Sunday, July 8, 2018

equities - How do I reproduce the cross-sectional regression in "Intraday Patterns in the Cross-section of Stock Returns"?


Recently I was trying to reproduce the results of "Intraday Patterns in the Cross-section of Stock Returns" (published in the Journal of Finance 2010). The authors used cross-sectional regression to determine which intraday lags have predictive power.


From my understanding when doing cross-sectional regression all variables have to be from the same time period. For example, I can take the one day returns of all stocks and regress them against the number of employees in each company.


The following is a short description of how cross-sectional regression was used in the research:




For each lag, k, we run cross-sectional regressions of half-hour stock returns on returns lagged by k half-hour periods, ri,t=αk,t+γk,tri,tk+ui,t,

where ri,t is the return on stock i in the half-hour interval t. The slope coefficients γk,t represent the response of returns at half-hour t to returns over a previous interval lagged by k half-hour periods, the “return responses.”



If I understood well, the returns of one period were regressed against the returns of another period and a slope was obtained from each regression. Later, autocorrelation analysis has been done on the slopes.


Unless my thoughts are wrong, I don't see the point of regressing the returns of one period against another - R2 values are close to zero. Here is an example: image


Did I get the cross-sectional regression wrong? By the way, I was working with a relatively small number of stocks, but I thought that 38 should be enough.




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