Autocorrelation vs Stationarity

[Toni2]

Could you please someone explain very simply if the below are correct ? 

Based on the below definitions for autocorrelation and stationarity my understanding is :

1. a non-stationary variable will express autocorrelation  
2. a time series with no-autocorrelation is stationary  

• Autocorrleation = it is the correlation of a variable between its current value and a period before. Autocorrelation refers to the degree of correlation of the same variables between two successive time intervals
• A stationary time serie is one whose properties do not depend on the time at which the series is observed. A stationary time series is one whose statistical properties such as mean, variance, autocorrelation, etc. are all constant over time. Thus, time series with trends, or with seasonality, are not stationary — the trend and seasonality will affect the value of the time series at different times. A stationarity test of the variables is required because Granger and Newbold (1974) found that regression models for non-stationary variables give spurious results.

[FreelanceReinh · Accepted solution]

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 X_t (t=1, 2, ...) with, say, X_t ~ 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.

[Ksharp]

You 'd better post it at Forecast forum.

https://communities.sas.com/t5/SAS-Forecasting-and-Econometrics/bd-p/forecasting_econometrics