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White noise

{title2=$W_t\overset{\mathrm{iid}}\sim F,\quad EW_t=0$}

A sequence of <independent and identically distributed random variables> with zero mean and finite variance is strong <white noise>. It is <weak white noise>, but need not have a <normal distribution>.

Strong white noise

Covariance of quadratic transforms of a linear process

Long-run variance of a stationary process

Moving-average root reflection

Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 208 / 1 / 1 / 3 / Solution

Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 208 / 1 / 1 / 7 / Solution

Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 208 / 1 / 1 / Solution

Seasonal difference operator

Seasonal differencing does not remove periodic variance

Strong white noise ( $W_{t} \sim iid F, E W_{t} = 0$ )

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Strong white noise (Wt​∼iidF,EWt​=0)

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Strong white noise ( $W_{t} \sim iid F, E W_{t} = 0$ )

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