ﺝﺭﺎﺧ ﻱﺎﻫ ﻖﻓﺍ ﻱﺍﺮﺑ ﺯﺭﺍ ﺥﺮﻧ ﻱ
ﻒﻠﺘﺨﻣ ﻱﺎﻫ 1
ﺎﺗ
12 ﻲﻣ ﻪﻫﺎﻣ ﺪﺷﺎﺑ . ﺶﻴﭘ ﺮﻳﺩﺎﻘﻣ ﻝﻭﺪﺟ ﻦﻳﺍ ﺭﺩ ﻩﺪﺷ ﻲﻨﻴﺑ
ﻱ ﻩﺎﻣ ﻱﺍﺮﺑ ﺯﺭﺍ ﺥﺮﻧ ﺭﻮﻳﺮﻬﺷ ﻱﺎﻫ
1390 ﻝﺎﺳ ﺩﺍﺩﺮﻣ ﺎﺗ 1391
ﻝﺪﻣ ﺱﺎﺳﺍ ﺮﺑ ﻝﻭﺪﺟ ﺱﺎﺳﺍ ﺮﺑ ﻪﻛ MJD
3 ﻢﻛ ﻱﺍﺭﺍﺩ ﻦﻳﺮﺗ
ﺶﻴﭘ ﻱﺎﻄﺧ ﻝﺪﻣ ﻦﻴﺑ ﺭﺩ ﻪﻧﻮﻤﻧ ﺯﺍ ﺝﺭﺎﺧ ﻲﻨﻴﺑ
ﺖﺳﺍ ﻩﺪﻣﺁ ،ﻩﺩﻮﺑ ﺐﻴﻗﺭ ﻱﺎﻫ .
ﻝﻭﺪﺟ 4 - ﺶﻴﭘ ﺮﻳﺩﺎﻘﻣ ﻩﺪﺷ ﻲﻨﻴﺑ
ﺯﺍ ﺝﺭﺎﺧ ﻪﻧﻮﻤﻧ ﻱ ﻝﺪﻣ ﺱﺎﺳﺍ ﺮﺑ ﺯﺭﺍ ﺥﺮﻧ ﻪﻟﺎﺳ ﻚﻳ MJD
6 ﻪﻫﺎﻣ 5
ﻪﻫﺎﻣ 4
ﻪﻫﺎﻣ 3
ﻪﻫﺎﻣ 2
ﻪﻫﺎﻣ 1
ﻪﻫﺎﻣ ﻖﻓﺍ
ﺶﻴﭘ ﺭﺍﺪﻘﻣ ﻩﺪﺷ ﻲﻨﻴﺑ
12 ﻪﻫﺎﻣ 11 ﻪﻫﺎﻣ 10 ﻪﻫﺎﻣ 9 ﻪﻫﺎﻣ 8 ﻪﻫﺎﻣ 7 ﻪﻫﺎﻣ ﻖﻓﺍ
ﺶﻴﭘ ﺭﺍﺪﻘﻣ ﻩﺪﺷ ﻲﻨﻴﺑ
ﻊﺒﻨﻣ : ﺕﺎﺒﺳﺎﺤﻣ ﺶﻫﻭﮋﭘ ﺮﮔ ﻥﺍ
7 - ﺠﻴﺘﻧ ﻭ ﻪﺻﻼﺧ ﻪ
ﺮﻴﮔ ﻱ
ﺭﺩ ﻝﺪﻣ ﺭﻮﻈﻨﻣ ﻪﺑ ﺶﻫﻭﮋﭘ ﻦﻳﺍ ﺶﻴﭘ ﻭ ﻱﺯﺎﺳ
ﻲﻤـﺳﺭ ﺭﺍﺯﺎـﺑ ﺯﺭﺍ ﺥﺮـﻧ ﻲﻧﺎـﻣﺯ ﻱﺮﺳ ﻲﻨﻴﺑ
ﻥﺍﺮﻳﺍ ) ﺭﻻﺩ ﻞﺑﺎﻘﻣ ﺭﺩ ﻝﺎﻳﺭ (
ﻩﺩﺍﺩ ﻱﺍﺮﺑ ﻩﺭﻭﺩ ﻚـﻳ ﺭﺩ ﻲﻧﺎـﻣﺯ ﻱﺮﺳ ﻦﻳﺍ ﺯﺍ ﻪﻧﺍﺯﻭﺭ ﻱﺎﻫ
ﻱ 10
ﺖـﺳﺍ ﻪـﺘﻓﺮﮔ ﺭﺍﺮـﻗ ﻩﺩﺎﻔﺘـﺳﺍ ﺩﺭﻮـﻣ ﻲﻓﺩﺎﺼﺗ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎﻌﻣ ﺱﺎﺳﺍ ﺮﺑ ﻝﺪﻣ ﻭﺩ ،ﻪﻟﺎﺳ .
