1. ## time series

What is the difference between a time series without autocorrelation, and a stationary time series?

If they are the same, why do we need to do both the Ljung-Box test and unit root test?

2. Originally Posted by eulerian
What is the difference between a time series without autocorrelation, and a stationary time series?

If they are the same, why do we need to do both the Ljung-Box test and unit root test?
Consider a time series where the value at epoc $\displaystyle i$ is normally distributed with zero mean and variance $\displaystyle \sigma_i^2=|i|$ and independedent of the values at all other epocs. The autocorrelation of this process is clearly zero for all non-zero lags and it is also clearly non-stationary.

CB

3. Originally Posted by CaptainBlack
Consider a time series where the value at epoc $\displaystyle i$ is normally distributed with zero mean and variance $\displaystyle \sigma_i^2=|i|$ and independedent of the values at all other epocs. The autocorrelation of this process is clearly zero for all non-zero lags and it is also clearly non-stationary.

CB
One definition of a weakly stationary process is $\displaystyle E(yt-\mu)^2={\sigma}^2$or with constant variance.

So, why do the above process with non-zero value of autocorrelation function for zero lags is stationary?

4. Originally Posted by eulerian
One definition of a weakly stationary process is $\displaystyle E(yt-\mu)^2={\sigma}^2$or with constant variance.

So, why do the above process with non-zero value of autocorrelation function for zero lags is stationary?
Try that again what you have written is incomprehensible.

The process I have described is non-stationary

CB