Anticipating a simple-average crossover with a threshold-close

How the next-bar averages are determined

A simple-moving-average is the equal-weighted average of the most recent closes over a chosen lookback. A K-period simple-moving-average can be written from the latest close and the previous (K-1)-period simple-moving-average. Once tomorrow's close is known, the next-bar pair of averages is therefore determined.

Solving for the threshold-close

Setting the next-bar K-period and P-period simple-moving-averages equal and solving for that close produces an explicit threshold-close in the predecessor averages and the two lengths. The threshold-close is the next-bar close that would make two chosen simple-moving-averages equal, derived from their one-bar-shorter predecessors.

For lengths 20 and 30, the equality condition simplifies to a linear combination of the 29-period and 19-period simple-moving-averages.

Crossover-anticipation on the chart

A moving-average-crossover is the event in which a shorter simple-moving-average and a longer simple-moving-average become equal and then change order. On a daily NASDAQ 100 chart with 20-day and 30-day simple-moving-averages, a close crossing the threshold-close series typically appears one bar before the two averages cross.

Crossover-anticipation uses a close-versus-threshold-close cross as a one-bar-ahead hypothesis that the simple-moving-averages will later touch. The construction defines a descending-cross hypothesis when the threshold-close crosses the close, and an ascending-cross hypothesis when the close crosses the threshold-close.

Accuracy-lag-buckets and same-sample scores

Each hypothesis is scored by an accuracy-lag-bucket: whether the matching average cross arrives on the next bar, one bar later, two bars later, on the same bar, or never. Last-bar open predictions are counted as false.

On NASDAQ 100 members from January 2000 through July 2003, 20-day versus 30-day simple-average tests produced 1772 descending and 1766 ascending threshold predictions, with same-sample false rates of 2.19% and 2.31%. In that same sample, 85.79% of descending predictions and 88.09% of ascending predictions were confirmed on the immediately following bar.