Evaluating a weighted dual rate-of-change momentum filter

Freeze the construction

This archive article shows how to evaluate a long-horizon-filter without changing its construction mid-test. The filter is constructed by summing a 14-month rate-of-change and an 11-month rate-of-change of a major industrial average's monthly close, then smoothing that sum with a 10-month front-weighted moving average.

The rate-of-change is the percent change in a sampled close over a fixed lookback. This construction uses two monthly horizons and then adds them. The weighted-moving-average is a smoother that gives more weight to recent observations. Here a 10-month front-weighted average is applied after the two rates of change are summed. The long-horizon-filter is meant to suppress short-term and intermediate swings so only the slower trend reading remains.

Test bottom-reversal rules on their own

The original early-1960s design specified a buy when the 10-month smoothing dropped below zero and then reversed upward, with the aim of marking major bottoms rather than short-term swings. A reversal-threshold is a level the series must cross before a subsequent turn counts as a signal. Zero is that level in the original design.

A later computerized search on the same construction, using a sample that began in July 1957, identified a nearby buy rule: the series falls below 1.3 and then reverses upward. Editorial: the later rule keeps the same frozen series. It should not replace the original statement unless the evaluation treats replacement as its own hypothesis.

Keep the sell rule separate

The same series was also given a sell rule: it rises above 1.3, forms a peak, and then falls by 11 points. The momentum-strategy is the full entry, exit, and abstention procedure applied to the smoothed series, including a below-threshold-then-reverse buy and an above-threshold-then-drop sell. Under the stated sell rule, a sell was recorded at the November 1992 monthly close unless that month's industrial-average close exceeded 3485.

Run a peak-timing-check

The accompanying timing study defined a bull-market top as a peak after a rise of at least 30 percent, or after a 15 percent rise spanning 155 days. A peak-timing-check is a comparison of highs in the filter with independently defined market tops, scored as lead, coincidence, or lag.

Peaks in the filter led or slightly lagged 10 of 12 examined bull-market tops. The median lead among the seven leading cases was 6.5 months, and the median across all 12 cases was 3.4 months. Of the three lagging peak cases, only the episode after the September 1978 bull-market top lagged by more than six months.

Treat unmatched highs as a distinct claim

Industrial-average highs in 1986, 1987, 1989, and 1992 were treated as a long-term divergence because the filter stayed below its 1983 high and then printed successively lower highs. An unconfirmed-high is a new price high that is not matched by a new high in the filter. Editorial: those unmatched highs are a classification of the historical series. They are not a forecast of later industrial-average behavior.