Stationary refers to a time series or data set in which the statistical properties such as mean, variance, and autocorrelation remain constant over time. Autocorrelation, on the other hand, is a measure of the linear relationship between a variable and itself over time.
There are several statistical tests that can be used to determine if a time series is stationary, such as the Augmented Dickey-Fuller Test or the Kwiatkowski-Phillips-Schmidt-Shin Test. Autocorrelation can be assessed by plotting the autocorrelation function (ACF) or conducting the Durbin-Watson test.
Stationary and autocorrelation can affect the accuracy and reliability of time series analysis. Stationary data is easier to analyze and can provide more accurate forecasts. Autocorrelated data can lead to biased results and inflated confidence intervals.
Yes, it is possible for a time series to be stationary but still exhibit autocorrelation. A time series can be stationary in terms of mean and variance, but still have a pattern or trend that repeats itself over time, resulting in autocorrelation.
There are several methods for addressing autocorrelation in time series analysis. These include using differencing techniques, such as first-differencing or seasonal differencing, or incorporating ARIMA (autoregressive integrated moving average) models which take into account the autocorrelation in the data.