df_est <- data.frame(
  t = c(0.000, 0.125, 0.250, 0.375, 0.500, 0.625, 0.750, 0.875, 1.000),
  X = c(0.0000000, 0.4180608, -0.9353571, -0.5412875, -0.4287447, -0.2009225, -0.3568059, -0.2420837, 0.2255240))