{ "schema": "forecast_lab/1", "generated_at": "2026-09-26T12:40:30Z", "built_by": "build_forecast.py", "schedule": null, "series": { "title": "Advance Retail Sales: Retail Trade and Food Services", "label": "U.S. retail trade and food services", "units": "Millions of Dollars", "seasonal_adjustment": "Not Seasonally Adjusted", "frequency": "Monthly", "page": "https://fred.stlouisfed.org/series/RSAFSNA", "source_agency": "U.S. Census Bureau, via FRED (Federal Reserve Bank of St. Louis)", "id": "RSAFSNA", "csv": "data/fred/RSAFSNA.csv", "url": "https://fred.stlouisfed.org/graph/fredgraph.csv?id=RSAFSNA", "bytes": 7513, "sha256": "2bbe15d2fc830b6bd4f69184734d4373a6d94ec3840a7621570e43e221a8a4bf", "rows": 416, "first": { "month": "1992-01", "value": 142051.0 }, "last": { "month": "2026-08", "value": 784846.0 }, "retrieved_at": "2026-09-23T06:47:06Z", "http_status": 200, "last_modified_header": "Wed, 16 Sep 2026 12:39:52 GMT" }, "companion_series": { "title": "Advance Retail Sales: Retail Trade and Food Services", "label": "U.S. retail trade and food services, seasonally adjusted", "units": "Millions of Dollars", "seasonal_adjustment": "Seasonally Adjusted", "frequency": "Monthly", "page": "https://fred.stlouisfed.org/series/RSAFS", "source_agency": "U.S. Census Bureau, via FRED (Federal Reserve Bank of St. Louis)", "id": "RSAFS", "csv": "data/fred/RSAFS.csv", "url": "https://fred.stlouisfed.org/graph/fredgraph.csv?id=RSAFS", "bytes": 7511, "sha256": "c57685eed78fe9d2c961e7ed540c88c2c0161bc356672f0ebf8cf2b83cb9ed88", "rows": 416, "first": { "month": "1992-01", "value": 159177.0 }, "last": { "month": "2026-08", "value": 773947.0 }, "retrieved_at": "2026-09-23T06:47:06Z", "http_status": 200, "last_modified_header": "Wed, 16 Sep 2026 12:39:53 GMT" }, "data": { "first": "1992-01", "last": "2026-08", "n_months": 416, "span": "34 years 8 months" }, "covid_window": { "start": "2020-03", "end": "2021-06", "n_months": 16 }, "models": [ { "id": "naive", "kind": "baseline", "name": "Naive (last value)", "how": "Every future month equals the last observed month." }, { "id": "snaive", "kind": "baseline", "name": "Seasonal naive", "how": "Each future month equals the same month one year earlier." }, { "id": "drift", "kind": "baseline", "name": "Drift", "how": "The last value, growing at the average monthly log change of the whole history (pandemic-window changes excluded). It ignores seasonality." }, { "id": "snaive_drift", "kind": "baseline", "name": "Seasonal naive with drift", "how": "The same month one year earlier, grown by the average 12-month log change of the whole history (pandemic-window changes excluded). A seasonal random walk with drift." }, { "id": "holt", "kind": "fitted", "name": "Damped Holt (log, deseasonalised)", "how": "Seasonal factors are removed, a damped-trend exponential smoother is fitted on the log level by one-step squared error over a parameter grid, then the factors are put back." }, { "id": "loglinear", "kind": "fitted", "name": "Log-linear trend + season", "how": "Least squares on the log level over the last 10 years: a straight trend plus 11 month effects, then shifted so it starts from where the