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使用 MATLAB 实现支持向量回归 (SVR) 预测未来数据

news 2026/4/25 10:47:33

1. 基础实现：使用 MATLAB 内置函数

代码示例

%% 1. 数据准备
% 生成示例数据（正弦波 + 噪声）
t = linspace(0, 20, 200)';
y = sin(2*pi*0.2*t) + 0.1*randn(size(t));%% 2. 创建训练集和测试集
train_ratio = 0.8;
n_train = floor(length(y) * train_ratio);% 训练集
X_train = t(1:n_train);
y_train = y(1:n_train);% 测试集
X_test = t(n_train+1:end);
y_test = y(n_train+1:end);%% 3. 训练 SVR 模型
% 使用 fitrsvm 函数
svr_model = fitrsvm(X_train, y_train, ...'KernelFunction', 'gaussian', ...  % RBF核函数'Standardize', true, ...'KernelScale', 'auto', ...'BoxConstraint', 1, ...  % 正则化参数C'Epsilon', 0.1);         % ε-不敏感区域参数%% 4. 预测
% 测试集预测
y_pred = predict(svr_model, X_test);% 预测未来时间点
future_time = linspace(t(end)+1, t(end)+10, 10)';  % 预测未来10个点
future_pred = predict(svr_model, future_time);%% 5. 可视化结果
figure;
subplot(2,1,1);
plot(t, y, 'b-', 'LineWidth', 1.5); hold on;
plot(X_train, y_train, 'ro', 'MarkerSize', 5, 'DisplayName', '训练数据');
plot(X_test, y_pred, 'g-', 'LineWidth', 2, 'DisplayName', 'SVR预测');
plot(future_time, future_pred, 'm--', 'LineWidth', 2, 'DisplayName', '未来预测');
xline(t(n_train), 'k--', '训练结束');
legend('Location', 'best');
xlabel('时间'); ylabel('数值');
title('SVR 时间序列预测');
grid on;subplot(2,1,2);
plot(X_test, y_test, 'b-', 'LineWidth', 1.5); hold on;
plot(X_test, y_pred, 'r-', 'LineWidth', 1.5);
legend('真实值', '预测值');
xlabel('时间'); ylabel('数值');
title('测试集预测对比');
grid on;

2. 多步超前预测实现

%% 多步超前预测函数
function [predictions] = svr_multi_step_predict(data, lookback, horizon)% data: 输入时间序列% lookback: 回看窗口大小% horizon: 预测步数n = length(data);% 准备训练数据X = zeros(n - lookback - horizon + 1, lookback);y = zeros(n - lookback - horizon + 1, horizon);for i = 1:(n - lookback - horizon + 1)X(i, :) = data(i:i+lookback-1)';y(i, :) = data(i+lookback:i+lookback+horizon-1)';end% 划分训练测试train_size = floor(0.8 * size(X, 1));X_train = X(1:train_size, :);y_train = y(1:train_size, :);X_test = X(train_size+1:end, :);y_test = y(train_size+1:end, :);% 训练多个SVR模型（每个预测步一个）models = cell(horizon, 1);predictions = zeros(size(y_test));for h = 1:horizon% 训练单个步长的SVR模型model = fitrsvm(X_train, y_train(:, h), ...'KernelFunction', 'gaussian', ...'Standardize', true, ...'KernelScale', 'auto', ...'OptimizeHyperparameters', 'auto', ...'HyperparameterOptimizationOptions', ...struct('AcquisitionFunctionName', 'expected-improvement-plus'));models{h} = model;% 预测predictions(:, h) = predict(model, X_test);end% 可视化结果figure;for h = 1:min(4, horizon)  % 最多显示前4个预测步subplot(2, 2, h);plot(y_test(:, h), 'b-', 'LineWidth', 1.5); hold on;plot(predictions(:, h), 'r--', 'LineWidth', 1.5);title(sprintf('预测步长: %d', h));xlabel('时间点'); ylabel('数值');legend('真实值', '预测值');grid on;end% 计算评估指标mse = mean((predictions - y_test).^2, 1);mae = mean(abs(predictions - y_test), 1);rmse = sqrt(mse);fprintf('各预测步长的性能指标:\n');for h = 1:horizonfprintf('步长 %d: RMSE=%.4f, MAE=%.4f\n', h, rmse(h), mae(h));end
end