ﻚﻠﺑ ﻡﺎﻬﺳ ﺖﻤﻴﻗ ﻝﺪﻣ ،ﻝﻭﺍ ﻝﺪﻣ -
ﻟﻮﺷ ﺰ - ﻝﺪـﻣ ﻭ ﻱﺮﺘﻣﻮـﺋژ ﻲﻧﻭﺁﺮﺑ ﺖﻛﺮﺣ ﻝﺪﻣ ﺎﻳ ﻦﺗﺮﻣ
ﺭﺎﺸﺘﻧﺍ ﻝﺪﻣ ،ﻡﻭﺩ -
ﻲﻣ ﻦﺗﺮﻣ ﺵﺮﭘ ﺪﺷﺎﺑ
. ﺪﻧﻭﺭ ﺵﺯﺍﺮﺑ ﻪﺑ ﺭﺩﺎﻗ ﻱﺮﺘﻣﻮﺋژ ﻲﻧﻭﺁﺮﺑ ﺖﻛﺮﺣ ﻝﺪﻣ
ﻲﻤﻧ ﻲﻟﻭ ،ﺖﺳﺍ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺭﺩ ﺩﻮﺟﻮﻣ ﺕﺎﻧﺎﺳﻮﻧ ﻭ ﻲﻧﺎﻣﺯ ﺵﺮﭘ ﺪﻧﺍﻮﺗ
ﻱﺮـﺳ ﺭﺩ ﺩﻮـﺟﻮﻣ ﻱﺎﻫ
ﺪﻳﺎﻤﻧ ﺵﺯﺍﺮﺑ ﺍﺭ ﻲﻧﺎﻣﺯ .
ﺭﺎﺸﺘﻧﺍ ﻝﺪﻣ ،ﻝﺪﻣ ﻦﻳﺍ ﻑﻼﺧ ﺮﺑ -
ﻼﻋ ﻦﺗﺮﻣ ﺵﺮﭘ ﻭ ﻲﻧﺎﻣﺯ ﺪﻧﻭﺭ ﺮﺑ ﻩﻭ
ﻲﻣ ،ﺕﺎﻧﺎﺳﻮﻧ ﺵﺮﭘ ﺪﻧﺍﻮﺗ
ﺪﻨﻛ ﺵﺯﺍﺮﺑ ﺰﻴﻧ ﺍﺭ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺭﺩ ﺩﻮﺟﻮﻣ ﻱﺎﻫ .
ﻦﻳﺍ ﻦﻴﻤﺨﺗ ﺯﺍ ﺲﭘ
ﻪﻧﻮﻤﻧ ﻱﺍﺮﺑ ﻝﺪﻣ ﻭﺩ ﻩﺩﺍﺩ ﺯﺍ ﻲﻳﺎﻫ
ﻪﺴﻳﺎﻘﻣ ،ﺯﺭﺍ ﺥﺮﻧ ﻲﻌﻗﺍﻭ ﻱﺎﻫ ﻝﺪـﻣ ﻦﻳﺍ ﻦﻴﺑ ﻱﺍ
ﻝﺪـﻣ ﻭ ﺎـﻫ
ﻲﻧﺎﻣﺯ ﻱﺮﺳ ARIMA
ﺖﺳﺍ ﻪﺘﻓﺮﮔ ﻡﺎﺠﻧﺍ .
ﻥﺎـﺸﻧ ﻱﺭﺍﺩﻮـﻤﻧ ﺞﻳﺎـﺘﻧ ﻪـﻧﻮﻤﻧ ﻞﺧﺍﺩ ﺵﺯﺍﺮﺑ ﺭﺩ
ﻲﻣ ﺩ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﻝﺪﻣ ﻑﻼﺧ ﺮﺑ ﻪﻛ ﺪﻫ ARIMA
ﻝﺪﻣ ، ﺭﺎـﺘﻓﺭ ﻲﺑﻮـﺧ ﻪـﺑ ﻱﺩﺎﻬﻨﺸﻴﭘ ﻱﺎﻫ
ﻲﻣ ﺵﺯﺍﺮﺑ ﺍﺭ ﺯﺭﺍ ﺥﺮﻧ ﺮﻴﻐﺘﻣ ﺵﺮﭘ ﻭ ﻥﺎﺳﻮﻧ ﺎﺑ ﻩﺍﺮﻤﻫ ﻲﻌﻗﺍﻭ ﺪﻨﻨﻛ
. ﻢﻫ ﺶﻴـﭘ ﺭﺩ ﻦﻴﻨﭼ ﻲـﻨﻴﺑ
ﻪـﻧﻮﻤﻧ ﺯﺍ ﺝﺭﺎﺧ ﻲـﻘﻓﺍ ﻱﺍﺮـﺑ ﺯﺭﺍ ﺥﺮـﻧ ﻱ
1 ﻝﺪـﻣ ،ﻪـﻫﺎﻣ ﻱﺩﺎﻬﻨـﺸﻴﭘ ﻱﺎـﻫ
ﻭGBM MJD
ﻝﺪﻣ ﻪﺑ ﺖﺒﺴﻧ ﻱﺮﺘﻬﺑ ﺩﺮﻜﻠﻤﻋ ARIMA