series actually is (the mean of the last 3 residuals)." } ], "backtest": { "design": { "n_origins": 24, "first_origin": "2023-09", "last_origin": "2025-08", "horizons": 12, "forecasts_per_model": 288, "refit_every_origin": true, "band_pool_first_origin": "2012-01", "band_pool_origins": 148, "band_quantiles": [ 0.1, 0.9 ], "min_pool": 10, "mase_scale": "mean absolute 12-month difference over the 120 months before each origin, pairs touching the pandemic window excluded" }, "scores": { "naive": { "overall": { "n": 288, "mae": 45426.8438, "mape": 6.3465, "mase": 2.3043 }, "by_h": [ { "h": 1, "n": 24, "mae": 40125.5417, "mape": 5.7853, "mase": 2.0398 }, { "h": 2, "n": 24, "mae": 48270.0833, "mape": 7.019, "mase": 2.467 }, { "h": 3, "n": 24, "mae": 44948.5, "mape": 6.3757, "mase": 2.3057 }, { "h": 4, "n": 24, "mae": 45769.0833, "mape": 6.4585, "mase": 2.3241 }, { "h": 5, "n": 24, "mae": 38112.875, "mape": 5.3316, "mase": 1.9248 }, { "h": 6, "n": 24, "mae": 53982.0, "mape": 7.5475, "mase": 2.7245 }, { "h": 7, "n": 24, "mae": 42826.6667, "mape": 6.0142, "mase": 2.1664 }, { "h": 8, "n": 24, "mae": 46258.375, "mape": 6.4265, "mase": 2.3415 }, { "h": 9, "n": 24, "mae": 56409.4583, "mape": 7.8553, "mase": 2.8543 }, { "h": 10, "n": 24, "mae": 51810.5, "mape": 7.0277, "mase": 2.628 }, { "h": 11, "n": 24, "mae": 47126.5417, "mape": 6.3456, "mase": 2.3896 }, { "h": 12, "n": 24, "mae": 29482.5, "mape": 3.9711, "mase": 1.4857 } ] }, "snaive": { "overall": { "n": 288, "mae": 25268.1424, "mape": 3.4809, "mase": 1.2764 }, "by_h": [ { "h": 1, "n": 24, "mae": 23840.1667, "mape": 3.3481, "mase": 1.2057 }, { "h": 2, "n": 24, "mae": 24054.3333, "mape": 3.3675, "mase": 1.2163 }, { "h": 3, "n": 24, "mae": 23455.2083, "mape": 3.2767, "mase": 1.1872 }, { "h": 4, "n": 24, "mae": 23471.625, "mape": 3.2658, "mase": 1.1874 }, { "h": 5, "n": 24, "mae": 24014.7917, "mape": 3.3429, "mase": 1.216 }, { "h": 6, "n": 24, "mae": 23561.9167, "mape": 3.265, "mase": 1.1932 }, { "h": 7, "n": 24, "mae": 24398.9583, "mape": 3.3674, "mase": 1.2345 }, { "h": 8, "n": 24, "mae": 24761.5417, "mape": 3.4017, "mase": 1.2498 }, { "h": 9, "n": 24, "mae": 25623.7917, "mape": 3.4996, "mase": 1.2928 }, { "h": 10, "n": 24, "mae": 28091.125, "mape": 3.8169, "mase": 1.4158 }, { "h": 11, "n": 24, "mae": 28461.75, "mape": 3.8482, "mase": 1.433 }, { "h": 12, "n": 24, "mae": 29482.5, "mape": 3.9711, "mase": 1.4857 } ] }, "drift": { "overall": { "n": 288, "mae": 42401.3119, "mape": 6.0031, "mase": 2.1513 }, "by_h": [ { "h": 1, "n": 24, "mae": 39837.0504, "mape": 5.7536, "mase": 2.0237 }, { "h": 2, "n": 24, "mae": 48476.9737, "mape": 7.0703, "mase": 2.4754 }, { "h": 3, "n": 24, "mae": 47331.4426, "mape": 6.7402, "mase": 2.4245 }, { "h": 4, "n": 24, "mae": 45105.4067, "mape": 6.4244, "mase": 2.2944 }, { "h": 5, "n": 24, "mae": 39340.1157, "mape": 5.5539, "mase": 1.9886 }, { "h": 6, "n": 24, "mae": 54501.9104, "mape": 7.6981, "mase": 2.7462 }, { "h": 7, "n": 24, "mae": 39374.004, "mape": 5.6067, "mase": 1.99 }, { "h": 8, "n": 24, "mae": 44882.994, "mape": 6.3141, "mase": 2.2692 }, { "h": 9, "n": 24, "mae": 48747.0362, "mape": 6.9238, "mase": 2.4609 }, { "h": 10, "n": 24, "mae": 