Constructing a moving regression oscillator

The moving linear-regression line

The long-horizon line is a three-month moving linear-regression of closing prices over 63 trading days. Each session rebuilds the fit by adding the newest close and dropping the close from 63 days earlier.

The linear-regression is a rolling least-squares fit of those closes on a trading-day index. It yields a slope and an intercept and advances by replacing the oldest observation in the lookback.

Scaling slope into a daily-return forecast

Slope is divided by the latest close to form slope-over-close. A 0.10 daily slope on a 20 close equals 0.5 percent per trading day. A higher-priced issue would need a 0.50 daily slope to print the same scaled reading.

Stated as a percentage return per trading day, slope-over-close keeps issues at different price levels comparable.

Percent distance as a mean-reversion timer

The predicted-close is the current-day value on the moving regression line. The regression-oscillator is the latest close relative to that predicted-close, minus one. A 21 close against a 20 predicted-close equals plus 5 percent. A close the same distance below the line equals minus 5 percent.

The construction treats the predicted-close as an estimate of average value. A large percentage gap below the line is read as an oversold mean-reversion condition. A still larger gap is treated as possible reversal of the long-term trend.

Mean-reversion here is the working assumption that closes gravitate toward the regression-predicted average unless percent distance from that average breaks far below the issue's historically observed normal-lower-limit. That band is read from prior pullbacks rather than taken as a universal constant.

In an established uptrend, a large positive oscillator reading is not treated as a reliable exit. Closes can sit at or near new highs and keep the reading elevated for an extended period.

Guides and worked examples

On the illustrated series, oscillator guides were drawn at 14 percent, zero, and minus 14 percent. Several 1995-1996 pullbacks approached that lower guide without remaining far below it until 11 June 1996.

A worked April 1996 example combined an oscillator near minus 12 percent with a slope-over-close of 0.92 percent per day, after that scaled slope had risen from 0.15 percent since mid-January.

The same construction treated a one-session drop from about minus 13 percent to about minus 19 percent as a significant break of the minus 14 percent lower limit. A 15-day high-low range-placement oscillator stayed near 5 percent and did not separate ordinary from abnormal volatility.

A spreadsheet identity

A spreadsheet identity sets predicted-close equal to the moving intercept plus 63 times the moving slope. It sets the oscillator to 100 times close divided by predicted-close minus one. The intercept's trading-day index stays fixed at the 1-through-63 positions so the window does not shift on the x-axis.

A three-rule screen

A three-rule screen requires a scaled slope above 0.5 percent per trading day and an oscillator between minus 15 and minus 5 percent. It then further narrows the universe with a relative-strength-index rank of 85 or higher.

That relative-strength-index is a twelve-month percentage price-change ranking with extra weight on the latest three months. Editorial note: the rank is used as a long-uptrend universe filter so ordinary pullbacks are not confused with trend failure.