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# p tp ut ut is a classical not autocorrelated error

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Unformatted text preview: t−1 + ρ2 εt−2 + . . . + ρp εt−p + ut ut is a classical (not autocorrelated) error term ρk are autocorrelation coefﬁcients (between -1 and 1) 4 / 30 E XAMPLES OF PURE AUTOCORRELATION Distribution of the error term has a autocorrelation nature First order autocorrelation εt = ρ1 εt−1 + ut positive serial correlation: ρ1 is positive negative serial correlation: ρ1 is negative no serial correlation: ρ1 is zero positive autocorrelation very common in time series data e.g.: a shock to GDP persists for more than one period Seasonal autocorrelation εt = ρ4 εt−4 + ut 5 / 30 E XAMPLES OF IMPURE AUTOCORRELATION Autocorrelation caused by speciﬁcation error in the equation: omitted variable incorrect functional form How can misspeciﬁcation cause autocorrelation in the error term? Recall that the error term includes the omitted variables, nonlinearities, measurement error, and the classical error term. If we omit a serially correlated variable, it is included in the error term, causing the autocorrelation problem. Impure autocorrelation can be corrected by bette...
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