a) Explain the auto-correlation function, and its use in time-series analysis. b) In time-series analysis, one often relies on decomposition, by which the time-series is decomposed into a "trend" and a "remainder". The remainder component is often expected to be uncorrelated, i.e., close to random noise. Describe the auto-correlation of perfect random noise. c) Stationarity is a fundamental concept in time-series analysis. Give one of its multiple definitions, and give an example of a stationary process and of a non-stationary process