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MATLAB基于一阶预测有效度的IGOWLA算子模糊组合预测方法

news 2025/11/13 15:55:51

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1. 基本概念与理论基础

核心概念定义

classdef PredictionConceptsproperties% 一阶预测有效度first_order_efficiency% IGOWLA算子 (Induced Generalized Ordered Weighted Logarithmic Averaging)% 诱导广义有序加权对数平均算子% 模糊组合预测fuzzy_combinationendmethodsfunction obj = PredictionConcepts()fprintf('基于一阶预测有效度的IGOWLA算子模糊组合预测方法\n');endend
end

2. 数学模型构建

2.1 一阶预测有效度计算

function [efficiency, accuracy] = calculateFirstOrderEfficiency(actual, predicted, time_window)% 计算一阶预测有效度% 输入：%   actual - 实际值序列%   predicted - 预测值序列%   time_window - 时间窗口n = length(actual);efficiency = zeros(n - time_window + 1, 1);accuracy = zeros(n - time_window + 1, 1);for t = time_window:n% 提取窗口数据actual_window = actual(t-time_window+1:t);predicted_window = predicted(t-time_window+1:t);% 计算预测精度relative_errors = abs(actual_window - predicted_window) ./ abs(actual_window);accuracy(t-time_window+1) = 1 - mean(relative_errors);% 计算一阶有效度（考虑趋势一致性）actual_trend = diff(actual_window);predicted_trend = diff(predicted_window);trend_correlation = corr(actual_trend(:), predicted_trend(:));if isnan(trend_correlation)trend_correlation = 0;end% 一阶预测有效度 = 精度 × 趋势一致性efficiency(t-time_window+1) = accuracy(t-time_window+1) * (1 + abs(trend_correlation));end
end

2.2 IGOWLA算子实现

function aggregated_value = IGOWLA_operator(values, weights, lambda, inducing_variable)% IGOWLA算子实现% 输入：%   values - 待聚合的值%   weights - 权重向量%   lambda - 广义参数%   inducing_variable - 诱导变量（一阶预测有效度）n = length(values);% 根据诱导变量对值进行排序[sorted_inducing, sort_index] = sort(inducing_variable, 'descend');sorted_values = values(sort_index);sorted_weights = weights(sort_index);% 检查权重归一化if abs(sum(sorted_weights) - 1) > 1e-10sorted_weights = sorted_weights / sum(sorted_weights);end% IGOWLA聚合计算if lambda == 0% 当lambda=0时的特殊情况log_values = log(sorted_values);aggregated_value = exp(sum(sorted_weights .* log_values));else% 广义对数平均weighted_powers = sorted_weights .* (sorted_values .^ lambda);aggregated_value = (sum(weighted_powers)) .^ (1/lambda);end% 添加诱导变量调整efficiency_factor = mean(sorted_inducing(1:ceil(n/2)));aggregated_value = aggregated_value * (1 + 0.1 * (efficiency_factor - 0.5));
end

3. 模糊组合预测系统

3.1 模糊隶属度函数

function membership = fuzzy_membership(efficiency, method)% 计算模糊隶属度% 基于一阶预测有效度确定各预测方法的隶属度switch methodcase 'gaussian'% 高斯隶属函数center = 0.8;  % 有效度中心sigma = 0.2;   % 标准差membership = exp(-(efficiency - center).^2 / (2 * sigma^2));case 'trapezoidal'% 梯形隶属函数a = 0.6; b = 0.7; c = 0.9; d = 1.0;if efficiency <= amembership = 0;elseif efficiency <= bmembership = (efficiency - a) / (b - a);elseif efficiency <= cmembership = 1;elseif efficiency <= dmembership = (d - efficiency) / (d - c);elsemembership = 0;endcase 'sigmoid'% S型隶属函数alpha = 10; beta = 0.7;membership = 1 ./ (1 + exp(-alpha * (efficiency - beta)));otherwiseerror('不支持的隶属函数类型');end
end

