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

Misspecification issues

`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)