50402.191, "mape": 6.9724, "mase": 2.5588 }, { "h": 11, "n": 24, "mae": 42564.3455, "mape": 5.8303, "mase": 2.1656 }, { "h": 12, "n": 24, "mae": 8252.2723, "mape": 1.1495, "mase": 0.4178 } ] }, "snaive_drift": { "overall": { "n": 288, "mae": 8879.1339, "mape": 1.2749, "mase": 0.4515 }, "by_h": [ { "h": 1, "n": 24, "mae": 9155.7361, "mape": 1.3451, "mase": 0.4649 }, { "h": 2, "n": 24, "mae": 9009.292, "mape": 1.321, "mase": 0.4583 }, { "h": 3, "n": 24, "mae": 9696.0887, "mape": 1.4139, "mase": 0.4926 }, { "h": 4, "n": 24, "mae": 9789.3412, "mape": 1.4248, "mase": 0.4983 }, { "h": 5, "n": 24, "mae": 9292.3793, "mape": 1.341, "mase": 0.4731 }, { "h": 6, "n": 24, "mae": 8937.8081, "mape": 1.2843, "mase": 0.4548 }, { "h": 7, "n": 24, "mae": 8430.6957, "mape": 1.2097, "mase": 0.4298 }, { "h": 8, "n": 24, "mae": 8356.1457, "mape": 1.1974, "mase": 0.4281 }, { "h": 9, "n": 24, "mae": 8454.1394, "mape": 1.206, "mase": 0.4317 }, { "h": 10, "n": 24, "mae": 8397.7143, "mape": 1.1777, "mase": 0.424 }, { "h": 11, "n": 24, "mae": 8672.5453, "mape": 1.2124, "mase": 0.4395 }, { "h": 12, "n": 24, "mae": 8357.7214, "mape": 1.1651, "mase": 0.4227 } ] }, "holt": { "overall": { "n": 288, "mae": 11913.5567, "mape": 1.6511, "mase": 0.6027 }, "by_h": [ { "h": 1, "n": 24, "mae": 10151.7209, "mape": 1.4333, "mase": 0.516 }, { "h": 2, "n": 24, "mae": 10101.2972, "mape": 1.4176, "mase": 0.5135 }, { "h": 3, "n": 24, "mae": 8752.2014, "mape": 1.236, "mase": 0.4449 }, { "h": 4, "n": 24, "mae": 10220.01, "mape": 1.447, "mase": 0.5196 }, { "h": 5, "n": 24, "mae": 9303.8568, "mape": 1.3157, "mase": 0.4722 }, { "h": 6, "n": 24, "mae": 8904.5927, "mape": 1.251, "mase": 0.4529 }, { "h": 7, "n": 24, "mae": 12127.4203, "mape": 1.6938, "mase": 0.6157 }, { "h": 8, "n": 24, "mae": 12240.3125, "mape": 1.7002, "mase": 0.6181 }, { "h": 9, "n": 24, "mae": 12690.496, "mape": 1.7481, "mase": 0.6409 }, { "h": 10, "n": 24, "mae": 15011.2763, "mape": 2.0486, "mase": 0.7568 }, { "h": 11, "n": 24, "mae": 16363.2108, "mape": 2.2123, "mase": 0.8217 }, { "h": 12, "n": 24, "mae": 17096.2851, "mape": 2.3098, "mase": 0.8598 } ] }, "loglinear": { "overall": { "n": 288, "mae": 12967.059, "mape": 1.815, "mase": 0.6613 }, "by_h": [ { "h": 1, "n": 24, "mae": 10579.9933, "mape": 1.4978, "mase": 0.5374 }, { "h": 2, "n": 24, "mae": 11617.435, "mape": 1.6481, "mase": 0.5918 }, { "h": 3, "n": 24, "mae": 12421.9474, "mape": 1.7528, "mase": 0.6325 }, { "h": 4, "n": 24, "mae": 12861.8782, "mape": 1.815, "mase": 0.6533 }, { "h": 5, "n": 24, "mae": 13498.5274, "mape": 1.8996, "mase": 0.6888 }, { "h": 6, "n": 24, "mae": 13699.4854, "mape": 1.9244, "mase": 0.6991 }, { "h": 7, "n": 24, "mae": 13406.9551, "mape": 1.8746, "mase": 0.6836 }, { "h": 8, "n": 24, "mae": 13660.6632, "mape": 1.8985, "mase": 0.6981 }, { "h": 9, "n": 24, "mae": 13722.9763, "mape": 1.9097, "mase": 0.7024 }, { "h": 10, "n": 24, "mae": 13302.4251, "mape": 1.8461, "mase": 0.6783 }, { "h": 11, "n": 24, "mae": 13271.4979, "mape": 1.8411, "mase": 0.6779 }, { "h": 12, "n": 24, "mae": 13560.9239, "mape": 1.8718, "mase": 0.6919 } ] } }, "ranking": [ "snaive_drift", "holt", "loglinear", "snaive", "drift", "naive" ], "champion": "snaive_drift", "coverage": { "nominal": 