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1 The more I learn, the more I realize I dont know. The more I realize I dont know, the more I want to learnalbert Einstein

2 pdqpdq pdqd pdq ytt

3 f s e is s scovytyts fc d d f s s L d yttd LLytyt twn ytl d t L d jd jjd L j

4 x z x e z dz yt yt jd jjd tj pd q LL d ytltt twn z z d ytd yt pdq f e i d e i e i e i d d d d pdq f d d

5 LL d ytlt d f e i d e i d as IT T T yje ij j fj mh h hm h ITjm jj TjT pdq

6 d yyyyty yyt fyyytd T exp y y Ld T y y i,jij

7 T T pdqs q s p l q j l jcdpl sj l jjcdh minqql l ssl smaxl x p jx j p j j ij jm i mj Cdh d d h d hd d p Fd hd h Fd hd h Fabcx Fabcx anbn n cn n x n ab c xaabb cc x aaabbb x ccc

8 nanaaan M d d L d ytttt tn dyt yt t t,jytj j vtvarytyt y t j,j j d yvaryt d

9 rt rt vt d d d r d rt ttrt t j,j j L T T rt T t T Ty ty t T t rt l l Ty ty t T t rt t,jt,j jd td j t,jtcj d td k j tkkd ktd k jt t,jtt jm t td td

10 t,jt,j t jjd jtd j jt j,j d jd t,t d td t M tjytj tjytj t jytj j j jm M tjytj MM j d M t d y MtM y M tm tm tm M jmyj L d jl j k j j jd j d jd d as j d M d M M M d d M is large t jm j t jm j d d d t M u d du d d t d M d

11 M d d d M t d MM d M t d d d LL d ytlttt tn yt t ytl L tkytk k M L L tkytk MM k d M t d y MtM minmt L tkytkytk k MM d M t d y MtM minmt minmtj tj ytjkytjk k j k MM d M t d y MtM vtvarytyt y t jj j d yvaryt d

12 rt rt vt t d jj d j r d d rt ttrt Ty ty t T t rt d l pdq pdq LL d ytlttt yt ytl L t tkytk k M yt vtvarytyt y t jj j

13 d yvaryt d pq pqrt rt vt t d jj d j ytytrt Ty ty t T t rt l d d L d ytttt tn L d kl k k

14 kd k kd kd kd k jd j j d d d k k jd j j k kd k k t kytktt k et t kytkyt t k k kytktt ey eyy eyyy etyt t kytk k

15 etyt T kytk k Eyt etyty t kytky tt k et T t et Lberan T T d LL d ytttt LL d L kl k k kl k kl k k k kkl k k kkk kd k kd kd kd kd k kd kd d k kd kd

16 d k k jd j j etyt t kytktt k d L d ytlttt L L d j L j j kkl k k k j j kj L k k k j j kj L k k k j kj et etyt t kytktt k d LL d ytlttt L LL d j L jl j kl k j j L j k kl k kkl k

17 k k j j kj L k k k j j kj L k k k j j kj k j kj L k j k k j kj k j j j kj et etyt t kytktt k pdq pdq LL d ytlttt L LL d jl j j et etyt t kytktt k T t et Lberan T T

18 pdqd j j jt ITj T W T L W T j fjitj fj TL T W jfj T ITj jfj const y y pdq pdq f e i d e i e i

19 zz z q jz z p iz j i ij e i q je i e i p ie i j i dd d d d T T T

20 T d d T d d T d d M m T T d T

21 d RVt RVtc n r i,t i c T trtr T t n ir i,t RtR ri,ttc T c RVt RVt RtRt

22 RVt RVt Rt R t Rt Rtp Rt RVt

23 RVt RVt RVt

24

25 d d d td d t d d

26 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables Statistics for LongMemory Processes Journal of the Royal Statistical Society. Ser. B Time Series Theory and Methods Annals of Statistics Journal of Econometrics An-

27 nals of Statistics Journal of Empirical Finance LongRange Dependence Theory and Applications Annals of Statistics Journal of Time Series Analysis Tables of Integrals, Series, and Products Journal of Time Series Analysis Journal of Applied Econometrics Journal of the Royal Statistical Society. Ser. C Biometrika LongMemory Time Series Theory and Methods Annals of Statistics Time Series with Long Memory Journal of Econometrics Long Memory in Economics

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