ﺮﺑ ﺸﮔ ﺱﺎﺳﺍ ﺭﻭﺎﺘ
ﺪﻧﺭﺍﺩRMSE . ﻢﻫ ﺞﻳﺎﺘﻧ ﻦﻴﻨﭼ
ﻲﻣ ﻥﺎﺸﻧ ﻪﻛ ﺪﻫﺩ
ﻲﻓﺩﺎﺼﺗ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎﻌﻣ ﻝﺪﻣ ﻭﺩ ﻦﻴﺑ ﻭGBM
،MJD ﻝﺪـﻣ MJD
ﺭﺩ ﺍﺭ ﻱﺮـﺘﻬﺑ ﺩﺮـﻜﻠﻤﻋ ﺯﺭﺍ ﺥﺮﻧ ﻲﻧﺎﻣﺯ ﻱﺮﺳ ﺪﻧﻭﺭ ﺭﺩ ﺩﻮﺟﻮﻣ ﻲﻧﺎﻬﮔﺎﻧ ﺵﺮﭘ ﺵﺯﺍﺮﺑ ﻞﻴﻟﺩ ﻪﺑ ﺶﻴﭘ ﻲﻨﻴﺑ ﺯﺍ ﺝﺭﺎﺧ ﻪﻧﻮﻤﻧ ﻱ ﻥﺎﺸﻧ ﺩﻮﺧ ﺯﺍ ﺯﺭﺍ ﺥﺮﻧ ﻲﻣ
ﺪﻫﺩ .
ﺩ ﻩﺯﺎﺗ ﺕﺎﻘﻴﻘﺤﺗ ﻡﺎﺠﻧﺍ ﻱﺍﺮﺑ ﻲـﻣ ﺩﺎﻬﻨﺸﻴﭘ ﻪﻨﻴﻣﺯ ﻦﻳﺍ ﺭ
ﻝﺪـﻣ ﻪـﻛ ﺩﻮـﺷ ﺕﻻﺩﺎـﻌﻣ ﻱﺎـﻫ
ﻝﺪﻣ ﺎﺑ ﻲﻓﺩﺎﺼﺗ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺖﻟﺎﺣ ﻱﺎﻫ
-
١ﺎﻀﻓ ﻭ ﻝﺪﻣ ﻩﺩﺍﻮﻧﺎﺧ ﻱﺎﻫ
٢STAR ﺪﻧﻮﺷ ﻪﺴﻳﺎﻘﻣ .
ﺖﺳﺮﻬﻓ ﻊﺑﺎﻨﻣ
1 - ﻮﻟﺎﺧ ﻩﺩﺍﺯ ﺪﻴﻤﺣ ﻲﻠﻋ ﻖﻳﺪﺻ ﻲﻛﺎﺧ ، )
1383 (
، ﻝﺪﻣ ﺯﺎﺳ ﻭ ﻱ ﺶﻴﭘ ﻲﻨﻴﺑ ﻡﺎﻬـﺳ ﺖـﻤﻴﻗ
ﻲﻓﺩﺎﺼﺗ ﻞﻴﺴﻧﺍﺮﻔﻳﺩ ﺕﻻﺩﺎﻌﻣ ﺱﺎﺳﺍ ﺮﺑ ،
ﻠﺠﻣ ﻪ ﻱ ،ﻥﺍﺮـﻬﺗ ﻩﺎﮕﺸﻧﺍﺩ ﻱﺩﺎﺼﺘﻗﺍ ﺕﺎﻘﻴﻘﺤﺗ
ﻩﺭﺎﻤﺷ ﻱ 69 ، ﺺﺻ : 1 - 26 .
2 - ﺪﻨﻓﺎﺑ ﻩ ﻱ ﻥﺎﻤﻳﺍ ﺖﺳﻭﺩ ﻕﺩﺎﺻ ، ﻲﻤﻴﻬﻓ ﺩﺮﻓ ﺪﻴﺳ ﺪﻤﺤﻣ ، ﻱﺩﺍﺯﺮﻴـﺷ
ﻪﻴﻤـﺳ ) 1388 (
ﺶﻴﭘ ﻲﻨﻴﺑ ﺥﺮﻧ ﺯﺭﺍ ﺎﺑ ﻝﺪﻣ ﺎﻫ ﻱ -ﻲﺒﺼﻋ ﻱﺯﺎﻓ ANFIS ، ﻲﻧﻮﻴـﺳﺮﮔﺭﺩﻮﺧ NNARX
ﻭ ﺩﻮﺧ ﻲﻧﻮﻴـﺳﺮﮔﺭ ARIMA
ﺭﺩ ﺩﺎـﺼﺘﻗﺍ ﻥﺍﺮـﻳﺍ ) 1381 - 1387 ( ، ـﻠﺠﻣ ﻪ ﻱ ﺶـﻧﺍﺩ ﻭ
،ﻪﻌﺳﻮﺗ ﺭﺎﻤﺷ ﻩ ﻱ 28
، ﺺﺻ : 177 - 192 .
