 In addition, the usual "plug-in" method using the estimated asymptotic variance is only valid pointwise . The central goal is to make inference about the effect on the betas of firms' instruments, and to conduct out-of-sample forecast of integrated volatilities using estimated factors. Both procedures should be valid uniformly over a broad class of data generating processes for idiosyncratic betas with various signal strengths and degrees of time-variant.
<clarity>  In addition, the usual "plug-in" method using the estimated asymptotic variance is only valid pointwise . The central goal is to make inference about the effect on the betas of firms' instruments, and to conduct out-of-sample forecast of integrated volatilities using estimated factors. Both procedures should be valid uniformly over a broad class of data generating processes for idiosyncratic betas with various signal strengths and degrees of time-variant.
 In addition, the usual "plug-in" method using the estimated asymptotic variance is only valid pointwise and may produce either over- or under- coveraging probabilities.