Log-change regression and binomial outlier clusters as an evaluation pipeline

From levels to log-changes

Editorial: TradersWeek treats a market-move forecast as an evaluation pipeline rather than as a single reading. The archive describes the historical workflow that follows, beginning with the input series.

Absolute price and yield levels stay close to nearby observations, so they are a poor input for methods that assume a more regular, level-free distribution. Differencing the natural log converts those levels into a log-change series that can be compared across instruments and that approximates a rate of return over a modest percentage range. Successive observations can then be compared without the level of the series dominating the result.

Pretests before any forecast

Before any forecast is read from the series, a stationarity-pretest and a serial-dependency-pretest are required so that later inferences are not drawn from a shifting or auto-repeating process.

The stationarity-pretest places log-changes of the index into mutually exclusive bins, compares first-half and second-half counts, and summarizes the mismatch with a chi-square statistic. That check asks whether the rules generating the series stay stable enough across halves of the sample that later inferences are not driven by a shifting process.

The serial-dependency-pretest asks whether one observation is simply a function of the previous one, so a later test is not counting the same information twice.

Regression baseline and the expected band

After those pretests, a regression-baseline is formed by a linear regression of log-changes in the related yield series onto log-changes in the index. The fitted linear map, here from a Treasury yield onto the target index, defines the band in which later observations are expected to fall. It is used to define an expected band rather than a trade.

Outlier clusters and the binomial count

Residuals outside a 1.96 residual-spread band are treated as outliers. A binomial-count-test then calculates a probability on the number of out-of-band observations in a short window and asks whether that outlier-cluster is consistent with independent chance under the fitted model.

In the supplied sample, a dense cluster of such outliers appeared only in the weeks just before a large late-1994 rise in the index. The evaluation treats that cluster as a candidate break in the fitted rate-index relationship rather than as a standalone signal.