pd qpdq pdqd pdq ytt f s e is s scovytyts fc d d L d ytt d LLytyt twn ytl d t L d jd jjd L j x z x e z dz
pd q LL d ytltt twn z zd ytpdq f e i d e i e i f d pdq pdq d LL d ytlt
fracdiff tt d d
d pdq pdq T pdq LL d ytlttt t pdq yt!jtjtt j!j!!z j!jz j z zz d
ttvt yttwt tttt T T!t!t!!t!t t!t!t!! vttwtt EvtEv t EwtEw t l l T T TT TyyTTT T Tr,sT fe iwrs d pqd tettt tv artt t ij TT ytytt
t ij t i!i!j t t yt t t t i t yt t!i t t i!i t j!j t ij!i!j t ytt t t t i!i i T it ij T it orjt i,j ij ijpdq lt lt T T tt t T ytyt t t ltpq d d L d ytt ytl d t
L d j jl j j jd jd d!jjjt t tt tt tt vtt wtt i,j ij dh h d dd hd hd
ytyt ztlytyt zt m ytztj yt!j ztmm m mt pdq yt!jtj j yt LytL!jtj j zt j!jtj!jtj j j!jtj!iti i!t!j!jtj j t jtj j
!j!j!j ztmm m ttvt zttwt tmmmm m tmtm tmtm t Im mt m vttwtt EvtEv t EwtEw t tettmtv art t t ij mmztzt t t ijij t ij ij t t zt t t t i t t i zt t i t ztt t t t ii t jj t ii i m im i,j m im orjm
i,j T ikjk k lt T T tt t T ztzt t t d LL d ytlttt d ytll L d t L k k L k j jl j t k k L k j jl j jl j t j j j k j jk L k j j k j jk L k t j j k j jk j k j jk L k t d!!i j k jk j k k k jk d!jj jm m
pdq LL d ytlttt tl LL d yt jytj j j t ete t st et t jytj j T st e T t t
ett m T T st p p stt T t t st L T T st d d tl d yt jytj j j jd j dj j id i i et
et t jytj j st T e t t st T Ld T T st d d LL d ytlt tl LL d yt L L jjytj k L k j jl j yt jjl j yt j j k k jk L j yt j j k j j k k jk j k k jk L j yt k jk L j yt j jytj j j k k jk j k jk k
et et t jytj j st T e t t st T Ld T T st m m d d dtt dt
d d dd mtm m dd m m dtd mtdm
TdmTd m dt d mm d d m mt T Td m mdm md m m mtm mt
d m d T d d d T d d m d T d d d T d d Td md mtt dm m m
d d m T T d T Tm dm dd m d d d m m dtm dm ddm
d m d T d d d T d d m d m m dmm d m d
d d d d T d T d Td Td d
d m m T d dd
d d d d d d T m dd d Td d d
d d T m d d d T m d d d T m d d d T m d d T d
d d T T d fracdiff d T dd d T d dd d
d d T m d d d T m d d d d d d
dd dd T d d d d d d dd
d d T m d d d T m d d d d d d
d dm Tm mm dm d Tm m d d dt
d d d d d dd
Statistics for LongMemory Processes Journal of the Royal Statistical Society Time Series Analysis Forecasting and Control Time Series Theory and Methods Annals of Statistics Annals of Statistics Journal of Empirical Finance Ox Object Oriented Matrix Programming Language Long Range Dependence Theory and Applications Annals of Statistics Journal of Time Series Analysis Journal of Time Series Analysis
Journal of the Royal Statistical Society. Ser. C Biometrika R Packagefracdiff LongMemory Time Series Theory and Methods Annals of Statistics Time Series with Long Memory Time Series and Related Topics In Memory of Ching Zong Wei Journal of Econometrics Long Memory in Economics