(a) Show that (left(1-mathrm{B}^{2} ight)left(x_{t} ight)=(1-mathrm{B})(1+mathrm{B})left(x_{t} ight)). (b) Show that (triangle^{k}left(x_{t} ight)=sum_{h=0}^{k}(-1)^{h}binom{k}{h} x_{t-h}) (equation (5.26)). (c) Show...

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(a) Show that $\left(1-\mathrm{B}^{2}\right)\left(x_{t}\right)=(1-\mathrm{B})(1+\mathrm{B})\left(x_{t}\right)$.

(b) Show that $\triangle^{k}\left(x_{t}\right)=\sum_{h=0}^{k}(-1)^{h}\binom{k}{h} x_{t-h}$ (equation (5.26)).

(c) Show that for any integer $k,\left(1-\mathrm{B}^{k}\right)\left(x_{t}\right)=\triangle_{k}\left(x_{t}\right)$.

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Statistical Analysis Of Financial Data

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Authors: James Gentle

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(a) Show that (left(1-mathrm{B}^{2} ight)left(x_{t} ight)=(1-mathrm{B})(1+mathrm{B})left(x_{t} ight)). (b) Show that (triangle^{k}left(x_{t} ight)=sum_{h=0}^{k}(-1)^{h}binom{k}{h} x_{t-h}) (equation (5.26)). (c) Show...

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Statistical Analysis Of Financial Data

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