1. weak stationarity

1. WEAK STATIONARITY

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  A stochastic process is said to be weakly, covariance or second-order stationary if its:
  

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  Mean is constant;
  

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  Variance is constant over time;
  

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  the value of covariance between two periods depends only on the distance or gap between the two time periods and not the actual time at which the covariance is computed. Example
  

e.g. (i) One lag difference:

Where , the covariance (or autocovariance) at lag k, is the covariance between the values of and that is, between two X values k periods apart.

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  If k=0, we obtain which is simply the variance of X (=).
  

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  The simplest, purely statistical time series model is the first order autoregression, or AR(1) process;
  

where

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  An nth order autoregressive process, or AR(n) can be written as
  

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  In this case n lags of X are deemed to be important in determining the time series behaviour of X.
  
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  The stationarity is imposed by .
  
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    If we then X would tend to get bigger and bigger each period, in absolute value and so would be an explosive