Kalman pairs spread

// A pairs trade's spread: the chart's market against another, hedged by a ratio a Kalman filter
// re-estimates on every bar. Both are logs of price, so the ratio is how many percent the chart's
// market moves for one percent of the other. The spread is a z-score over its last 200 bars:
// past ±2 it has stretched further than usual from the hedge.
indicator('Kalman pairs spread', { shortName: 'Pairs z', precision: 2 });

const against = input.market('Hedge with', 'ETH');
const delta = input.float('Drift', 0.0001, { min: 0.0000001, max: 0.1, step: 0.0001, legend: false, tooltip: 'How fast the hedge ratio may move. Larger follows the pair faster and flattens the spread.' });

const chart = bars();
const other = bars(against === null ? {} : { market: against });
const hedge = ml.kalmanBeta({ delta });
const usual = stats.zscore(200);

const z = plot.line('Spread z', { width: 2 });
const ratio = plot.line('Hedge ratio', { hidden: true, precision: 3 });
plot.level('Stretched up', 2, { style: 'dashed' });
plot.level('Stretched down', -2, { style: 'dashed' });
const stretched = plot.background('Stretched');

chart.onBar(() => {
  const r = hedge.update(Math.log(chart.close), Math.log(other.close));
  const spread = usual.update(r.spread);
  z.set(spread, spread >= 0 ? color.up : color.down);
  ratio.set(r.beta);
  stretched.set(Math.abs(spread) > 2 ? color.withAlpha(spread > 0 ? color.up : color.down, 0.12) : null);
});