Two of the timeliest U.S. economic indicators are initial claims and continuing claims from the Unemployment Insurance (UI) program. These series are collected and processed weekly by the States, and are seasonally and calendar adjusted by the Bureau of Labor Statistics for release by the Department of Labor. Weekly data are difficult to seasonally adjust as the series do not have constant periodicity. Seasonal adjustment is carried out utilizing a locally-weighted regression approach originally described in Cleveland (1993). Week-to-week changes can be both relatively large and variable, so the changes can be difficult to interpret. To account for this problem, we utilize the parametric bootstrap. Standard errors for week-to-week changes from this method are analyzed for both initial claims and continued claims series.