3.2 主要预测方法类

classdef FuzzyCombinationPredictionproperties% 预测方法集合methods% 历史数据historical_data% 一阶有效度first_order_efficiency% IGOWLA参数igowla_lambda% 模糊权重fuzzy_weightsendmethodsfunction obj = FuzzyCombinationPrediction(data, method_names)obj.historical_data = data;obj.methods = method_names;obj.igowla_lambda = 1.0;  % 默认参数obj = obj.initializeWeights();endfunction obj = initializeWeights(obj)% 初始化权重n_methods = length(obj.methods);obj.fuzzy_weights = ones(1, n_methods) / n_methods;obj.first_order_efficiency = zeros(1, n_methods);endfunction [combined_forecast, individual_forecasts] = predict(obj, new_data_point)% 执行组合预测% 1. 获取各方法预测值individual_forecasts = obj.getIndividualForecasts(new_data_point);% 2. 更新一阶预测有效度obj = obj.updateEfficiency(individual_forecasts, new_data_point);% 3. 计算模糊权重obj = obj.updateFuzzyWeights();% 4. 应用IGOWLA算子进行组合combined_forecast = obj.applyIGOWLA(individual_forecasts);endfunction forecasts = getIndividualForecasts(obj, data_point)% 获取各单一预测方法的预测值n_methods = length(obj.methods);forecasts = zeros(1, n_methods);for i = 1:n_methodsswitch obj.methods{i}case 'ARIMA'forecasts(i) = obj.arimaForecast(data_point);case 'NeuralNetwork'forecasts(i) = obj.nnForecast(data_point);case 'ExponentialSmoothing'forecasts(i) = obj.esForecast(data_point);case 'SVM'forecasts(i) = obj.svmForecast(data_point);otherwiseforecasts(i) = data_point * (0.95 + 0.1 * rand());endendendfunction obj = updateEfficiency(obj, forecasts, actual)% 更新一阶预测有效度n_methods = length(obj.methods);for i = 1:n_methods% 计算预测误差error = abs(forecasts(i) - actual) / abs(actual);% 更新有效度（指数平滑更新）alpha = 0.1;  % 平滑参数new_efficiency = 1 - error;obj.first_order_efficiency(i) = alpha * new_efficiency + ...(1 - alpha) * obj.first_order_efficiency(i);endendfunction obj = updateFuzzyWeights(obj)% 基于一阶有效度更新模糊权重n_methods = length(obj.methods);new_weights = zeros(1, n_methods);for i = 1:n_methods% 计算模糊隶属度membership = fuzzy_membership(obj.first_order_efficiency(i), 'sigmoid');new_weights(i) = membership;end% 归一化权重if sum(new_weights) > 0obj.fuzzy_weights = new_weights / sum(new_weights);elseobj.fuzzy_weights = ones(1, n_methods) / n_methods;endendfunction combined_value = applyIGOWLA(obj, forecasts)% 应用IGOWLA算子进行组合预测combined_value = IGOWLA_operator(...forecasts, ...obj.fuzzy_weights, ...obj.igowla_lambda, ...obj.first_order_efficiency);endend
end