0.8, "k": 237, "n": 288, "rate": 0.8229, "wilson95": [ 0.7747, 0.8627 ], "min_pool_size": 90, "by_h": [ { "h": 1, "k": 20, "n": 24, "rate": 0.8333, "wilson95": [ 0.6415, 0.9332 ] }, { "h": 2, "k": 20, "n": 24, "rate": 0.8333, "wilson95": [ 0.6415, 0.9332 ] }, { "h": 3, "k": 20, "n": 24, "rate": 0.8333, "wilson95": [ 0.6415, 0.9332 ] }, { "h": 4, "k": 19, "n": 24, "rate": 0.7917, "wilson95": [ 0.5953, 0.9076 ] }, { "h": 5, "k": 19, "n": 24, "rate": 0.7917, "wilson95": [ 0.5953, 0.9076 ] }, { "h": 6, "k": 21, "n": 24, "rate": 0.875, "wilson95": [ 0.69, 0.9566 ] }, { "h": 7, "k": 21, "n": 24, "rate": 0.875, "wilson95": [ 0.69, 0.9566 ] }, { "h": 8, "k": 20, "n": 24, "rate": 0.8333, "wilson95": [ 0.6415, 0.9332 ] }, { "h": 9, "k": 19, "n": 24, "rate": 0.7917, "wilson95": [ 0.5953, 0.9076 ] }, { "h": 10, "k": 19, "n": 24, "rate": 0.7917, "wilson95": [ 0.5953, 0.9076 ] }, { "h": 11, "k": 19, "n": 24, "rate": 0.7917, "wilson95": [ 0.5953, 0.9076 ] }, { "h": 12, "k": 20, "n": 24, "rate": 0.8333, "wilson95": [ 0.6415, 0.9332 ] } ], "judgeable": true, "independence_note": "forecasts from neighbouring origins overlap in time, so the Wilson interval is optimistic; cluster95 resamples whole target months instead", "cluster95": { "lo": 0.6834, "hi": 0.9379, "reps": 10000, "seed": 20260923, "target_months": 35, "target_months_with_misses": 8, "method": "bootstrap over target months: every forecast of the same month is resampled together (10000 draws, seed 20260923, 2.5th to 97.5th percentile)" } }, "realtime_selection": { "method": "at each scored origin, the method with the lowest MASE on the errors known by then (earlier forecasts whose target month was already observed, from 2012-01 on) is used for that origin's 12 forecasts; ties go to the first method id", "picks": [ { "origin": "2023-09", "model": "loglinear" }, { "origin": "2023-10", "model": "loglinear" }, { "origin": "2023-11", "model": "loglinear" }, { "origin": "2023-12", "model": "loglinear" }, { "origin": "2024-01", "model": "loglinear" }, { "origin": "2024-02", "model": "loglinear" }, { "origin": "2024-03", "model": "loglinear" }, { "origin": "2024-04", "model": "loglinear" }, { "origin": "2024-05", "model": "snaive_drift" }, { "origin": "2024-06", "model": "snaive_drift" }, { "origin": "2024-07", "model": "snaive_drift" }, { "origin": "2024-08", "model": "snaive_drift" }, { "origin": "2024-09", "model": "snaive_drift" }, { "origin": "2024-10", "model": "snaive_drift" }, { "origin": "2024-11", "model": "snaive_drift" }, { "origin": "2024-12", "model": "snaive_drift" }, { "origin": "2025-01", "model": "snaive_drift" }, { "origin": "2025-02", "model": "snaive_drift" }, { "origin": "2025-03", "model": "snaive_drift" }, { "origin": "2025-04", "model": "snaive_drift" }, { "origin": "2025-05", "model": "snaive_drift" }, { "origin": "2025-06", "model": "snaive_drift" }, { "origin": "2025-07", "model": "snaive_drift" }, { "origin": "2025-08", "model": "snaive_drift" } ], "times_picked": { "loglinear": 8, "snaive_drift": 16 }, "n": 288, "mape": 1.5102, "fixed_champion": "snaive_drift", "fixed_champion_mape": 1.2749, "selection_effect_pp": 