Complete the “easy to see” part of the convergence in (2.8).
A physicist studies the amount of carbon dioxide, W(t), at time t, near a highly trafficked road and models the amount by a stationary process.
During one day she gets the measurements w(1),w(2),...,w(50), which she regards as a realization of the stationary stochastic process W(t). In order to study the dependence between W(t), W(t + 1), and
W(t + 2) she makes two scatter plots at time lags 1 and 2 of the observed data, that is, she plots the points (w(t),w(t +1)) and (w(t),w(t +2)); What can you tell from them? She has to choose amongst the following two different stochastic processes:
where e(t) are zero-mean, independent, identically distributed random variables with variance 1. Which one should she choose?