3. 自动超参数优化

%% 使用贝叶斯优化自动调参
function optimized_model = optimize_svr(X, y)% 定义可调超参数范围vars = [optimizableVariable('BoxConstraint', [0.1, 100], 'Transform', 'log')optimizableVariable('KernelScale', [0.1, 10], 'Transform', 'log')optimizableVariable('Epsilon', [0.01, 1], 'Transform', 'log')];% 交叉验证函数cv_fun = @(params) kfoldLoss(fitrsvm(X, y, ...'KernelFunction', 'gaussian', ...'Standardize', true, ...'KFold', 5, ...'BoxConstraint', params.BoxConstraint, ...'KernelScale', params.KernelScale, ...'Epsilon', params.Epsilon));% 贝叶斯优化results = bayesopt(cv_fun, vars, ...'MaxObjectiveEvaluations', 30, ...'AcquisitionFunctionName', 'expected-improvement-plus', ...'PlotFcn', {@plotObjectiveModel, @plotMinObjective});% 用最优参数训练最终模型best_params = results.XAtMinObjective;optimized_model = fitrsvm(X, y, ...'KernelFunction', 'gaussian', ...'Standardize', true, ...'BoxConstraint', best_params.BoxConstraint, ...'KernelScale', best_params.KernelScale, ...'Epsilon', best_params.Epsilon);fprintf('最优参数:\n');fprintf('BoxConstraint (C): %.4f\n', best_params.BoxConstraint);fprintf('KernelScale: %.4f\n', best_params.KernelScale);fprintf('Epsilon: %.4f\n', best_params.Epsilon);
end

4. 完整应用示例：股票价格预测

%% 股票价格预测示例
function stock_price_prediction()% 加载示例数据load('Data_EquityIdx.mat');  % 假设有股票数据% 使用价格和成交量作为特征prices = USPrice;volume = USVolume;% 创建特征矩阵n = length(prices);lookback = 20;  % 使用过去20天的数据features = zeros(n - lookback, 5);target = zeros(n - lookback, 1);for i = lookback+1:n-1% 特征工程features(i-lookback, 1) = mean(prices(i-lookback:i-1));  % 过去20天均价features(i-lookback, 2) = std(prices(i-lookback:i-1));   % 波动率features(i-lookback, 3) = prices(i-1)/prices(i-lookback) - 1;  % 收益率features(i-lookback, 4) = mean(volume(i-lookback:i-1));  % 平均成交量features(i-lookback, 5) = (prices(i-1) - min(prices(i-lookback:i-1))) / ...(max(prices(i-lookback:i-1)) - min(prices(i-lookback:i-1)));  % 相对位置% 预测目标：未来1天的价格target(i-lookback) = prices(i+1);end% 划分训练集和测试集train_ratio = 0.8;n_train = floor(size(features, 1) * train_ratio);X_train = features(1:n_train, :);y_train = target(1:n_train);X_test = features(n_train+1:end, :);y_test = target(n_train+1:end);% 训练优化后的SVR模型svr_model = optimize_svr(X_train, y_train);% 预测y_pred = predict(svr_model, X_test);% 评估mse = mean((y_pred - y_test).^2);mae = mean(abs(y_pred - y_test));rmse = sqrt(mse);mape = mean(abs((y_pred - y_test) ./ y_test)) * 100;fprintf('\n股票价格预测性能:\n');fprintf('RMSE: %.4f\n', rmse);fprintf('MAE:  %.4f\n', mae);fprintf('MAPE: %.2f%%\n', mape);% 可视化figure;subplot(2,1,1);plot(y_test, 'b-', 'LineWidth', 1.5); hold on;plot(y_pred, 'r--', 'LineWidth', 1.5);legend('实际价格', '预测价格');xlabel('交易日'); ylabel('价格');title('股票价格预测结果');grid on;subplot(2,1,2);error = y_pred - y_test;histogram(error, 50);xlabel('预测误差'); ylabel('频数');title('预测误差分布');grid on;% 计算方向准确性direction_acc = sum(sign(y_pred(2:end) - y_pred(1:end-1)) == ...sign(y_test(2:end) - y_test(1:end-1))) / (length(y_test)-1) * 100;fprintf('方向准确性: %.2f%%\n', direction_acc);
end

5. 关键注意事项

数据预处理：

% 标准化（推荐）
[X_scaled, mu_X, sigma_X] = zscore(X);
[y_scaled, mu_y, sigma_y] = zscore(y);% 反标准化预测结果
y_pred_original = y_pred_scaled * sigma_y + mu_y;

特征工程：
- 添加滞后特征
- 添加移动平均
- 添加技术指标（RSI, MACD等）
- 季节性特征
模型选择：
- 线性核：适用于线性关系
- 多项式核：适用于多项式关系
- RBF核（高斯核）：适用于复杂非线性关系
参数调优顺序：
1. 先调 ε（Epsilon）
2. 再调 C（BoxConstraint）
3. 最后调核参数（KernelScale）

参考代码通过实现支持向量回归可以预测未来数据 www.youwenfan.com/contentcnt/54902.html

6. 替代方案：使用深度学习工具箱

%% 使用深度学习工具箱的回归层
function svr_with_dl()% 创建简单的SVR-like网络layers = [featureInputLayer(1)fullyConnectedLayer(10)reluLayerfullyConnectedLayer(5)reluLayerfullyConnectedLayer(1)huberRegressionLayer('HuberDelta', 0.1)  % 类似SVR的ε不敏感损失];options = trainingOptions('adam', ...'MaxEpochs', 50, ...'MiniBatchSize', 32, ...'Plots', 'training-progress');% 训练网络net = trainNetwork(X_train, y_train, layers, options);
end

这些代码示例展示了 MATLAB 中实现 SVR 进行时间序列预测的多种方法。关键是根据具体问题调整窗口大小、核函数和超参数。

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