数学建模TimeSeries时间序列案例matlab程序

%% 三次指数平滑法(数据呈现二次曲线形态上升) clc, clear yt = [20.04 20.06 25.72 34.61 51.77 55.92 80.65 131.11 148.58 162.67 232.26]'; n = length(yt); alpha = 0.3; st1_0 = mean(yt(1:3)); st2_0 = st1_0; st3_0 = st2_0; st1(1) = alpha*yt(1) + (1-alpha)*st1_0; st2(1) = alpha*st1(1) + (1-alpha)*st2_0; st3(1) = alpha*st2(1) + (1-alpha)*st3_0; for i = 2:n st1(i) = alpha*yt(i) + (1-alpha)*st1(i-1); st2(i) = alpha*st1(i) + (1-alpha)*st2(i-1); st3(i) = alpha*st2(i) + (1-alpha)*st3(i-1); end st1 = [st1_0,st1]; st2 = [st2_0,st2]; st3 = [st3_0,st3]; at = 3*st1 - 3*st2 + st3; bt = 0.5 * alpha / (1-alpha)^2*((6-5*alpha)*st1-2*(5-4*alpha)*st2+(4-3*alpha)*st3); ct = 0.5 * alpha^2 / (1-alpha)^2 * (st1-2*st2+st3); yhat = at + bt + ct; plot(1:n, yt, '*', 1:n, yhat(1:n), 'O') legend('实际值', '预测值', 2) coeff = [ct(n+1), bt(n+1), at(n+1)]; y_predict = polyval(coeff, 2) % 直接用二次曲线的插值结果