The textbook authors cover themselves by stating the assumptions. Unwashed readers misuse the textbook solution because they were not told in clear language that the approach did not apply to their problem. We attempt here to expand upon simple but incorrect textbook solutions to cover possible time series problem sets. This replay studies the impact of non-random error terms on time series data. We created four time series each of length 50 which were generated via simulation.
Simulation starts with an error process which is used as the input.
This random input is then used with a known deterministic model to create a realization of a series. In this way we generate a series of numbers which is autocorrelated. First the two statistics summarizing central tendency and dispersion. Thus we can readily see that the level shift has contaminated the ACF so that the identification of the underlying model is more difficult than simply looking for decays and cutoffs. The replay illustrates bringing in these four series and then plotting them.