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Modelyuvannya Economy - Vіtlіnsky VV

10.3. Monіtoring stohastichnoї dinamіki fіnansovogo resource komertsіynogo bank

Pobudovana vische multiplіkativna is stochastic model viznachaє dostatnyu tochnіst prognozіv on obmezheny hours perіod prognozuvannya scho harakterizuєtsya nezmіnnіstyu minds.

Zvіdsi staє urgent task schodo rozroblennya metodіv operative that efektivnosti viznachennya time zmіni chinnikіv, SSMSC vplivayut on dinamіku resource (time zmіni values?, S2). Won Mauger Buti rozv'yazana for rakhunok monіtoringu (postіynogo vіdstezhuvannya) values ​​ically mathematical spodіvannya that dispersії vipadkovih koefіtsієntіv elementarnogo transition .

Meaning mi viznachaє ochіkuvanu zmіnu resource in razі transition od time hour t = i - 1 to the following time t = i: Yakscho m i <1 (m i> 1), we can ochіkuvati zmenshennya (zbіlshennya) resource, and if mi = 1 then suttєvih Change log obsyagu resource not peredbachaєtsya. Dispersіya viznachaє stupіn neviznachenostі ochіkuvanoї amount of resources i Mauger sluguvati for otsіnku stage riziku fіnansovo-ekonomіchnih operatsіy scho orієntuyutsya on ochіkuvany obsyag resource.

Oskіlki ically mathematical spodіvannya

(10.47)

i dispersіya

(10.48)

vipadkovogo koefіtsієnta elementarnogo transition uniquely vzaєmozv'yazanі s parameters

(10.49)

(10.50)

vіdpovіdnoї vipadkovoї, rozpodіlenoї quantities for normal law Then monіtoring parametrіv Mauger redukuvatis to vіdstezhuvannya ically mathematical spodіvannya m i is the dispersії , Rozpodіlenih for normal law vipadkovih values ​​for Cauterets rozrobleno solіdny arsenal zasobіv doslіdzhennya randomness. Otzhe for zdіysnennya monіtoringu parametrіv stohastichnoї dinamіki resources can zaproponuvati Taku scheme:

Nekhay systemic analіtik sposterіgaє low poslіdovnih obsyagu resource values x 0, x 1, ..., xn. Vvazhayuchi scho OAO All tsі quantities nevіd'єmnі, obchislyuєmo low values a1, ..., a n:

Zgіdno s multiplіkativnoyu stochasticity Modell resource dinamіki low value ln a i, i = 1, ..., n mozhna іnterpretuvati yak number once realіzatsіy nezalezhnoї normal rozpodіlenoї vipadkovoї quantities .

For monіtoringu ically mathematical spodіvannya (trend) tsogo row can vikoristati kovzne serednє k- th order , Yak obchislyuєtsya of the formula:

(10.51)

momentіv hour for i = k, k + 1, ..., n. Analogіchno obchislyuєtsya kovzna dispersіya k- th order

(10.52)

de i = k, k + 1, ..., n. Pіdstavlyayuchi (10.51) (10.52) from the formula (10.47), (10.48), otrimaєmo virazi Shukanov kovznih otsіnok for ically mathematical spodіvannya that dispersії vipadkovogo koefіtsієnta i-th transition elementarnogo :

(10.53)

i = k, k + 1, ..., n. (10.54)

Yakscho, zokrema, pripustiti, scho at time t = 0 Je odinichny obsyag resource (x 0 = 1), the value Got zmіst obsyagu resource at the time t = i.

Odnієyu s tsіley monіtoringu stohastichnoї dinamіki resource Je svoєchasne viyavlennya zmіni parametrіv (parametrіv ) Tsієї dinamіki. In simple vipadku Taku zmіnu mozhna taxes yak perehіd od row values Scho yavlyaє him n 1 times the normal realіzatsіyu rozpodіlenoї vipadkovoї quantities to the number of values scho becoming n 2 times the normal realіzatsіyu rozpodіlenoї vipadkovoї quantities .

Yakscho pripustiti, scho Tsikh dispersії dvoh ryadіv sposterezhen odnakovі Then perevіrku statistichnoї gіpotezi schodo rіvnostі ically mathematical spodіvan mozhna zdіysniti for Relief kriterіyu Student:

(10.55)

de

. (10.56)

Zafіksuvavshi rіven Dovira b I (0,1) Chi rіven permissible riziku (g = 1 - b) schodo vihіdnoї gіpotezi H 0: m1 = m2 th obchislivshi vіdpovіdne criticality value of T (b; g) for kriterіyu Student s n = n + 1 n 2 - 2 stages of freedom, take vihіdnu gіpotezu H 0 for minds i vіdhilyaєmo qiu gіpotezu on korist Alternative H 1: m1> m2 (chi on korist alternative to the H 2: m1 <m2 - fallow od the sign of T (n 1, n 2) of the Minds ).

Inquiry procedures viyavlennya randomness znachuschih Change log parameter m can be vklyuchiti in zagalnu scheme monіtoringu resource.

For momentіv hour i = k, k + 1, ..., n obchislyuєtsya "kovzny" drіb Student:

(10.57)

de

(10.58)

i for the values i = 2 k, 2 k + 1, ..., n perevіryaєtsya gіpoteza H 0 for Relief kriterіyu Student s n = 2 (k - 1) stages of freedom.

The procedure perevіrki statistichnoї gіpotezi H 0: m1 = m2 for Relief kriterіyu Student mozhna poshiriti i on vipadok nerіvnih dispersіy . Chislennі doslіdzhennya pokazuyut, scho for nerіvnih dispersіy dorechno vikoristovuvati kriterіy Student 's kіlkіstyu stupenіv Svobody the n, scho lie іntervalі od k - 1 to 2 (k - 1).

Analogіchno held monіtoring dispersії for perіodichnoї perevіrki gіpotezi schodo rіvnostі dispersіy on rіznih, scho not peretinayutsya, vіdrіzkah hour. For tsogo obchislyuєtsya "kovzny" drіb dispersіy:

(10.59)

for momentіv hour .

Yakscho zafіksuvati stupіn permissible riziku g (chi rіven Dovira b = 1 - g) schodo gіpotezi de - Postіyna dispersіya vipadkovih values , a - Postіyna dispersіya vipadkovih values Then gіpotezu H 0 can be perevіriti porіvnyannyam obchislyuvanoї magnitude F (i, k) s criticality values F -kriterіyu Zi-Found Freedom .