0.2353 }, "gate": { "verdict": "RECOMMEND", "reason": "champion chosen out of sample; its 80% band has not been shown to be off", "champion_beats_seasonal_naive": true, "champion_beats_naive": true, "coverage_in_range": true, "coverage_range": [ 0.65, 0.95 ], "champion_is_baseline": true }, "origins": [ { "origin": "2023-09", "months": [ "2023-10", "2023-11", "2023-12", "2024-01", "2024-02", "2024-03", "2024-04", "2024-05", "2024-06", "2024-07", "2024-08", "2024-09" ], "actual": [ 685078.0, 694957.0, 751657.0, 622927.0, 631639.0, 693859.0, 686711.0, 730332.0, 688151.0, 713406.0, 720251.0, 670818.0 ], "forecasts": { "naive": [ 669120.0, 669120.0, 669120.0, 669120.0, 669120.0, 669120.0, 669120.0, 669120.0, 669120.0, 669120.0, 669120.0, 669120.0 ], "snaive": [ 665357.0, 666992.0, 722313.0, 616100.0, 595432.0, 679701.0, 661990.0, 708199.0, 688753.0, 683349.0, 705135.0, 669120.0 ], "drift": [ 671476.3, 673840.8, 676213.7, 678594.9, 680984.5, 683382.6, 685789.1, 688204.0, 690627.5, 693059.5, 695500.0, 697949.2 ], "snaive_drift": [ 694221.3, 695927.2, 753648.1, 642827.4, 621262.8, 709187.6, 690708.2, 738921.8, 718632.2, 712993.8, 735724.9, 698147.5 ], "holt": [ 680589.1, 694089.3, 782186.3, 627307.0, 621547.6, 709686.2, 692202.6, 731901.5, 706140.4, 707604.7, 723843.4, 675750.1 ], "loglinear": [ 686800.1, 699316.5, 779381.6, 632137.0, 623759.2, 720925.2, 705475.4, 749564.4, 725072.7, 729830.9, 742950.2, 698843.2 ] }, "champion_lo80": [ 674920.8, 676521.5, 732596.9, 624799.4, 603815.4, 689201.1, 671174.6, 717918.1, 698123.5, 692505.6, 714952.4, 678403.4 ], "champion_hi80": [ 709102.3, 708455.7, 766964.4, 652991.4, 629458.5, 718715.7, 700070.1, 747738.1, 727350.3, 721767.8, 744976.0, 707218.9 ] }, { "origin": "2023-10", "months": [ "2023-11", "2023-12", "2024-01", "2024-02", "2024-03", "2024-04", "2024-05", "2024-06", "2024-07", "2024-08", "2024-09", "2024-10" ], "actual": [ 694957.0, 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"trend": 696208.7, "seasonal_pct": 1.01, "remainder_pct": -2.146, "census_seasonal_pct": -0.621, "in_covid_window": false }, { "month": "2024-07", "observed": 713406.0, "trend": 698969.8, "seasonal_pct": 1.77, "remainder_pct": 0.291, "census_seasonal_pct": 2.085, "in_covid_window": false }, { "month": "2024-08", "observed": 720251.0, "trend": 700370.3, "seasonal_pct": 3.254, "remainder_pct": -0.403, "census_seasonal_pct": 3.33, "in_covid_window": false }, { "month": "2024-09", "observed": 670818.0, "trend": 701687.2, "seasonal_pct": -3.341, "remainder_pct": -1.094, "census_seasonal_pct": -4.585, "in_covid_window": false }, { "month": "2024-10", "observed": 718256.0, "trend": 704530.6, "seasonal_pct": 0.011, "remainder_pct": 1.937, "census_seasonal_pct": 1.407, "in_covid_window": false }, { "month": "2024-11", "observed": 722947.0, "trend": 706928.2, "seasonal_pct": 1.018, "remainder_pct": 1.235, "census_seasonal_pct": 1.558, "in_covid_window": false }, { "month": "2024-12", "observed": 786673.0, "trend": 709041.2, "seasonal_pct": 11.98, "remainder_pct": -0.921, "census_seasonal_pct": 9.677, "in_covid_window": false }, { "month": "2025-01", "observed": 654511.0, "trend": 