Keep or drop an RSI threshold with a complementary-sample test

Evaluate the setup before a trade backtest

Before a full trade backtest, a defined setup can be evaluated by locating past occurrences, sampling the subsequent price path, and testing whether that path usually moved in the intended direction.

The first-cross rule

The Relative Strength Index used here is a 14-period oscillator of average upward versus downward closes, used to flag the first cross above 70 or below 30 as a candidate short or long setup.

The worked setup used 14-period RSI, counted only the first hourly cross above 70 or below 30, and ignored later bars until RSI left that region.

Complementary-sample tests

Hypothesis testing is a pre-specified comparison of a no-difference null with a directional-bias alternative, applied here at 95% significance to 14-bar forward percent changes after RSI crosses.

A chi-square test is a count-based check of whether subsequent prices rise versus fall after a setup at a different rate than they do in the complementary non-setup sample.

What the hourly sample showed

On the hourly S&P 500 sample dated 21 January 2013, 95.49% of bars were non-crossovers, 2.68% were first RSI crosses up through 70, and 1.82% were first RSI crosses down through 30.

Forward percent-change bands after non-crossover bars were centered near zero, while bands after the RSI-70 up-cross showed a downside tilt with the most extreme negative outcomes about twice the most extreme positive ones.

A two-sample t-test of 14-bar percent changes after RSI-70 up-crosses versus other bars produced a statistic of 2.3, above the 95% critical value of about 1.7, so the no-difference null was rejected in favor of a relative downside bias.

The same 14-bar t-test after RSI-30 down-crosses produced a negative sample mean and a statistic of -0.5, so the null of no relative upside bias was retained.

Constituent counts as reference only

Across S&P 500 constituents, 22.3% at the 95% level and 50.1% at the 75% level showed a downside bias after RSI 70, versus 8.2% and 28.4% showing an upside bias after RSI 30. Those 70-cross rates exceeded the 5% and 25% chance benchmarks, while the 30-cross rates did not. The multi-name counts were offered only as reference because the tests are designed for a single case.

One specification, not a system

The evaluation covered one specification only: 14-period RSI, hourly sampling, a 14-bar horizon, and the 30/70 thresholds. Those choices were treated as parameters that could be varied rather than as a finished trading system.