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.
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.