A careful analysis of influenza. The analysis builds on previous projects, but pays additional attention to loss of immunity, an important feature of flu transmission dynamics.
Plotting, ACF, spectral analysis and ARMA are all best done on a log scale. Then, the log-ARMA likelihood needs to be computed with care (see the measles case study in Chapter 18).
The project acknowledges building on two previous projects on flu in Oklahoma (W24 #5) and aggregated for USA (W22 #43). The project makes a clear statement about how it progresses beyond these previous projects, for example, by including profile likelihood plots. However, there are other 531 projects on flu with profiles, e.g., W24 #16. Review of past 531 work on flu could have been more complete, but readers were satisfied that this project goes beyond previous work in ways other than just using a different dataset.
Formally, it is incorrect to say “a strong autocorrelation at lag one that decays gradually across subsequent lags indicates a non-stationary time series”. The usual motivation for the sample ACF assumes a stationary model. The rate of decay in that case just depends on the timescale of dependence.
There is some confusion in: “The ODEs can be solved by Euler’s numerical method. Specifically, the RHS can be expressed as a binomial approximation with exponential transition probability”. The ODE model and stochastic models are different things.
The main value of ARMA is probably to provide a benchmark to check when the mechanistic model is becoming well specified. The ARMA likelihood is not discussed in this context (and is not presented, though it can be back-calculated from the reported AIC).