# 时间序列验证与信息泄漏 按一个预测原点重建训练、预处理与标签成熟，解释未来缩放不必改善成绩。 Entry: zh-qt21 | Node: QT21 | Language: zh | Editorial revision: 2026-09-21 ## Teaching instructions 请以具有微积分、线性代数与基本概率背景的高年级本科至研究生为对象，围绕“时间序列验证与信息泄漏”完成一次学习。先实际取得并读完 required_readings 的完整指定单元，记录实际版本/定位/假设/支持范围；目录、摘要或入口不抵扣阅读。可先读取本篇所有必读以备课，但不要把它们全变成读者额外作业。来源打不开时先尝试同版作者可读入口；仍缺承重单元应说明具体缺口，不伪称已读，也不要求无关新批准。先要求读者逐项填写预测2010-01的时间账本；随后比较p12 OLS/ridge未来尺度，最后完成2020-03时点的三期标签成熟题。反馈先定位违规信息，再讨论分数；received_at未知不能补造。 先让读者尝试，再根据本文完整解析反馈；引用范围内解释，不把模拟当市场事实、不把最优目标当收益保证。只在读者选择分支时启用 optional_readings。完成后用一项新输入迁移检验，明确其能独立完成什么。 Before substantive teaching, actually retrieve every required reading unit for the selected scope. Read its complete designated section, including necessary assumptions, tables and footnotes. A working URL or an editorial access date is not a runtime reading receipt. Record the actual version, location, scope and what it supports. If unavailable, use a previously verified equivalent source; if the required unit remains unavailable, identify that gap rather than teach it from memory. Start runtime_reading_log empty. Once reading is complete, use a substantive diagnostic or follow the reader's request for direct explanation. Advance one complete reasoning task at a time; skip mastered basics. Distinguish original facts, supplied teaching assumptions and inference. ## Required readings and runtime protocol ```json { "export_mode": "public", "required_readings": [ { "source_id": "QTDE-TSCV", "access": { "kind": "html_full_text", "uri": "https://otexts.com/fpp3/tscv.html", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "§5.10 全节", "scope": "单步/多步rolling origin及代码", "purpose": "核原点与标签期限" }, "version": "3e online; accessed 2026-09-21", "supports": "单步/多步rolling origin及代码", "title": "Forecasting: Principles and Practice, §5.10", "authors": [ "Rob J Hyndman", "George Athanasopoulos" ] }, { "source_id": "QTDE-ACCURACY", "access": { "kind": "html_full_text", "uri": "https://otexts.com/fpp3/accuracy.html", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "§5.8 全节", "scope": "训练残差和新样本误差", "purpose": "区分调参与评价" }, "version": "3e online; accessed 2026-09-21", "supports": "训练残差和新样本误差", "title": "Forecasting: Principles and Practice, §5.8", "authors": [ "Rob J Hyndman", "George Athanasopoulos" ] }, { "source_id": "QTDE-BEA-A", "access": { "kind": "html_full_text", "uri": "https://www.bea.gov/news/2020/gross-domestic-product-2nd-quarter-2020-advance-estimate-and-annual-update", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "发布时间与GDP开篇、版本说明完整单元", "scope": "2020Q2初值与时间", "purpose": "重建公共信息版本" }, "version": "2020-07-30 08:30 EDT", "supports": "2020Q2初值与时间", "title": "GDP 2020Q2 Advance Estimate", "authors": [ "U.S. Bureau of Economic Analysis" ] }, { "source_id": "QTDE-BEA-B", "access": { "kind": "html_full_text", "uri": "https://www.bea.gov/news/2020/gross-domestic-product-2nd-quarter-2020-second-estimate-corporate-profits-2nd-quarter", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "发布时间、GDP开篇及Updates to GDP完整表", "scope": "2020Q2次值与修订", "purpose": "区分发布和接收" }, "version": "2020-08-27 08:30 