ﺑﺮآورد ﻣﺎﮐﺴﯿﻤﻢ درﺳﺘﻨﻤﺎﯾﯽ ﻣﺎﺗﺮﯾﺲ ﮐﻮوارﯾﺎﻧﺲ ﻣﺪلARMA ﺑﺎ اﺳﺘﻔﺎده از ﻣﺎﺗﺮﯾﺲ ﺑﺎﻧﺪ

Maximum Likelihood Estimating of the Covariance Matrix of the ARMA Model Using Band Matrix

ﭼﮑﯿﺪه: در اﯾﻦ ﻣﻘﺎﻟﻪ ﯾﮏ روش ﺑﺮاي ﺑﺮآورد ﻣﺎﺗﺮﯾﺲ ﮐﻮوارﯾﺎﻧﺲ ﻣﺪلARMA ﺑﺎ ﺑﻬﺮه ﮔﯿﺮي از ﻣﺎﺗﺮﯾﺲ ﺑﺎﻧﺪ ﭘﯿﺸﻨﻬﺎد ﺷﺪه اﺳﺖ. ﺗﺎﺑﻊ درﺳﺘﻨﻤﺎﯾﯽ ﻣﺪلARMA ﺑﺎ ﻣﺎﺗﺮﯾﺲ ﮐﻮوارﯾﺎﻧﺲ ﻗﻄﺮي ﺑﻪ دﺳﺖ آﻣﺪه و ﺗﻘﺮﯾﺐ ﻫﺎﯾﯽ ﻧﯿﺰ ﺑﺮاي ﻣﻌﯿﺎرﻫﺎﯾﯽ ﻣﺎﻧﻨﺪ ﮐﻮﻟﺒﮏ-ﻟﯿﺒﻠﺮ و ﭼﺮﻧﻮف اراﺋﻪ ﺷﺪه اﺳﺖ. ﺑﻌﻼوه دو ﻗﺎﻋﺪه ﺑﺮاي ﻣﻤﯿﺰي ﻣﺪل ﻫﺎيARMA ﺑﺎ اﺳﺘﻔﺎده از ﺗﻘﺮﯾﺐ ﻫﺎي ﺑﻪ دﺳﺖ آﻣﺪه ﭘﯿﺸﻨﻬﺎد ﺷﺪه اﺳﺖ. ﺳﭙﺲ ﺑﺎ اﺳﺘﻔﺎده از داده ﻫﺎي ﺷﺒﯿﻪ ﺳﺎزي ﺷﺪه و واﻗﻌﯽ، ﺗﻮاﻧﺎﯾﯽ روش ﭘﯿﺸﻨﻬﺎدي در ﻣﻤﯿﺰي ﻣﺪل ﻫﺎي ﻣﺨﺘﻠﻒARMA ﻧﺸﺎن داده ﺷﺪه اﺳﺖ. ﮐﺎﻫﺶ ﻗﺎﺑﻞ ﻣﻼﺣﻈﻪ ﺗﻌﺪاد ﻣﺤﺎﺳﺒﺎت ﺑﺮاي ﺳﺮي ﻫﺎي زﻣﺎﻧﯽ ﺑﺰرگ و ﻧﺮخ ﺧﻄﺎي ﻣﻤﯿﺰي ﭘﺎﯾﯿﻦ از وﯾﮋﮔﯽ ﻫﺎي ﻗﻮاﻋﺪ ﭘﯿﺸﻨﻬﺎد ﺷﺪه اﺳﺖ. ﻫﻤﭽﻨﯿﻦ ﻋﺪم ﻧﯿﺎز ﺑﻪ ﻓﺮض ﻧﺮﻣﺎل ﺑﻮدن در ﯾﮏ ﻗﻀﯿﻪ ﻧﺸﺎن داده ﺷﺪه اﺳﺖ.

In this paper, using Band matrix, a method has been proposed to estimating the covariance matrix of the ARMA model and the likelihood function of the ARMA model with diagonal covariance matrix has been obtained and approximations for Kullback-Leibler and Chernoff criteria were presented. In addition, two rules for discriminating the ARMA models has been proposed. A simulation and real data sets are used to illustrate the performance of the proposed rules. Significant reduction of the calculations for large time series and low discrimination error rate are two characteristics of the proposed rules. In addition no need to normal assumption is showed in a theorem.