I have a time series of log-returns of a stock. I want to determine whether the time series is just white noise or if there are some other pattern. How to I use the definition of white noise to make a conclusion?
You want to look at an autocorrelation function (ACF) plot. If no lags are significantly correlated, then you basically have white noise or a MA(q) process aka moving average.
You can use this guide here to compare what your ACF plot looks like to determine if your time-series is "white noise" or not. Guide to ACF/PACF Plots
Also, feel free to browse through previous time-series related posts like: