I am considering two simple regression models. The error term of each follow AR(1) model. I am looking for the examples where the error terms of the two models have equal autocorrelation coefficients. I would appreciate if someone give me examples from time series. What is the relation between the slope of a model and the autocorrelation coefficient? Thanks.
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$\begingroup$ Are you concerned with a simple lag1 regression model where y is predicted by the lag of y 1 period ? I think you are but I could be wrong . $\endgroup$ – IrishStat Sep 22 '15 at 19:47
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The slope of an equation is proportional to the correlation coefficient multiplied by the ratio of the two standard deviations (sigmay/sigmax) . Since x is y lag 1 the ratio is nearly unity thus the regression coefficient is "nearly equal" to the correlation coefficient. I hope this is what you are after.
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$\begingroup$ "Since x is y lag 1" suggests you are talking about regressing a lagged time series on itself. That narrow interpretation does not seem to be justified by the information provided in the question, which refers only to the "error terms" in otherwise undifferentiated "simple regression models." You might consider posting comments asking the OP for clarification. $\endgroup$ – whuber♦ Sep 22 '15 at 19:15