EDT", "supports": "2020Q2次值与修订", "title": "GDP 2020Q2 Second Estimate", "authors": [ "U.S. Bureau of Economic Analysis" ] }, { "source_id": "QTDE-FRENCH", "access": { "kind": "html_full_text", "uri": "https://mba.tuck.dartmouth.edu/pages/Faculty/ken.french/Data_Library/det_30_ind_port.html", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "30 Industry Portfolios完整构造说明；随包432行冻结CSV", "scope": "原始组合、频率、单位", "purpose": "识别重建快照" }, "version": "frozen CRSP database vintage 202607; CIZ reconstruction", "supports": "原始组合、频率、单位", "title": "30 Industry Portfolios", "authors": [ "Kenneth R. French" ] }, { "source_id": "QTDE-FRENCH-REGIME", "access": { "kind": "html_full_text", "uri": "https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "页面FIZ/CIZ生产说明完整单元", "scope": "版本与生产方法", "purpose": "防止将当前历史重建当PIT" }, "version": "accessed 2026-09-21; source transition 2025-01", "supports": "版本与生产方法", "title": "French Data Library：FIZ/CIZ methodology", "authors": [ "Kenneth R. French" ] } ], "optional_readings": [ { "source_id": "QTDE-KMZ", "access": { "kind": "pdf_full_text", "uri": "https://economics.yale.edu/sites/default/files/2024-01/The%20Journal%20of%20Finance%20-%202023%20-%20KELLY%20-%20The%20Virtue%20of%20Complexity%20in%20Return%20Prediction%20%281%29.pdf", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "§V.A p.487完整数据单元及footnote33", "scope": "研究日期约定", "purpose": "辨认信息集假设，不把约定当可执行事实" }, "version": "Journal of Finance 79(1), 459–503, February 2024", "supports": "研究日期约定", "branch": "论文日期约定" } ], "runtime_reading_log": [], "supplied_inputs": { "input_identity": "QT-DE-adopted-inputs-20260921-v1", "config": { "content_version": "2026-09-21-QT-DE-review-v2", "input_version": "QT-DE-adopted-inputs-20260921-v1", "dataset": { "file": "https://ou-liu-red-sugar.github.io/notebook/labs/qt-de/data/BusEq-value-weighted-monthly-199001-202512.csv", "origin_input_version": "QT-C-inputs-20260921-v1", "transport_sha256": "72dd0f35d9437d268971de8553827a5c7a4f85ebcf9712c0c1b85ea2ec7cfa74", "source_url": "https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ftp/30_Industry_Portfolios_CSV.zip", "source_details_url": "https://mba.tuck.dartmouth.edu/pages/Faculty/ken.french/Data_Library/det_30_ind_port.html", "regime_url": "https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html", "vintage": "202607 CRSP database; current CIZ reconstruction", "download_date": "2026-09-21", "block": "Average Value Weighted Returns -- Monthly", "column": "BusEq", "sample": [ "199001", "202512" ], "n": 432, "source_lines": [ 775, 1206 ], "missing_removed": 0, "missing_codes": [ -99.99, -999 ], "raw_unit": "percent", "internal_unit": "monthly decimal return", "display_errors": "百分点/月", "annualized": false, "identity": "单一当前重建快照；不是FIZ/CIZ时间拼接，不是逐月当时可见版本。" }, "forecast": { "experiment_id": "EXP-QT-D-FORECAST-01", "p_grid": [ 1, 3, 12 ], "lambda_grid": [ 0.0, 0.1, 1.0, 10.0 ], "default_candidate": "p1-l10", "target": "y_t=r_t", "features": "(r_(t-1),...,r_(t-p))", "warmup": [ "199001", "199012" ], "initial_train": [ "199101", "200912", 228 ], "validation": [ "201001", "201912", 120 ], "historical_evaluation": [ "202001", "202512", 72 ], "train_start_index": 12, "objective": "RSS/n + lambda*||beta||^2", "matrix_penalty": "n*lambda*I", "standardization_ddof": 0, "intercept_penalized": false, "selection": "minimum validation SSE including zero and expanding-mean baselines", "tie_rule": "regression grid: smaller p then smaller lambda", "frozen_hyperparameters_after_validation": true, "refit": "每原点用新成熟标签扩展重拟合；不再次选择p或lambda", "availability": "教学月末可知收益假设；French历史真实发布和接收时点未重建", "future_scaling_control": { "p": 12, "lambdas": [ 0.0, 0.1 ], "scope": "validation only", "identity": "故意信息越界对照" }, "default_clock_month": "201001", "default_clock_lambda": 0.1 }, "selection": { "experiment_id": "EXP-QT-D-SELECT-01", "B": 5000, "m_grid": [ 1, 10, 100, 500 ], "default_m": 100, "seed_all_null": 2201, "seed_mixed": 2202, "rng": "numpy.random.Generator(PCG64)", "n_development": 120, "n_holdout": 120, "sigma": 0.05, "alpha": 0.05, "hypothesis": "事前单侧H0:mu=0 versus H1:mu>0; sigma known", "pvalue": "0.5*erfc(Z/sqrt(2))", "draw_order": "先取(5000,500)开发Z矩阵，再取独立保留Z矩阵；M为共同500列前缀。mixed另重置2202。", "bh_adopted_comparison": "strict <", "source_pilot_comparison": "<=", "empty_BH": "k=0, no rejections, FDP=0", "mixed": { "m": 100, "signals": 10, "signal_mu": 0.01, "null_mu": 0.0 }, "identity": "直接模拟正态样本均值的Z分布；不含逐月路径，不是真实策略面板", "equal_example": { "p": [ 0.025, 0.06 ], "q": 0.05 }, "manual_example": { "p": [ 0.006, 0.012, 0.601, 0.756, 0.918 ], "q": 0.05 } }, "cost": { "experiment_id": "EXP-QT23-COST-01", "rf": 0, "continuous_default": { "mu": 0.015, "rho": 0, "sigma": 0.1, "gamma": 2, "w0": 0.5, "kappa": 0.002, "cap": 0.8, "cash_min": 0.2 }, "integer_default": { "mu": 0.002, "rho": 0, "sigma": 0.02, "gamma": 10, "wealth": 10000, "initial_shares": 0, "mid": 100, "ask": 100.05, "cap": 80, "cash_min": 2000, "mode": "spread_and_commission" }, "fee": { "id": "QTDE-IBKR", "url": "https://www.interactivebrokers.com/en/pricing/commissions-stocks.php?re=amer", "accessed_at": "2026-09-21", "scope": "IBKR Pro US Fixed ordinary whole-share single-order commission component only", "formula": "q=0:0; otherwise min(0.01*execution_price*abs(q),max(1,0.005*abs(q)))" }, "identity": "收益、波动、风险系数、报价、价差、容量为教学设定；佣金是有日期的实际规则组件", "end_value": "期末中价标记；没有退出委托，非往返净利", "excluded_costs": [ "监管/交易所/清算等其他收费", "税", "市场冲击", "持仓融资费", "退出交易费", "零股及改单最低费规则" ] }, "clocks": { "view_id": "EXP-QT-D-CLOCK-01", "shared_experiment": "EXP-QT-D-FORECAST-01", "BEA": [ { "period": "2020Q2", "vintage": "advance", "release_at": "2020-07-30T08:30:00-04:00", "received_at": null, "value_percent_SAAR": -32.9 }, { "period": "2020Q2", "vintage": "second", "release_at": "2020-08-27T08:30:00-04:00", "received_at": null, "value_percent_SAAR": -31.7 } ], "h3_task": { "formula": "prod(1+r_(s+j),j=1..3)-1", "cutoff": "202003", "latest_mature_origin": "201912", "performance_run": false } }, "scale_examples": { "raw_x": [ -1, 1 ], "y": [ -1, 1 ], "lambda": 1.0, "default_feature_scale": 10.0, "response_scale": 100.0 }, "source_identities": { "d_pilot": { "file": "qt-d-experiment-pilot.py", "sha256": "b8a23b01294d543b3b74c6a153168529db74ab7c84837ea3724a55f5071fd3fb", "read_scope": "1–193" }, "ef_pilot": { "file": "qt-ef-calculations.py", "sha256": "28eff60cf87400805af145fabd22d4fe17e2c25bac3708cd9e71506d939acb20", "adopted_scope": "commission, continuous_case, integer_case, decision_calculation" }, "approval": { "file": "qt-de-draft-approved.md", "read_scope": "1–7", "sha256": "80e92333d057772de9463d786a9be435c6dc1208744bf828d5eb2a4d2a5e9a48" }, "plan_review": { "file": "qt-def-plan-review.md", "read_scope": "1–20", "sha256": "56fddfa847ca0f83ec4822652c506f847e9da4e45f7223c039b31428f3aedfd4" } } }, "static_equivalent_html": "

预测2010-01：原点2009-12月末；训练目标1991-01—2009-12（228行），训练滞后特征最晚2009-11，新输入最晚2009-12。预测后等2010-01标签成熟再评价。

p12模型合法尺度RMSE pp/月未来尺度RMSE pp/月
λ=05.135414965.13541496
λ=0.15.120765735.12283553

OLS 带截距、无约束、同一可逆仿射转换且本设计满秩时不变；ridge 惩罚改变。本例越界并未改善RMSE。

BEA 2020Q2版本release_at值% SAARreceived_at
advance2020-07-30T08:30:00-04:00-32.9未知
second2020-08-27T08:30:00-04:00-31.7未知

2020-08-03公开截面只能选advance；系统接收时间未记录。三期标签Y_s=∏(1+r_s+j)−1，在2020-03月末最多纳入原点2019-12；相邻标签重叠。本篇没有h=3历史RMSE。虚构1%、−2%、3%的复合收益为1.9494%。

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"return_decimal": "0.0353", "loss_decimal": "-0.0353", "source_line": "776" }, { "month": "199003", "BusEq_percent": "4.10", "return_decimal": "0.0410", "loss_decimal": "-0.0410", "source_line": "777" }, { "month": "199004", "BusEq_percent": "-1.46", "return_decimal": "-0.0146", "loss_decimal": "0.0146", "source_line": "778" }, { "month": "199005", "BusEq_percent": "11.64", "return_decimal": "0.1164", "loss_decimal": "-0.1164", "source_line": "779" }, { "month": "199006", "BusEq_percent": "-2.00", "return_decimal": "-0.0200", "loss_decimal": "0.0200", "source_line": "780" }, { "month": "199007", "BusEq_percent": "-6.52", "return_decimal": "-0.0652", "loss_decimal": "0.0652", "source_line": "781" }, { "month": "199008", "BusEq_percent": "-12.22", "return_decimal": "-0.1222", "loss_decimal": "0.1222", "source_line": "782" }, { "month": "199009", "BusEq_percent": "-6.16", "return_decimal": "-0.0616", "loss_decimal": "0.0616", "source_line": "783" }, { "month": "199010", "BusEq_percent": "-3.82", "return_decimal": "-0.0382", "loss_decimal": "0.0382", "source_line": "784" }, { "month": "199011", "BusEq_percent": "10.47", "return_decimal": "0.1047", "loss_decimal": "-0.1047", "source_line": "785" }, { "month": "199012", "BusEq_percent": "3.93", "return_decimal": "0.0393", "loss_decimal": "-0.0393", "source_line": "786" }, { "month": "199101", "BusEq_percent": "14.36", "return_decimal": "0.1436", "loss_decimal": "-0.1436", "source_line": "787" }, { "month": "199102", "BusEq_percent": "5.98", "return_decimal": "0.0598", "loss_decimal": "-0.0598", "source_line": "788" }, { "month": "199103", "BusEq_percent": "-0.61", "return_decimal": "-0.0061", "loss_decimal": "0.0061", "source_line": "789" }, { "month": "199104", "BusEq_percent": "-3.01", "return_decimal": "-0.0301", "loss_decimal": "0.0301", "source_line": "790" }, { "month": "199105", "BusEq_percent": "3.47", "return_decimal": "0.0347", "loss_decimal": "-0.0347", "source