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8. Non-stationary Time series

8. Non-stationary Time series - EC 421 Non Stationary Time...

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EC 421 Non- Stationary Time Series 1) Intro 2) Stationary, Non Stationary 3) Consequences 4) Detecting 5) Cointegration Non- Stationary Time Series Stationary Variance will explode on you A) Stationary Time Series:- (1) AR Model If expected value and population variance are independent of t. Covariance between two different points in time depend only on difference in time we call the time series weakly stationary. (bounded by 1 in absolute value) Lag Sub this in is getting smaller geometrically declining that means past is going away. Continue to do substitutions for Now take expected value of (2) and if t is large And and therefore independent of time.
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If is not auto correlated, i.e. Cov( As Therefore is independent of t. It can be shown that The covariance depends upon not on t but on difference of t and s. B) Stationary Time Series:- 1) Random Walk Let be at Note: effect of pat error does not decline they are permanent. We call this “integrated” that means errors are integrated. is independent of time However Variance of time series of X at time t depends on time t. So variance depends on time and is not stationary. Key thing
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