ch11 - Stationary Stochastic Process A stochastic process...

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Economics 20 - Prof. Anderson 1 Stationary Stochastic Process A stochastic process is stationary if for every collection of time indices 1 ≤ t 1 < …< t m the joint distribution of ( x t1 , …, x tm ) is the same as that of ( x t1+h , … x tm+h ) for h ≥ 1 Thus, stationarity implies that the x t ’s are identically distributed and that the nature of any correlation between adjacent terms is the same across all periods
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Economics 20 - Prof. Anderson 2 Covariance Stationary Process A stochastic process is covariance stationary if E( x t ) is constant, Var( x t ) is constant and for any t , h ≥ 1, Cov( x t , x t+h ) depends only on h and not on t Thus, this weaker form of stationarity requires only that the mean and variance are constant across time, and the covariance just depends on the distance across time
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Economics 20 - Prof. Anderson 3 Weakly Dependent Time Series A stationary time series is weakly dependent if x t and x t+h are “almost independent” as h increases If for a covariance stationary process
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ch11 - Stationary Stochastic Process A stochastic process...

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