Our study focuses on determining the best weight windows for a weighted moving average smoother under squared loss. We show that there exists an optimal weight window that is symmetrical around its center. We study the class of tapered weight windows, which decrease in weight as they move away from the center. We formulate the corresponding least squares problem as a quadratic program and finally as a projection of the origin onto a convex polytope. Additionally, we provide some analytical solutions to the best window when some conditions are met on the input data.

翻译：我们的研究聚焦于确定平方损失下加权移动平均平滑器的最优权重窗口。我们证明存在一个关于中心对称的最优权重窗口。我们研究了锥形权重窗口类别，其权重随远离中心而递减。我们将对应的最小二乘问题表述为二次规划，最终转化为原点到凸多面体的投影。此外，当输入数据满足某些条件时，我们提供了最优窗口的若干解析解。