Estimating a time-dependent covariance scaling. Consider a vector time series xt Rn, t = 1, 2, . . .. Wewanttofitamodeloftheformxt N(0,at),whereSn isgiven,andat >0. (We assume xt and xs are independent for t = s.) Roughly speaking, the covariance matrix of xt scales up and down with time; at is the scale factor at time t. We are given the base covariance matrix , and a sample sequence x1, . . . , xT . We are to find the scale factor time series at, t = 1,...,T. We will fit the scale factor times series by minimizing the negative log likelihood, plus a term that regularizes the variation in a(t)