711552.4, "seasonal_pct": -9.21, "remainder_pct": 1.315, "census_seasonal_pct": -7.979, "in_covid_window": false }, { "month": "2025-02", "observed": 630744.0, "trend": 713877.8, "seasonal_pct": -10.941, "remainder_pct": -0.791, "census_seasonal_pct": -11.359, "in_covid_window": false }, { "month": "2025-03", "observed": 726888.0, "trend": 716517.3, "seasonal_pct": 1.772, "remainder_pct": -0.319, "census_seasonal_pct": 0.491, "in_covid_window": false }, { "month": "2025-04", "observed": 722319.0, "trend": 719164.7, "seasonal_pct": -0.481, "remainder_pct": 0.924, "census_seasonal_pct": -0.017, "in_covid_window": false }, { "month": "2025-05", "observed": 753313.0, "trend": 720743.9, "seasonal_pct": 5.204, "remainder_pct": -0.651, "census_seasonal_pct": 5.43, "in_covid_window": false }, { "month": "2025-06", "observed": 716698.0, "trend": 722419.3, "seasonal_pct": 1.01, "remainder_pct": -1.784, "census_seasonal_pct": -0.387, "in_covid_window": false }, { "month": "2025-07", "observed": 745651.0, "trend": 724438.9, "seasonal_pct": 1.77, "remainder_pct": 1.138, "census_seasonal_pct": 2.448, "in_covid_window": false }, { "month": "2025-08", "observed": 745232.0, "trend": 726533.2, "seasonal_pct": 3.254, "remainder_pct": -0.659, "census_seasonal_pct": 2.081, "in_covid_window": false }, { "month": "2025-09", "observed": 708379.0, "trend": 729123.8, "seasonal_pct": -3.341, "remainder_pct": 0.513, "census_seasonal_pct": -3.252, "in_covid_window": false }, { "month": "2025-10", "observed": 743117.0, "trend": 731901.9, "seasonal_pct": 0.011, "remainder_pct": 1.522, "census_seasonal_pct": 1.651, "in_covid_window": false }, { "month": "2025-11", "observed": 736533.0, "trend": 734974.0, "seasonal_pct": 1.018, "remainder_pct": -0.798, "census_seasonal_pct": 0.247, "in_covid_window": false }, { "month": "2025-12", "observed": 816411.0, "trend": 739134.0, "seasonal_pct": 11.98, "remainder_pct": -1.362, "census_seasonal_pct": 11.119, "in_covid_window": false }, { "month": "2026-01", "observed": 674374.0, "trend": 743182.0, "seasonal_pct": -9.21, "remainder_pct": -0.053, "census_seasonal_pct": -8.186, "in_covid_window": false }, { "month": "2026-02", "observed": 656082.0, "trend": 746369.4, "seasonal_pct": -10.941, "remainder_pct": -1.298, "census_seasonal_pct": -11.493, "in_covid_window": false }, { "month": "2026-03", "observed": 761135.0, "trend": null, "seasonal_pct": 1.772, "remainder_pct": null, "census_seasonal_pct": 0.945, "in_covid_window": false }, { "month": "2026-04", "observed": 755742.0, "trend": null, "seasonal_pct": -0.481, "remainder_pct": null, "census_seasonal_pct": -0.442, "in_covid_window": false }, { "month": "2026-05", "observed": 796140.0, "trend": null, "seasonal_pct": 5.204, "remainder_pct": null, "census_seasonal_pct": 3.909, "in_covid_window": false }, { "month": "2026-06", "observed": 776516.0, "trend": null, "seasonal_pct": 1.01, "remainder_pct": null, "census_seasonal_pct": 1.032, "in_covid_window": false }, { "month": "2026-07", "observed": 784603.0, "trend": null, "seasonal_pct": 1.77, "remainder_pct": null, "census_seasonal_pct": 2.635, "in_covid_window": false }, { "month": "2026-08", "observed": 