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Unformatted text preview: covariance can be any number and is not normalized have to compare it to the data to know if it is big or small white noise ~WN(0,sigma^2) = N(0,sigma^2) → normal distribution Random walk xt = w1 + w2 + … + wt E[Xt] = 0, Var[Xt] = t*sigma^2 s > t and cov(Ws, Xt) = 0 [what happens when t>s?] s = 10, t =5 cov(W10, w1+w2+. ..+w10). ..10th days news compared to 5 days news combined gamma (t+h, t) = 2*sigma^2 = t*sigma^2 where t is the # of things in common cov ( xt+h, xt) t = 2, h = 1 cov(x3, x2) = cov(w1+w2+w3, w1+w2) just count how many things are related → w1 and w2 in this case Is {Xt} stationary? NO, it depends on t (stationary should not depend on where you are) Var(Xt) = Var(phi Xt1) + sigma^2 = phi^2 * Var(Xt1) + sigma^2 If we have stationarity, Var(Xt) = Var(Xt1) so they are constant Var(Xt) = sigma^2 / 1phi^2...
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 Fall '13
 Lin
 Normal Distribution, Variance, Probability theory, Autocorrelation, Stationary process

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