4. 完整的预测系统实现

4.1 主控制系统

classdef PredictionSystempropertiescombination_modelperformance_metricsprediction_historyendmethodsfunction obj = PredictionSystem(historical_data)% 初始化预测系统method_names = {'ARIMA', 'NeuralNetwork', 'ExponentialSmoothing', 'SVM'};obj.combination_model = FuzzyCombinationPrediction(historical_data, method_names);obj.performance_metrics = struct();obj.prediction_history = [];endfunction obj = runPrediction(obj, test_data)% 运行预测实验n_test = length(test_data);predictions = zeros(n_test, 1);actual_values = zeros(n_test, 1);fprintf('开始基于IGOWLA算子的模糊组合预测...\n');for t = 1:n_test% 获取测试点current_point = test_data(t);actual_values(t) = current_point;% 执行组合预测[combined_pred, individual_preds] = obj.combination_model.predict(current_point);predictions(t) = combined_pred;% 记录历史obj.prediction_history(t).time = t;obj.prediction_history(t).actual = current_point;obj.prediction_history(t).combined = combined_pred;obj.prediction_history(t).individual = individual_preds;obj.prediction_history(t).weights = obj.combination_model.fuzzy_weights;obj.prediction_history(t).efficiency = obj.combination_model.first_order_efficiency;% 显示进度if mod(t, 10) == 0fprintf('已完成 %d/%d 个预测点\n', t, n_test);endend% 计算性能指标obj = obj.calculatePerformanceMetrics(actual_values, predictions);endfunction obj = calculatePerformanceMetrics(obj, actual, predicted)% 计算预测性能指标errors = actual - predicted;obj.performance_metrics.MAE = mean(abs(errors));obj.performance_metrics.MSE = mean(errors.^2);obj.performance_metrics.RMSE = sqrt(mean(errors.^2));obj.performance_metrics.MAPE = mean(abs(errors ./ actual)) * 100;obj.performance_metrics.R2 = 1 - sum(errors.^2) / sum((actual - mean(actual)).^2);endfunction plotResults(obj)% 可视化预测结果figure('Position', [100, 100, 1400, 900]);% 1. 预测值与实际值对比subplot(2, 3, 1);actual = [obj.prediction_history.actual];combined = [obj.prediction_history.combined];plot(actual, 'b-', 'LineWidth', 2, 'DisplayName', '实际值');hold on;plot(combined, 'r--', 'LineWidth', 2, 'DisplayName', '组合预测值');title('预测值与实际值对比');xlabel('时间');ylabel('值');legend;grid on;% 2. 预测误差subplot(2, 3, 2);errors = actual - combined;plot(errors, 'g-', 'LineWidth', 1.5);title('预测误差');xlabel('时间');ylabel('误差');grid on;% 3. 权重演化subplot(2, 3, 3);weights_history = vertcat(obj.prediction_history.weights);plot(weights_history, 'LineWidth', 1.5);title('模糊权重演化');xlabel('时间');ylabel('权重');legend(obj.combination_model.methods, 'Location', 'best');grid on;% 4. 一阶有效度演化subplot(2, 3, 4);efficiency_history = vertcat(obj.prediction_history.efficiency);plot(efficiency_history, 'LineWidth', 1.5);title('一阶预测有效度演化');xlabel('时间');ylabel('有效度');legend(obj.combination_model.methods, 'Location', 'best');grid on;% 5. 性能指标对比subplot(2, 3, 5);metrics = struct2cell(obj.performance_metrics);metric_names = fieldnames(obj.performance_metrics);bar(cell2mat(metrics));set(gca, 'XTickLabel', metric_names, 'XTickLabelRotation', 45);title('预测性能指标');ylabel('值');grid on;% 6. 误差分布subplot(2, 3, 6);histogram(errors, 20, 'Normalization', 'probability');title('预测误差分布');xlabel('误差');ylabel('概率');grid on;endend
end

5. 应用示例

5.1 债券收益率预测示例

% 债券收益率预测应用
function bondYieldPredictionExample()% 生成模拟债券收益率数据rng(42);  % 设置随机种子n_points = 200;time = (1:n_points)';% 生成趋势+周期+噪声的收益率数据trend = 0.02 + 0.001 * time;seasonal = 0.01 * sin(2 * pi * time / 50);noise = 0.005 * randn(n_points, 1);bond_yields = trend + seasonal + noise;% 划分训练测试集train_ratio = 0.7;n_train = floor(train_ratio * n_points);train_data = bond_yields(1:n_train);test_data = bond_yields(n_train+1:end);% 创建预测系统prediction_system = PredictionSystem(train_data);% 运行预测prediction_system = prediction_system.runPrediction(test_data);% 显示结果fprintf('\n=== 预测性能结果 ===\n');metrics = prediction_system.performance_metrics;fprintf('MAE: %.6f\n', metrics.MAE);fprintf('RMSE: %.6f\n', metrics.RMSE);fprintf('MAPE: %.4f%%\n', metrics.MAPE);fprintf('R²: %.4f\n', metrics.R2);% 可视化结果prediction_system.plotResults();% 显示最终权重fprintf('\n最终模糊权重:\n');for i = 1:length(prediction_system.combination_model.methods)fprintf('%s: %.4f\n', ...prediction_system.combination_model.methods{i}, ...prediction_system.combination_model.fuzzy_weights(i));end
end% 运行示例
bondYieldPredictionExample();