Constructing a correlation-divergence regime filter for yen and Nikkei context

Why a three-market construction

The historical workflow is a form of intermarket-analysis. It puts a single equity-index trade into a regime-aware context by using related currency and equity-index prices rather than the target market alone.

Correlation-divergence is the residual oscillator that measures how far one market’s short-horizon return has departed from the return predicted by a second market. Correlation-analysis supplies the rolling association that both fits that prediction and later screens a third market.

Returns and the rolling association

The construction measures short-horizon percentage returns on the target series and on two companion series, then estimates a rolling linear association between the target return and the second-market return.

The rolling association used in the fit is a Pearson-style correlation of two series, computed from summed cross-products and variances and then clipped to the interval from minus one to one. Correlation-analysis is that rolling Pearson-style association between two short-horizon return series, used both to fit a linear prediction and to screen a third market.

From residual to divergence-momentum

A predicted target return is formed from that association and subtracted from the observed target return to produce a residual. That residual is then scaled into a bounded divergence-momentum oscillator.

Divergence-momentum is a scaled reading of the prediction residual over a lookback window, mapped into a bounded oscillator that can be compared with fixed upper and lower thresholds.

Long and short setups

A long setup requires the oscillator to have recently been above an upper threshold, then to turn down while remaining above the complementary lower threshold. It also requires the target’s correlation with the third market to stay below a fixed ceiling.

A short setup is the mirror image. The oscillator must have recently been below the lower threshold, then turn up while remaining below the upper threshold, again only if third-market correlation is below the same ceiling.

The third-market-screen is a correlation filter that withholds a two-market divergence signal when the target remains too tightly associated with a third reference market.

Trend confirmation and stop-loss exits

Trend confirmation is required at entry. A long also needs a non-declining linear-regression slope or a close above a moving average. A short needs the opposite pair of conditions.

Open positions are bounded by a delayed initial percentage stop, a later trailing percentage stop, and a fixed-bar time exit that flatten both long and short trades. Stop-loss is a pre-specified exit that bounds loss or open-trade exposure after a minimum holding period, including an initial percentage stop, a later trailing stop, and a time exit.