3 - ﻱﺭﺎﺼﻧﺍ ،ﻦﺴﺣ ﻲﻫﺎﮔﺭﺩ ﺎـﺿﺭ
) 1386 (
، ﺩﻮـﺒﻬﺑ ﻝﺪـﻣ ﺯﺎـﺳ ﻪﻜﺒـﺷ ﻱ ﺎـﻫ
ﺭﺩ ﻲﺒـﺼﻋ ﻱ
ﺶﻴﭘ ﻲﻨﻴﺑ ﺺﺧﺎﺷ ﻱﺮﻴﮔﺭﺎﻛ ﻪﺑ ﺎﺑ ﺯﺭﺍ ﺥﺮﻧ ﺎﻫ
،ﻢﻃﻼﺗ ﻱ ـﻠﺠﻣ
ﻪ ﻱ ﻱﺩﺎـﺼﺘﻗﺍ ﺕﺎـﻘﻴﻘﺤﺗ
،ﻥﺍﺮﻬﺗ ﻩﺎﮕﺸﻧﺍﺩ ﺭﺎﻤﺷ
ﻩ ﻱ 85 ﺺﺻ ، : 117 - 144 .
4 - ﻞـﻴﻤﻛ ﺪﻴـﺳ ﻲﺒﻴﻃ
، ـﺻﺎﻧ ﺎـﻴﻧ ﺪـﺣﻮﻣ
،ﺮ ﻲﻨﻳﻮﻇﺎﻛ ﻪﻣﻮـﺼﻌﻣ
) 1387 (
، ﻱﺮﻴﮔﺭﺎـﻛ ﻪـﺑ
ﻪﻜﺒﺷ ﺎﻫ ﺭﺩ ﻲﻋﻮﻨﺼﻣ ﻲﺒﺼﻋ ﻱ ﺶﻴﭘ
ﻲﻨﻴﺑ ﺮﻴﻐﺘﻣ ﺎـﻫ ـﺴﻳﺎﻘﻣ ﻭ ﻱﺩﺎـﺼﺘﻗﺍ ﻱ ﻪ
ﻱ ﺎـﺑ ﻥﺁ
ﺵﻭﺭ ﺎﻫ ﻱ ﻨﺳﺩﺎﺼﺘﻗﺍ ﻲﺠ
: ﺶﻴﭘ ﻲﻨﻴﺑ
،ﻥﺍﺮﻳﺍ ﺭﺩ ﺯﺭﺍ ﺥﺮﻧ ﺪﻧﻭﺭ ﻠﺠﻣ
ﻪ ﻱ ﻲـﺸﻫﻭﮋﭘ ﻲـﻤﻠﻋ
ﻒﻳﺮﺷ ، ﺭﺎﻤﺷ ﻩ ﻱ 43 ، ﺺﺻ : 99 - 104 .
5 - ﻥﺎﺑﺯﺮﻣ ﺣ ﺎﺿﺭ ﻥﺎﻳﺮﺒﻛﺍ ،ﻦﻴﺴ ،
ﺟ ﻡﺎﻨﻬﺑ ﻱﺮﻫﺍﻮ ) 1384 (
، ﻝﺪـﻣ ﻦﻴـﺑ ﻪﺴﻳﺎﻘﻣ ﻚﻳ ﺎـﻫ
ﻱ
،ﻱﺭﺎﺘﺧﺎﺳ ﻲﺠﻨﺳﺩﺎﺼﺘﻗﺍ ﻭ ﻲﻧﺎﻣﺯ ﻱﺮﺳ
ﻪﻜﺒﺷ ﻱ ﺭﻮـﻈﻨﻣ ﻪﺑ ﻲﺒﺼﻋ ﺶﻴـﭘ
ﻲـﻨﻴﺑ ﺥﺮـﻧ
،ﺯﺭﺍ ﻪﻠﺠﻣ ﺍ ﺕﺎﻘﻴﻘﺤﺗ ﻱ ﻗ
ﻥﺍﺮﻬﺗ ﻩﺎﮕﺸﻧﺍﺩ ﻱﺩﺎﺼﺘ ،
ﺭﺎﻤﺷ ﻩ ﻱ 69 ، ﺺﺻ : 181 - 216 .
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