_line": "791" }, { "month": "199106", "BusEq_percent": "-9.19", "return_decimal": "-0.0919", "loss_decimal": "0.0919", "source_line": "792" }, { "month": "199107", "BusEq_percent": "4.15", "return_decimal": "0.0415", "loss_decimal": "-0.0415", "source_line": "793" }, { "month": "199108", "BusEq_percent": "1.37", "return_decimal": "0.0137", "loss_decimal": "-0.0137", "source_line": "794" }, { "month": "199109", "BusEq_percent": "-2.13", "return_decimal": "-0.0213", "loss_decimal": "0.0213", "source_line": "795" }, { "month": "199110", "BusEq_percent": "0.13", "return_decimal": "0.0013", "loss_decimal": "-0.0013", "source_line": "796" }, { "month": "199111", "BusEq_percent": "-5.01", "return_decimal": "-0.0501", "loss_decimal": "0.0501", "source_line": "797" }, { "month": "199112", "BusEq_percent": "7.05", "return_decimal": "0.0705", "loss_decimal": "-0.0705", "source_line": "798" }, { "month": "199201", "BusEq_percent": "7.35", "return_decimal": "0.0735", "loss_decimal": "-0.0735", "source_line": "799" }, { "month": "199202", "BusEq_percent": "4.45", "return_decimal": "0.0445", "loss_decimal": "-0.0445", "source_line": "800" }, { "month": "199203", "BusEq_percent": "-4.94", "return_decimal": "-0.0494", "loss_decimal": "0.0494", "source_line": "801" }, { "month": "199204", "BusEq_percent": "0.20", "return_decimal": "0.0020", "loss_decimal": "-0.0020", "source_line": "802" }, { "month": "199205", "BusEq_percent": "-0.75", "return_decimal": "-0.0075", "loss_decimal": "0.0075", "source_line": "803" }, { "month": "199206", "BusEq_percent": "-2.71", "return_decimal": "-0.0271", "loss_decimal": "0.0271", "source_line": "804" }, { "month": "199207", "BusEq_percent": "2.67", "return_decimal": "0.0267", "loss_decimal": "-0.0267", "source_line": "805" }, { "month": "199208", "BusEq_percent": "-5.32", "return_decimal": "-0.0532", "loss_decimal": "0.0532", "source_line": "806" }, { "month": "199209", "BusEq_percent": "2.38", "return_decimal": "0.0238", "loss_decimal": "-0.0238", "source_line": "807" }, { 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0.009218280753562538, 0.000675589000058761, 0.010541518844932499, 0.011885913373710253, 0.02713605504206639, 0.01199314748339458, 0.0019903716173173096, 0.01660118204770923 ], "max_abs_prediction_difference_decimal": 0.00039484640920822017 } }, "reading_base": "公开同源包；按完整 URL 取得冻结输入与复算文件。来源网站后续更新不覆盖本份 202607 快照。" }, "entry_id": "zh-qt21", "content_version": "2026-09-21-QT-DE-review-v2", "audience": "高年级本科至研究生；默认微积分、线性代数与基本概率", "learning_task": "按一个预测原点重建训练、预处理与标签成熟，解释未来缩放不必改善成绩。" } ``` ## Supplied entry 预测方法不是一个脱离时间的公式。它先接收记录，再拟合预处理和模型，最后等预测目标成熟，才能计算误差。本篇沿一段真实历史重放，把这些时点放回计算中。读完后，你应能为一个预测原点列出完整信息账本，指出违规发生在哪一步，而不只是看到好成绩便怀疑“有未来函数”。 ## 1. 在 2009 年末，我们到底算了什么？ 仍使用 202607 CRSP 数据库 vintage 下由当前 CIZ 生产链重建的 BusEq 月收益快照：1990-01—2025-12，共 432 月，无目标窗口缺失，百分数除以 100 后运算。它是历史计算材料，不是逐月当时可见的资料集合。先约定教学时钟：月份结束后可知该月收益，并预测下一月。来源真实发布时间和系统接收延迟没有在这份行业组合文件中重建。[^data] 以预测 2010-01 为例，训练目标为 1991-01 至 2009-12 的 228 行。1990 年只供最大 12 期滞后预热；各模型不能各自多取一批较早目标行，随后再比较不同样本的误差。 | 环节 | 本原点允许使用的对象 | |---|---| | 决策原点 | 2009-12 月末后的教学信息截面 | | 拟合目标 $y_s$ | 1991-01—2009-12 已成熟收益 | | 拟合特征 $x_s$ | 每个目标月之前的 $p$ 个滞后；所有训练特征中最晚的收益月是 2009-11 | | 标准化参数 | 仅由这些训练特征行求出的列均值与列标准差 | | 新预测输入 $x_t$ | 从 2009-12 起向前取 $p$ 个滞后；这行不参与本次 scaler 拟合 | | 当前输出 | 对 2010-01 的预测 | | 何时评价 | 2010-01 目标成熟后，才用真实 $r_t$ 计算误差 | 注意两个容易混在一起的范围：训练标签可以到 2009-12，而训练滞后特征最晚到 2009-11；2009-12 收益作为本次新输入出现。标准差必须说明“在哪些行上估计”，不能只写含糊的“用了截至今天的数据”。[^calculation] ## 2. 把一次预测写成可重复的过程 给定候选 $(p,\lambda)$，在每个目标月 $t$ 之前依次做： ```text train = 已成熟的共同目标行 1991-01,...,t-1 X_train[s] = (r[s-1],...,r[s-p]); y_train[s] = r[s] 从 X_train 拟合 mean、sd，不从完整文件拟合 Z_train = (X_train-mean)/sd 拟合不惩罚截距的 RSS/n + lambda*||beta||² 对 x_new=(r[t-1],...,r[t-p]) 使用相同 mean、sd 输出并保留 prediction[t]；目标成熟后才添加 error[t] ``` 这是扩展窗口：起点固定，终点随原点推进。滚动窗口则只保留固定长度的最近历史；二者估计目标与适应变化的方式不同，不是“移动原点”就自动意味着训练长度固定。FPP3 的 rolling forecasting origin 指评价原点向前滚动，其示例训练集可以扩展。[^cv] 本实验用 2010—2019 的 120 个原点比较 12 个回归候选与两条基线。选择完成后，进入 2020—2025 的 72 月历史评价：$p,\lambda$ 或基线身份已冻结，但模型系数仍按照原定扩展规则逐月重估。冻结超参数不等于冻结所有系数，也不等于禁止合法的新标签进入训练。[^calculation] 例如下一原点预测 2010-02 时，2010-01 收益已按教学时钟成熟，训练行增至 229。这时使用它是正常更新；把它提前用于 2010-01 的预测则是信息越界。残差来自参与拟合的数据，预测误差来自该原点尚未参与拟合的目标，两者不能混报。[^accuracy] ## 3. 一个真实对照：越界不一定让分数更好 我们故意构造一个错误版本：每个原点都用完整样本的滞后特征列拟合标准化参数。该池含目标月份 1991-01—2025-12 的特征行，最晚原始特征收益到 2025-11。对 2009 年末的原点而言，它显然包含未来信息。拟合标签仍只取过去，以便隔离“标准化范围”这一项变化。 | $p=12$，2010—2019 验证 | 合法训练窗标准化 RMSE | 越界全样本标准化 RMSE | 最大单月预测差 | |---|---:|---:|---:| | OLS，$\lambda=0$ | 5.13541496 | 5.13541496 | 约 $7.3\times10^{-15}$ | | Ridge，$\lambda=0.1$ | 5.12076573 | 5.12283553 | 0.03948464 | 表内三列误差单位均为百分点/月。OLS 的差异只有浮点量级；ridge 的越界版本反而稍差。我们不改参数来制造“泄漏让曲线更漂亮”的效果，因为要检验的是信息使用，而不是预先安排一个方向的答案。[^calculation] 为什么 OLS 会不变？设原输入 $x=m+Dz$，$D$ 为对角非奇异尺度矩阵。仿射预测函数可写成 $$ a+x^Tb=(a+m^Tb)+z^TDb. $$ 在有截距、斜率无约束、同一转换作用于训练和新输入时，这是一一对应的重参数化。OLS 最小化相同的残差集合。本例每个训练设计都满列秩，因此唯一预测函数被对应起来，样本外预测也相同。若秩不足，只能先说训练拟合向量与解集合在映射下相同；两种坐标下软件各自挑出的最小范数系数，其样本外外推未必一样。 Ridge 则额外惩罚系数。改了 $D$ 却仍用同一个坐标中的 $\lambda\|\beta\|^2$，等于改变了对原预测函数的代价，所以预测可以变。[预测目标与正则化](https://ou-liu-red-sugar.github.io/zh/notebook/prediction-regularization-complexity/) 已推导这一点。这个特例也不意味着 OLS 对标签泄漏、未来特征选择或其他预处理免疫。
在实验中先选一个验证月份，读训练标签终点、特征尺度及输入，再打开故意越界的对照。请先说哪项记录不应出现，最后才看 RMSE；不能反过来以“分数没有改善”证明流程合法。 ## 4. 日期排序之外，还要区分观察期、发布和接收 经济数据尤其能说明这个区别。美国 2020Q2 GDP 描述第二季度，但以下两个数并不是在季度末同时可得： | 观察期 | 版本 | BEA 发布时点 | 实际 GDP 环比年化率 | |---|---|---|---:| | 2020Q2 | Advance | 2020-07-30 08:30 EDT | −32.9% | | 2020Q2 | Second | 2020-08-27 08:30 EDT | −31.7% | 这两行是原始发布记录；它们的差为 1.2 个百分点，而非观察期移动。[^bea-a][^bea-b] 若信息截止在 2020-08-03，公开发布截面只能选择初值，不能把后来次值写回这个原点。 发布时点仍不等于研究系统收到、解析、完成计算的时点。没有 `received_at` 日志，就保留未知；不能由“08:30 发布”推出“08:30:01 系统已能下单”。历史重放可明确假设一个延迟，再研究该假设下的结果，但这不把假设变成历史事实。 前面 BusEq 的时间切分也因此有两层评价：运算确实不让后面标签参与前面拟合，但所用文件版本不是每个历史原点的原始可得版本。准确的描述是“当前冻结快照上的按时间算法重放”。只有额外恢复来源版本和接收过程，才可进一步评价当时的可执行性。 一个有分量的研究阅读例是 Kelly、Malamud、Zhou 的脚注33：作者交代了通胀数据的月度日期约定与实际发布滞后的区别。阅读论文时应把这种约定记入方法条件，而不是看到“样本外”三个字就忽略它。[^kmz] ## 5. 预测三个月时，标签什么时候成熟？ 假设在月份 $s$ 结束后预测接下来三个月的复合收益： $$ Y_s=(1+r_{s+1})(1+r_{s+2})(1+r_{s+3})-1. $$ 在月份 $t$ 结束时，训练可使用这行标签的必要条件是 $s+3\le t$，还要满足相关原始材料已接收。不能只因特征行的日期 $s\le t$ 就把未来三个月的完整标签拿来拟合。 | 当前信息截面：2020-03 月末 | 标签覆盖月份 | 是否成熟 | |---|---|---| | 原点 2019-12 | 2020-01—2020-03 | 是，在本例月末可知假设下 | | 原点 2020-01 | 2020-02—2020-04 | 否 | | 原点 2020-02 | 2020-03—2020-05 | 否 | | 原点 2020-03 | 2020-04—2020-06 | 否，这是新的预测对象 | 相邻原点的三个月标签会共享收益月。因此，即使每个预测都遵守信息约束，多个误差也可能相关，不能机械当作独立观测估计标准误。隔离范围应从标签成熟与评价问题推导，不是对所有时间序列统一“空三个月”。FPP3 对多步预测原点评价提供了相应结构，本篇没有为这个三个月目标运行新的 RMSE。[^cv] ## 6. 独立重建与解析 解释题。 在预测 2010-01 前，用全样本求标准差，随后发现 OLS 的预测完全不变。是否就证明未来标准化没有问题？ 解析。 没有。计算步骤仍依赖未来信息；本例不变来自明确条件下的仿射重参数化。它只能说明这一模型恰好对这项变换不敏感。把同一流程用于 ridge、筛选变量或选择模型，结论都需要另核。应修复流程，而不是用偶然的输出不变代替信息证明。 迁移题一。 截止 2020-08-03，分析规则比较 GDP 公布值是否大于 −32。用哪一版？能否断言自己的系统 7 月 30 日 08:30:01 已得到信号？ 解析。 在公开发布口径下，初值 −32.9 不满足规则；8 月 27 日才发布的 −31.7 会满足，但不能提前使用。系统是否收到及完成计算没有日志便不能判断。这项规则是教学设定，不是经检验可盈利的交易信号。 迁移题二。 2020-03 月末训练三个月目标，最新能纳入的原点是哪月？再用明确虚构的月收益 $1\%,-2\%,3\%$ 算一次标签。 解析。 最新是 2019-12；2020-01 原点的标签还含 4 月。虚构标签为 $1.01\times0.98\times1.03-1=0.019494$，即 1.9494%，不能简单加成 2%。这只是标签算式核对，不是新增的历史绩效结果。 最后再分开两件事：时间顺序正确，可以阻止某类未来信息进入拟合；它不能自动消除“尝试许多流程后只留下最好一个”的选择效应。下一篇保留全部尝试，研究后者。[选择效应与多重检验](https://ou-liu-red-sugar.github.io/zh/notebook/selection-multiple-testing/) [^data]: French [30 Industry Portfolios](https://mba.tuck.dartmouth.edu/pages/Faculty/ken.french/Data_Library/det_30_ind_port.html) 与 [FIZ/CIZ 来源说明](https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html)。具体样本身份和所有 432 行见[随包输入](https://ou-liu-red-sugar.github.io/notebook/labs/qt-de/shared_inputs.json)及 CSV。 [^calculation]: [实际计算结果](https://ou-liu-red-sugar.github.io/notebook/labs/qt-de/data/results.json)，forecast 的逐原点拟合与 future_scaling_controls；[复算程序](https://ou-liu-red-sugar.github.io/notebook/labs/qt-de/compute/reproduce.py)。原点、尺度与标签均可逐行重建。 [^accuracy]: FPP3，[§5.8 Evaluating point forecast accuracy 全节](https://otexts.com/fpp3/accuracy.html)。 [^cv]: FPP3，[§5.10 Time series cross-validation 全节](https://otexts.com/fpp3/tscv.html)。多期复合标签成熟条件由本文定义直接推出，未声称该书给出本例金融回测。 [^bea-a]: BEA，[2020Q2 Advance Estimate 原发布](https://www.bea.gov/news/2020/gross-domestic-product-2nd-quarter-2020-advance-estimate-and-annual-update)，页首发布时间及 GDP 开篇。 [^bea-b]: BEA，[2020Q2 Second Estimate 原发布](https://www.bea.gov/news/2020/gross-domestic-product-2nd-quarter-2020-second-estimate-corporate-profits-2nd-quarter)，页首、GDP 开篇和 Updates to GDP 表。 [^kmz]: Kelly、Malamud、Zhou，[2024 发表版](https://economics.yale.edu/sites/default/files/2024-01/The%20Journal%20of%20Finance%20-%202023%20-%20KELLY%20-%20The%20Virtue%20of%20Complexity%20in%20Return%20Prediction%20%281%29.pdf)，§V.A，p.487 脚注33。未读取的附录稳健性不作为本篇证据。 ## Experiment inputs and static equivalents ```json [ { "id": "EXP-QT-D-CLOCK-01", "title": "时间序列验证与信息泄漏：可复算实验", "anchor": "qt21-leakage", "description": "按一个预测原点重建训练、预处理与标签成熟，解释未来缩放不必改善成绩。", "inputs": { "identity": "QT-DE-adopted-inputs-20260921-v1", "manifest": "https://ou-liu-red-sugar.github.io/notebook/labs/qt-de/shared_inputs.json" }, "outputs": { "first_target": "201001", "train_targets": 228, "h3_latest_mature": "201912", "performance_h3_executed": false } } ] ``` ## Sources - [Forecasting: Principles and Practice, §5.8](https://otexts.com/fpp3/accuracy.html): 完整单元支持预测误差不同于残差，RMSE/MAE与mean/median的关系；书中实例不是本站交易绩效。 - [GDP 2020Q2 Advance Estimate](https://www.bea.gov/news/2020/gross-domestic-product-2nd-quarter-2020-advance-estimate-and-annual-update): 原始发布的-32.9%为实际GDP季度环比年化率。支持release，不提供本研究系统received_at。 - [GDP 2020Q2 Second Estimate](https://www.bea.gov/news/2020/gross-domestic-product-2nd-quarter-2020-second-estimate-corporate-profits-2nd-quarter): 原始发布-31.7%、相对初值上修1.2pp；原件不支持推断系统接收时间。 - [QT-D/E adopted teaching experiments](https://ou-liu-red-sugar.github.io/notebook/labs/qt-de/compute/reproduce.py): 本轮实际沙盒复算，预测遵守冻结算法及数据；选择沿PCG64调用顺序并核strict/inclusive，成本用Fraction。数学演算与假设模型不等于真实投资有效性。 - [30 Industry Portfolios](https://mba.tuck.dartmouth.edu/pages/Faculty/ken.french/Data_Library/det_30_ind_port.html): 冻结原件摘取的432个连续月；百分数除100。来自当前重建历史，不是各月当时可见vintage；无样本期缺失。 - [French Data Library：FIZ/CIZ methodology](https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html): 生产链转换与股息复投口径；本批坚持单次202607重建快照，未拼接旧vintage。 - [The Virtue of Complexity in Return Prediction](https://economics.yale.edu/sites/default/files/2024-01/The%20Journal%20of%20Finance%20-%202023%20-%20KELLY%20-%20The%20Virtue%20of%20Complexity%20in%20Return%20Prediction%20%281%29.pdf): 已读完整实证设置单元，用于配对研究选读：随机特征、训练窗口、信息日期约定、R²分母。未验证前部理论或附录，未复现论文，具体作者结果不普遍化。 - [Forecasting: Principles and Practice, §5.10](https://otexts.com/fpp3/tscv.html): 完整单元支持按原点训练、按期限评价；真实发布/接收时点仍需另核。 ## Content relations ```json [ { "from": "zh-qt21", "relation": "part_of", "to": "quant-estimation", "reason": "主要 topic 归属" }, { "from": "zh-qt21", "relation": "requires", "to": "zh-qt07", "required_competence": "区分决策前的信息与成交", "reason": "本篇使用该能力，不要求整门随机过程课程。" }, { "from": "zh-qt21", "relation": "requires", "to": "zh-qt20", "required_competence": "理解训练、目标与正则化", "reason": "本篇使用该能力，不要求整门随机过程课程。" }, { "from": "qt21-leakage", "relation": "illustrated_by", "to": "EXP-QT-D-CLOCK-01", "reason": "完整输入、默认及静态等价支持本篇独立任务。" }, { "from": "zh-qt21", "relation": "supported_by", "to": "QTDE-TSCV", "locator": "§5.10 全节", "scope": "单步/多步rolling origin及代码", "reason": "核原点与标签期限" }, { "from": "zh-qt21", "relation": "supported_by", "to": "QTDE-ACCURACY", "locator": "§5.8 全节", "scope": "训练残差和新样本误差", "reason": "区分调参与评价" }, { "from": "zh-qt21", "relation": "supported_by", "to": "QTDE-BEA-A", "locator": "发布时间与GDP开篇、版本说明完整单元", "scope": "2020Q2初值与时间", "reason": "重建公共信息版本" }, { "from": "zh-qt21", "relation": "supported_by", "to": "QTDE-BEA-B", "locator": "发布时间、GDP开篇及Updates to GDP完整表", "scope": "2020Q2次值与修订", "reason": "区分发布和接收" }, { "from": "zh-qt21", "relation": "supported_by", "to": "QTDE-FRENCH", "locator": "30 Industry Portfolios完整构造说明；随包432行冻结CSV", "scope": "原始组合、频率、单位", "reason": "识别重建快照" }, { "from": "zh-qt21", "relation": "supported_by", "to": "QTDE-FRENCH-REGIME", "locator": "页面FIZ/CIZ生产说明完整单元", "scope": "版本与生产方法", "reason": "防止将当前历史重建当PIT" }, { "from": "zh-qt21", "relation": "supported_by", "to": "QTDE-KMZ", "locator": "§V.A p.487完整数据单元及footnote33", "scope": "研究日期约定", "reason": "辨认信息集假设，不把约定当可执行事实" } ] ``` ## Related entries ## Optional reading path 理解模型并亲手算: step 7/9 重建滚动原点，区分合法更新、未来尺度和修订信息。 时间顺序正确后，还要把挑选候选的方法纳入评价。 Next: [选择效应与多重检验](https://ou-liu-red-sugar.github.io/zh/notebook/selection-multiple-testing/)