My time series shows no autocorrelation, can I consider this a white noise? And can somebody discuss the properties of a white noise?
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This depends on the definition of a white noise process. The most common one is a weak white noise. By definition $\left\{\epsilon_t\right\}$ is a weak white noise process if: \begin{align} E(\epsilon_t)&=0 \quad,\forall t \\ Var(\epsilon_t)&=\sigma^2<\infty \quad, \forall t \\ Cov(\epsilon_t,\epsilon_{t-h})&=0 \quad, \forall t ,h\neq 0 \end{align} So if your time series shows no autocorrelation, condition 3 seems to satisfied but you still need to check whether the mean is zero and the variance is constant and finite.
However, sometimes a strict white noise process is considered. In this case it is assumed that the $\epsilon_t$ are also iid. If you use this definition of a white noise process it is not enough to concentrate on the first two moments. A prominent example for this is a GARCH(1,1)-model: \begin{align} \epsilon_t&=\sigma_tu_t \quad, u_t\sim {\cal N}(0,1)\\ \sigma_t^2&=\alpha_0+\alpha_1\epsilon_{t-1}^2+\beta_1\sigma_{t-1}^2 \end{align} You can show that $\epsilon_t$ is indeed a weak white noise process under some parameter restrictions but it is not a strict white noise since you have dependencies in higher moments.
