Why does upward sloping time series imply it is not covariance stationary?? Any problem for this type of non-covariance stationary? Thanks.

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because the upward trend of variance indicates it is increasing over time. and therefore it is not mean reverting.

Like time series: a=b0 + b1 * t. All time series are upward sloping!

francis ur example is a simple linear trend. yes it is upward sloping. but for simple linear trend, covariance stationarity is not required. I think what u r trying to say is: “in order for AR(n) time series analysis to work, covariance must be stationary.” I got the above phrase from stalla lectures. when you would want to model an AR time series, you would want your graph to look as flat as possible with flutuations up and down evenly. AKA no persisitent up or down around the mean.

Only autoregressive time-series must be covariance stationary.