Could you please someone explain very simply if the below are correct ?
Based on the below definitions for autocorrelation and stationarity my understanding is :
Hello @Toni2,
Your statements 1 and 2 are basically equivalent. And false. Counterexample: Consider a stochastic process in discrete time, i.e., a sequence of random variables Xt (t=1, 2, ...) with, say, Xt ~ N(t, 1) -- normal distribution with mean t and variance 1 -- for all t and let X1, X2, ... be independent. Then there's no autocorrelation (independence implies uncorrelatedness), but the process (time series) is non-stationary because the mean is not constant over time.
Hello @Toni2,
Your statements 1 and 2 are basically equivalent. And false. Counterexample: Consider a stochastic process in discrete time, i.e., a sequence of random variables Xt (t=1, 2, ...) with, say, Xt ~ N(t, 1) -- normal distribution with mean t and variance 1 -- for all t and let X1, X2, ... be independent. Then there's no autocorrelation (independence implies uncorrelatedness), but the process (time series) is non-stationary because the mean is not constant over time.
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