KILLED · no memory edge
Hypothesis
Returns or volatility carry long memory (fractional integration $d$); an ARFIMA model exploits it for forecasting.
Math
$$ (1-L)^{d}\,(1-\phi L)\,x_t = (1+\theta L)\,\varepsilon_t,\quad 0
Method
Estimate $d$ (GPH / Whittle), fit ARFIMA to returns and to realized vol, forecast and trade returns; vol-forecast compared to HAR-RV.
Results
| Long memory in returns | negligible ($d\approx0$) |
| Long memory in volatility | strong ($d\approx0.4$) |
| Return forecast edge | none |
Long memory lives in volatility, not returns ($d\approx0$ for returns). ARFIMA on returns forecasts nothing; on volatility it just reproduces what HAR-RV (N-023 family) already gives more cheaply. No return edge. Killed.
The persistence in markets is in the second moment, not the first. Long-memory models confirm vol is forecastable and returns are not — again.
We publish the failures too.
This is one of 100+ documented hypotheses. Browse the full lab notebook, or see the strategies that survived into production.