How a two-sided continuation factor becomes a testable trend rule

Split the close-to-close difference

Daily construction begins with the close-to-close difference. That difference is then split so an up day stores the rise as the positive change and records zero as the negative change. A down day does the reverse: it stores the decline as the negative change and records zero as the positive change.

Build each continuation factor as a run sum

Each continuation factor is a same-direction run sum. It equals zero when that side's daily change is zero. Otherwise it equals today's change plus yesterday's continuation factor on that side.

The positive continuation factor therefore resets when the latest close is not higher, and otherwise adds today's up-move to yesterday's accumulator. The negative continuation factor is the downside counterpart: it resets when the latest close is not lower, and otherwise adds today's down-move to yesterday's accumulator.

Compare both sides over one window

Over a 35-session window, the positive trend continuation factor equals the window sum of positive changes minus the window sum of negative continuation factors. The negative trend continuation factor is the mirror comparison, using the window sum of negative changes minus the window sum of positive continuation factors.

A positive reading on the positive trend continuation factor is treated as an uptrend state. A positive reading on the negative trend continuation factor is treated as a downtrend state. The two sides cannot be positive together. Joint negative readings are a joint-negative state and are treated as consolidation rather than as a trend.

Attach a next-open reversal

The associated rule goes long at the next session's open after a positive reading on the positive factor. It goes short at the next open after a positive reading on the negative factor. Under the reversal-holding rule, the existing side is held until the opposite factor turns positive. The position is not flattened merely because both factors are negative.

Keep yesterday's position until the opposite side turns

Spreadsheet position logic maps a positive reading on the positive factor to long, a positive reading on the negative factor to short, and otherwise keeps yesterday's position. An entry price is written only when that state changes, and it uses the next session's open.

Apply one lookback to every market

The same lookback and reversal rules were applied as a one-contract-per-signal procedure across 15 markets from 4 January 1982 through 31 December 1998. A fixed cost of 75 was subtracted from each trade, and any remaining open trade was flattened at the final close. That shared-parameter basket uses one lookback and one rule set on every market so the construction is not refitted market by market.

Recheck nearby window lengths

Robustness checking reused the identical entry, exit, and cost rules while substituting lookbacks of 25, 30, 40, and 45 sessions in place of the 35-session default. The point was to inspect whether that default was unique to one fitted length.

The reported procedure did not include protective trailing stops. Those stops and separate money-management rules were described as optional later layers rather than part of the core construction.