介绍:我正在使用MATLAB的神经网络工具箱,试图预测未来一步的时间序列。目前,我只是试图预测一个简单的正弦函数,但希望在获得满意的结果后能够转向更复杂的内容。
问题:一切似乎都运行良好,然而预测的结果往往会滞后一个周期。如果神经网络只是延迟了一个时间单位输出系列,那么它的预测就没有多大用处,对吧?
代码:
t = -50:0.2:100;
noise = rand(1,length(t));
y = sin(t)+1/2*sin(t+pi/3);
split = floor(0.9*length(t));
forperiod = length(t)-split;
numinputs = 5;
forecasted = [];
msg = '';
for j = 1:forperiod
fprintf(repmat('\b',1,numel(msg)));
msg = sprintf('forecasting iteration %g/%g...\n',j,forperiod);
fprintf('%s',msg);
estdata = y(1:split+j-1);
estdatalen = size(estdata,2);
signal = estdata;
last = signal(end);
[signal,low,high] = preprocess(signal'); % pre-process
signal = signal';
inputs = signal(rowshiftmat(length(signal),numinputs));
targets = signal(numinputs+1:end);
%% NARNET METHOD
feedbackDelays = 1:4;
hiddenLayerSize = 10;
net = narnet(feedbackDelays,[hiddenLayerSize hiddenLayerSize]);
net.inputs{1}.processFcns = {'removeconstantrows','mapminmax'};
signalcells = mat2cell(signal,[1],ones(1,length(signal)));
[inputs,inputStates,layerStates,targets] = preparets(net,{},{},signalcells);
net.trainParam.showWindow = false;
net.trainparam.showCommandLine = false;
net.trainFcn = 'trainlm'; % Levenberg-Marquardt
net.performFcn = 'mse'; % Mean squared error
[net,tr] = train(net,inputs,targets,inputStates,layerStates);
next = net(inputs(end),inputStates,layerStates);
next = postprocess(next{1}, low, high); % post-process
next = (next+1)*last;
forecasted = [forecasted next];
end
figure(1);
plot(1:forperiod, forecasted, 'b', 1:forperiod, y(end-forperiod+1:end), 'r');
grid on;
注意: 函数“preprocess”只是将数据转换为对数差异,“postprocess”将对数差异转换回来进行绘图。(有关预处理和后处理代码,请查看EDIT)
结果:
蓝色:预测值
红色:实际值
请问我在这里做错了什么?或者推荐另一种方法来实现所需的结果(无滞后预测正弦函数,最终更混沌的时间序列)?非常感谢您的帮助。
编辑: 现在已经过去了几天,我希望每个人都度过了愉快的周末。由于没有出现解决方案,我决定发布辅助函数“postprocess.m”、“preprocess.m”及其辅助函数“normalize.m”的代码。也许这会有助于启动球。
postprocess.m:
function data = postprocess(x, low, high)
% denormalize
logdata = (x+1)/2*(high-low)+low;
% inverse log data
sign = logdata./abs(logdata);
data = sign.*(exp(abs(logdata))-1);
end
preprocess.m:
function [y, low, high] = preprocess(x)
% differencing
diffs = diff(x);
% calc % changes
chngs = diffs./x(1:end-1,:);
% log data
sign = chngs./abs(chngs);
logdata = sign.*log(abs(chngs)+1);
% normalize logrets
high = max(max(logdata));
low = min(min(logdata));
y=[];
for i = 1:size(logdata,2)
y = [y normalize(logdata(:,i), -1, 1)];
end
end
normalize.m:
function Y = normalize(X,low,high)
%NORMALIZE Linear normalization of X between low and high values.
if length(X) <= 1
error('Length of X input vector must be greater than 1.');
end
mi = min(X);
ma = max(X);
Y = (X-mi)/(ma-mi)*(high-low)+low;
end