Test whether a new indicator would have improved past decisions
Answers whether a chosen indicator rule would have helped on your assets historically. It reads up to 200 daily candles and backtests a configured indicator rule (RSI oversold/overbought or MACD cross-up) over a lookback window, counting each trigger and its 5-day forward return. It reports triggers generated, average forward return, win rate, and a 95% Wilson confidence interval, flagging small samples. Use it as an exploratory gauge of an indicator's edge, respecting the sample-size caveats rather than treating results as proof.
A backtest, and therefore a lesson in empirical method as much as in any indicator.
What it does: takes a rule (RSI oversold/overbought, or MACD crossing up), finds every historical instance over the lookback, and records the 5-day forward return after each. It reports the number of triggers, the mean forward return, the win rate, and a 95% Wilson confidence interval on that win rate.
The Wilson interval, E. B. Wilson (1927), is the right choice and worth teaching on its own. The familiar normal approximation p +/- 1.96*sqrt(p(1-p)/n) misbehaves badly at small n or when p is near 0 or 1 - it can produce bounds below 0 or above 1, and its real coverage is often far from 95%. Wilson's score interval is derived by inverting the score test and stays inside [0,1] with much better coverage. That advantage holds for INDEPENDENT Bernoulli trials, which is a condition worth checking before trusting it - see the overlap point below. When the interval is wide, that is the honest reading: the estimate is imprecise.
What a student must take from this, and what makes backtesting dangerous:
SAMPLE SIZE. Twenty triggers is evidence, but imprecise evidence - the interval around a win rate from twenty observations is very wide. Read the interval before the point estimate, and note that a win-rate interval says nothing about the uncertainty in the MEAN RETURN, nor whether the rule beats simply holding the asset over the same five days.
MULTIPLE TESTING. Try enough rules, parameters and assets and some will look excellent by chance alone. This is separate from the interval's coverage: a 95% interval is a statement about repeated sampling of ONE test, and it offers no protection against having quietly run twenty. This analysis tests one configured rule, so the discipline rests on whoever chooses what to test and how often.
NO TRANSACTION COSTS. Forward returns here are gross. Spread, fees and slippage are not deducted, and a rule that triggers often is affected most.
A FIXED 5-DAY HORIZON is an assumption, not a neutral choice - a rule can look strong at 5 days and vanish at 10.
OVERLAPPING WINDOWS. Triggers closer together than five days share daily return increments, so the observations are not independent and the effective sample is often smaller than the count suggests - how much smaller depends on the covariance. Wilson's interval does NOT repair this: it assumes independence, so what is reported should be read as a NOMINAL 95% interval. Handling it properly means non-overlapping events, clustering, or a block bootstrap.
SURVIVORSHIP. The universe is what exists today; assets that failed are not in it.
Status: exploratory. A positive result here is a reason to investigate, never proof of an edge.
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