Christian 1.0 2026-10-25 Optimal alpha for SES C22 ema_alpha_opt: Optimal alpha for SES This function finds the optimal smoothing parameter alpha for Simple Exponential Smoothing. It complements gretls native movavg()) function, which already performs SES but requires alpha as input. The optimal alpha is found by minimizing the sum of squared one-step forecast errors (excluding the first observation). Usage scalar alpha = ema_alpha_opt (y) series smooth = movavg (y,alpha) Returns the optimal alpha in (0,1) Note: Similar functionality for SES exists in the fcModels package (autoSES function), which prints the optimal alpha. This package differs by returning the optimal alpha as scalar for further use with movavg(). It also respects sub-sampled datasets errorif(sum(missing(y)), "found missings in input") scalar best = 0.5 scalar min = $huge loop i=1..99 --quiet scalar a = i / 100 series tmp = movavg(y,a) scalar sse = sum( (y - tmp(-1))^2) if sse < min min = sse best = a endif endloop return best include ema_tools.gfn open australia.gdt --quiet #Optimal alpha for PAU - interior solution series dPAU = diff(PAU) smpl dPAU --contiguous scalar a = ema_alpha_opt(dPAU) print a #Smoothed with optimal alpha using native function smpl full series suav_opt = movavg(dPAU, a) #Plot to compare gnuplot dPAU suav_opt --with-lines --time-series --output=display