I'll assume that readers are `familiar' with my previous Blog-entry. There, I emphasized mean-square issues and I presented results for orthodoxe (maximum likelihood) as well as unorthodoxe (a particular DFA) estimation procedures based on proprietary R-code (available on request) as well as examples in Excel. In my second tutorial on the topic I'd like to `leave behind' the orthodoxe approach with more insistance. In particular, I'll present filter designs which
emphasize turning points much more radically (at the expense of mean-square performances) and which
are likely to shaken main-stream conceptions about `nice' intuitive mean-square real-time designs.
For that purpose I will rely on my Excel sample files exclusively: anyone could replicate the results in my Blog-entry perfectly (please do so and more) and all calculation steps can be deduced directly from the corresponding formulas in the spreadheet's cells.
I suggested at various places in my Blog (for example 1 and 2) that real-time detection of turning-points is a deeply counterintuitive exercise. I suggested, also, that mean-square criteria often lead to intuitively straightforward -though frequently inefficient- solutions. Some recent feedback motivated me to provide a tutorial on the topic. The empirical material has been posted in an easily accessible Excel format, see 1, but I am aware that this lose form of tutorial is not well suited for `unexperienced' users. Therefore, I here propose a step-by-step instructions manual intended for the unexperienced among us. Experts are welcome as well, particularly maximum likelihood aficionados.
The following series of exercises in Excel intends to illustrate
`Interpretability' of mean-square (model-based) solutions
Inefficiency of model-based approaches with respect to turning-point detection
The complexity of the structure of real-time estimation problems
The deeply counterintuitive structure of turning-point problems and the particular gestalt of `improved solutions'.
Part I is devoted to the mean-square error norm. I distinguish two approaches:
The orthodoxe: the traditional maximum likelihood (ARIMA) approach as implemented, for example, in X-12-ARIMA or TRAMO.
An unorthodoxe: a particular version of the `direct' filter approach (DFA)