简介:我正在使用MATLAB的神经网络工具箱,试图将时间序列预测到未来的一步。目前我只是想预测一个简单的正弦函数,但希望在得到满意的结果后我能够继续进行更复杂的事情。
问题:一切似乎都运转正常,但预测的预测往往会滞后一个时期。如果神经网络预测只是输出延迟一个单位时间的系列,那么神经网络预测就不多了,对吗?
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'只是将数据转换为记录的%差异,'postprocess'将记录的%差异转换回绘图。 (检查编辑预处理和后处理代码)
结果:
蓝色:预测值
RED:实际值
谁能告诉我这里我做错了什么?或者可能会推荐另一种方法来实现预期的结果(正弦函数的无滞后预测,以及最终更混乱的时间序列)?非常感谢您的帮助。
修改 已经有几天了,我希望每个人都享受他们的周末。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。也许这会有助于滚球。
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
答案 0 :(得分:4)
我没有检查您的代码,但进行了类似的测试以使用NN预测sin()
。结果似乎合理,没有滞后。我认为,您的错误是预测值与实际值同步的某个地方。
这是代码:
%% init & params
t = (-50 : 0.2 : 100)';
y = sin(t) + 0.5 * sin(t + pi / 3);
sigma = 0.2;
n_lags = 12;
hidden_layer_size = 15;
%% create net
net = fitnet(hidden_layer_size);
%% train
noise = sigma * randn(size(t));
y_train = y + noise;
out = circshift(y_train, -1);
out(end) = nan;
in = lagged_input(y_train, n_lags);
net = train(net, in', out');
%% test
noise = sigma * randn(size(t)); % new noise
y_test = y + noise;
in_test = lagged_input(y_test, n_lags);
out_test = net(in_test')';
y_test_predicted = circshift(out_test, 1); % sync with actual value
y_test_predicted(1) = nan;
%% plot
figure,
plot(t, [y, y_test, y_test_predicted], 'linewidth', 2);
grid minor; legend('orig', 'noised', 'predicted')
和lagged_input()
函数:
function in = lagged_input(in, n_lags)
for k = 2 : n_lags
in = cat(2, in, circshift(in(:, end), 1));
in(1, k) = nan;
end
end