matlab-(含教程)基于ARIMA差分整合移动平均自回归模型的数据拟合预测matlab仿真

clc; clear; close all; warning off; addpath(genpath(pwd)); t = 0:0.1:10; t=t'; n = t/0.1; GaussNoise = 0.5*randn(length(t),1); b = [13 5 6]; a = [40 2 3 6 9]; ColoredNoise = filter(b,a,GaussNoise); TrendedNoise = ColoredNoise + sin(2*t); FFT_TrendedNoise = fft(TrendedNoise); plot(abs(FFT_TrendedNoise)); index = 4; len = length(FFT_TrendedNoise); A = 2*abs(FFT_TrendedNoise(index))/len; FFT_TrendedNoise = fft(TrendedNoise,1024*10); plot(abs(FFT_TrendedNoise)); index = 326; len = length(FFT_TrendedNoise); w = 2*pi*index/len; phi = angle(FFT_TrendedNoise(index)); DetrendedNoise = TrendedNoise - A*cos(w*n + phi); % Use the difference operator TrendedNoise_diff = SeasonalDiff(TrendedNoise,31); % Plot detrended residuals figure; plot(n(32:end),TrendedNoise_diff,'g','linewidth',2); hold on; plot(n,ColoredNoise,'b--','linewidth',2); hold on; plot(n,DetrendedNoise,'r','linewidth',2); axis([0 n(end) -2 2]); legend('ARIMA (first order diff)','Real Value','ARMA-SIN'); xlabel('Time Step','fontsize',14); % ylabel('Acceleration (m/s^2)','fontsize',14); set(gca,'fontsize',14); predLen = 20; data = TrendedNoise; len = length(data); dataModel = arima('Constant',0,'Seasonality',31,'MALags',1,'ARLags',4); dataFit = estimate(dataModel,data(1:len-predLen)); YY = []; for i = len-predLen:len yy = forecast(dataFit,1,'Y0',data(1:i)); YY = [YY; yy]; end figure; plot(1:len - predLen, data(1:len-predLen),'b','linewidth',2); hold on; plot(len - predLen:len, data(len-predLen:len),'b--','linewidth',2); hold on; plot(len - predLen:len, [data(len-predLen); YY(1:end-1)],'g','linewidth',2); err_arima = data(len - predLen+1:len) - YY(1:end-1); data = DetrendedNoise; len = length(data); dataModel = arima(4,0,1); dataFit = estimate(dataModel,data(1:len-predLen)); YY = []; for i = len-predLen:len yy = forecast(dataFit,1,'Y0',data(1:i)); YY = [YY; yy]; end NonstationaryTrend = (TrendedNoise - DetrendedNoise); % which is "A*cos(w*n + phi)" above ... hold on; plot(len - predLen:len, [data(len-predLen)+NonstationaryTrend(len - predLen); YY(1:end-1) + NonstationaryTrend(len - predLen + 1:len)],'m','linewidth',2); err_armasin = (TrendedNoise(len - predLen+1:len)) - (YY(1:end-1) + NonstationaryTrend(len - predLen+1:len)); axis([0 n(end) -2 2]); legend('Real Value','预测值','ARIMA','ARMA-SIN'); xlabel('Time Step','fontsize',14); set(gca,'fontsize',14);