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Ìàòåìàòè÷åñêèå âîïðîñû êèáåðíåòèêè è âû÷èñëèòåëüíîé òåõíèêè 23, 2004, 144–149.

Òåñòèðîâàíèå äëèòåëüíîñòè ïåðèîäîâ â ðÿäàõ áèðæåâûõ öåí
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Åâãåíèé À. Àðóòþíÿí, Èðèíà À. Ñàôàðÿí è Ìóøåã Ñ. Ñààêÿí

Èíñòèòóò ïðîáëåì èíôîðìàòèêè è àâòîìàòèçàöèè ÍÀÍ ÐÀ
e-mails evhar@ipia.sci.am, safari@ipia.sci.am, m.sahakianalumni@lse.ac.uk

Àííîòàöèÿ

Ðåøàåòñÿ çàäà÷à òåñòèðîâàíèÿ ïîñòîÿíñòâà ôóíêöèè ðèñêà ðÿäîâ
äèíàìèêè öåí àêöèé ïðîòèâ àëüòåðíàòèâû ìîíîòîííîãî ðîñòà ðèñêà.
Ïðåäëîæåíà íîâàÿ ðàíãîâàÿ ñòàòèñòèêà, ÿâëÿþùàÿñÿ ìîäèôèêàöèåé
ñòàòèñòèêè ëîã-ðàíãîâûõ ìåòîê. Îáîñíîâàíî åå ïðèìåíåíèå äëÿ
íåñòàáèëüíûõ ðûíêîâ.

Refer ences

[1 ] Ge n o n -Ca t a lo t V ., Je a n t h e a u T. a n d L a r e d o C. " P a r a m e t e r e s t im a t io n fo r d is c r e t e ly
o b s e r ve d s t o c h a s t ic vo la t ilit y m o d e ls " . B ernoulli, vo l. 4 , n o . 5 , p p . 8 5 5 -8 7 2 , 1 9 9 9 .

[2 ] K o ko s z ka L ., L e ip u s R ." Ch a n g e -p o in t e s t im a t io n in A R CH m o d e ls " . vo l. 6 , n o . 3 , p p .
5 1 3 -5 3 9 , 2 0 0 0 .

[3 ] Ch e n J., Gu p t a A . K . " Te s t in g a n d lo c a t in g va r ia n c e c h a n g e p o in t s wit h a p p lic a t io n t o
s t o c k p r ic e s " . J . Amer. Statist. Assoc. , vo l. 9 2 , p p . 7 3 9 -7 4 7 , 1 9 9 9 .

[4 ] Co m p t e F., R e n a u lt E . " L o n g m e m o r y in c o n t in u o u s -t im e s t o c h a s t ic vo la t ilit y m o d e l "
.M athematical F inance, vo l. 8 , n o . 4 , p p . 2 9 1 -3 2 3 , 1 9 9 8 .

[5 ] Êîêñ Ä. Ð., Îóêñ Ä. ”Àíàëèç äàííûõ òèïà âðåìåíè æèçíè”. Ì., Ôèíàíñû è ñòàòèñòèêà,
1988.

[6] Heckman J., Singer B. ”Econometric duration analysis”. J ournal of econometrics 24, pp.
63-132 , 1984.

[7] Anderson J. E., Thomas A. T. ”Survival analysis using a scale shange random effects
model”. J . Amer. Statist. Assoc., vol. 90, no. 430, pp. 669-679,

[8] Burgayzan E., Darolles S., ”Estimation of random time observed diffusions with application
to microstructure data”. P rague Stochastics 98, pp. 67-72.

¤Ðàáîòà áûëà ÷àñòè÷íî ïîääåðæàíà ôîíäîì INTAS, ãðàíò 00-738.

1 4 4



Å. À. Àðóòþíÿí, È. À. Ñàôàðÿí è Ì. Ñ. Ñààêÿí 1 4 5

[9] Matthews D. E., Farewell V. T. and Pyke R. ”Asymptotic score-statistic processes and
tests for constant hazard against a change-point alternative”. The Annals. of Statistics,
vol. 13, no. 2, pp. 583-591, 1985.

[10] Brodsky B. E., Darkhovsky B., S. ”Nonparametric Methods in Change-Point Problems”.
Dordrecht, Kluwer, 1993.

[11] Praagman J. ”Bahadur efficiency of rank test for the change-point problem”. The Annals.
of Statistics, vol. 16, no. 1, pp. 198-217 ,

[12] Àðóòþíÿí Å., Ñàôàðÿí È. ”Íåïàðàìåòðè÷åñêîå ñîñòîÿòåëüíîå îöåíèâàíèå ìîìåíòà
èçìåíåíèÿ ñâîéñòâ ñëó÷àéíîé ïîñëåäîâàòåëüíîñòè”. Òðóäû èíñòèòóòà ïðîáëåì
èíôîðìàòèêè è àâòîìàòèçàöèè ÍÀÍ ÐÀ è ÅÃÓ, âûï. 17, ññ. 76-85, 1997.

[13] Grandell J. ”Aspects of Risk Theory”. Berlin: Springer- Verlag, 1990.

[14] Ýìáðåõòñ Ï., Êëþïïåëüáåðã Ê. ”Íåêîòîðûå àñïåêòû ñòðàõîâîé ìàòåìàòèêè”. Òåîð.
Âåðîÿòíîñòåé è åå ïðèì., òîì 38, âûï. 3, ññ. 374-416, 1993.

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