
voldinte sidhaantham

sthithivivarakkanakkukali, herman voldinte peril ariyappedunna voldinte vighadanam allengil voold praathinidhya sidhaantham (weiner-khinchin sidhaanthathinte vyathiriktha-samaya analogaaya voold sidhaanthavumaayi thettidharikkaruthu), oro covarians-nischala samaya seerees soothravaakyavum _ 1 rund samaya shrenikalude aakethukayaayi ezhuthaamennu parayunnu, onnu "nirnnaayakavum onnu" yaadruchikavum ".
aupachaarikamaayi
evide
chalikkunna sharashari gunakangalkk eee gunangalunda
eee sidhaanthathe oru asthithwa sidhaanthamaayi kanakkakkaam eathoru nischala prakriyaykkum eee prathyeka praathinidhyam undennu thonnunnu. atharamoru lalithamaaya rekheeyavum krithyavumaaya praathinidhyatthinte nilanilpp sradheyamaanennu mathramalla, athilum kooduthal chalikkunna sharashari modalinte prathyeka swabhaavavumaanu. 1-4 enna gunavisheshathakale thripthippeduthaathe chalikkunna sharashari ulla oru prakriya srishtikkunnathu sangalppikkuka. udaaharanathinu, gunaka soothravaakyam _ 13 nuu oru akausalum modalum nirvachikkaan kazhiyum. ennirunnaalum eee prakriya krithyamaayi prathinidheekarikkunna oru kaaryakaaranatthinte nilanilpp sidhaantham urappunalkunnu. kaaryakaaranatthinte kaaryatthilum minimum delay propertyilum ithellaam engane pravarthikkunnuvennu scargilil (1981) charcha cheythittundu, avide voold decompositionte vipuleekaranam charchacheyyunnu.
oru variable formulayude chalanathmaka parinaamatthe oru leanier model upayogichu ekadeshamaayi kanakkakkaan ithu anuvadikkunnu ennathaanu voold sidhaanthathinte prayojanam. 15 enna puthumakalude soothravaakyam swathanthramaanengil, 1 enna soothravaakyathinte nireekshichu moolyathe athinte munkaala parinamavumaayi bandhapetta eaka saadhyamaaya praathinidhyam rekheeya maathrkayaanu. ennirunnaalum, formula _ 15 kevalam parasparabandhithamallaathum ennaal swathanthramaaya oru kramamallaathathumaayirikkum, rekheeya maathruka nilanilkkunnu, pakshe athu shreniyude chalanathmaka aashrithathvathinte eaka praathinidyamalla. eee randaamathe saahacharyathil, leanier model valare upayogapradamallaayirikkam, koodaathe formula _ 1-nte nireekshicha moolyathe athinte munkaala parinamavumaayi bandhapetta oru nonleeniyar model undayirikkaam. ennirunnaalum, praayogika samaya parambara vishakalanathil, bhaagikamaayi laalithyathinte adisthaanathil, rekheeya pravachanangal maathrame pariganikkunnullu, eee saahacharyathil voold vighadanam nerittu prasakthamaanu.
praayogikamaayi avaa saadhaaranayaayi athivegam kshayikkunnundengilum, voold praathinidhyam ananthamaaya alavukolukale aasrayichirikkunnu. anubandha chalikkunna sharaasharikk niravadhi gunakangal undengil kurachu gunakangal maathrame ulloo enna oru badalaanu autoregrassive model. eee rund modalukalum samyojippichu oru autoregrassive-moving aavarej (arma) modalo allengil noonn-staattarti ulppettittundengil oru autoregrassive-integrated-moving aavarej (arima) modalo aayi samyojippikkaam. avide kaanukayum paraamarsikkukayum cheyyuka; koodaathe eee prabandham chalikkunna sharaasharikk (sthirathayullathum kaaryakaaranaparavum kuranja kaalathamasavum allaathathum) kooduthal saamanyatha anuvadikkunna voold sidhaanthathinte oru vipuleekaranam nalkunnu, oppam naveekaranatthinte moorchayulla swabhaava savisheshathayum (parasparabandhithamallaathu mathramalla, samanamaayum swathanthramaayum vitharanam cheyyappedunnu). eee vipuleekaranam bhouthikamo jyothishbhouthikamo aaya prakriyakalodu kooduthal vishwasthathayullathum prathyekichu 'samayathinte ambu' manassilakkaan kazhiyunna modalukalude saadhyatha anuvadikkunnu." "