784846.0, "trend": null, "seasonal_pct": 3.254, "remainder_pct": null, "census_seasonal_pct": 1.408, "in_covid_window": false } ] }, "erratum_v1": { "sa_median_monthly_move_pct": 0.6089000075807816, "sa_cliff_limit_pct": 1.837845374848479, "series": "RSAFS", "fit_start": "2012-01", "fit_end": "2026-08", "n_fit_months": 176, "in_sample_mape": 4.949108022268338, "last_actual": { "month": "2026-08", "value": 773947.0 }, "first_forecast": { "month": "2026-09", "value": 743520.6238095221 }, "first_step_pct": -3.931325554653986, "twelfth_forecast": { "month": "2027-08", "value": 770579.836825395 }, "holdouts": [ { "first": "2025-09", "last": "2026-08", "v1_mape": 4.49710754445182, "naive_mape": 2.5625646802269215, "snaive_mape": 4.3538942310677875 }, { "first": "2024-09", "last": "2025-08", "v1_mape": 5.41456274712844, "naive_mape": 2.7380121361710437, "snaive_mape": 3.850260604225798 } ] }, "kpis": { "month": "2026-08", "sa_value": 773947.0, "sa_mom_pct": 1.2407418550562266, "sa_yoy_pct": 6.014763635267806, "nsa_value": 784846.0, "nsa_yoy_pct": 5.315660089743868 }, "display": { "series_label": "U.S. retail trade and food services", "data_first_month": "Jan 1992", "data_last_month": "Aug 2026", "data_span": "34 years 8 months", "data_n_months": "416", "covid_window": "Mar 2020 to Jun 2021", "backtest_origins": "24", "backtest_first_origin": "Sep 2023", "backtest_last_origin": "Aug 2025", "backtest_forecasts": "288", "champion_name": "Seasonal naive with drift", "champion_kind": "baseline", "champion_mape": "1.27%", "champion_mase": "0.45", "gate_verdict": "RECOMMEND", "gate_reason": "champion chosen out of sample; its 80% band has not been shown to be off", "coverage_k_of_n": "237 of 288", "coverage_pct": "82.3%", "coverage_ci": "77.5% to 86.3%", "coverage_ci_cluster": "68.3% to 93.8%", "coverage_miss_months": "8 of 35", "realtime_selection_mape": "1.51%", "selection_effect": "0.24 points", "forecast_first_month": "Sep 2026", "forecast_last_month": "Aug 2027", "forecast_first_value": "$738.8B", "forecast_first_lo80": "$718.2B", "forecast_first_hi80": "$751.9B", "forecast_last_value": "$818.5B", "forecast_last_lo80": "$795.1B", "forecast_last_hi80": "$829.0B", "first_step_nsa": "-5.9%", "first_step_sa": "+0.55%", "seasonal_peak": "Dec +12.0%", "seasonal_trough": "Feb -10.9%", "seasonal_max_gap_vs_census": "0.5 pp", "kpi_month": "Aug 2026", "kpi_sa_value": "$773.9B", "kpi_sa_mom": "+1.24%", "kpi_sa_yoy": "+6.01%", "kpi_nsa_value": "$784.8B", "kpi_nsa_yoy": "+5.32%", "v1_in_sample_mape": "4.95%", "v1_fit_months": "176", "v1_fit_span": "14 years 8 months", "v1_first_step": "-3.93%", "v1_last_actual": "$773.9B", "v1_first_forecast": "$743.5B", "v1_sa_typical_move": "0.61%", "mape_naive": "6.35%", "mase_naive": "2.30", "mape_snaive": "3.48%", "mase_snaive": "1.28", "mape_drift": "6.00%", "mase_drift": "2.15", "mape_snaive_drift": "1.27%", "mase_snaive_drift": "0.45", "mape_holt": "1.65%", "mase_holt": "0.60", "mape_loglinear": "1.81%", "mase_loglinear": "0.66", "v1_holdout_recent_window": "Sep 2025 to Aug 2026", "v1_holdout_recent_mape": "4.50%", "v1_holdout_recent_naive_mape": "2.56%", "v1_holdout_recent_snaive_mape": "4.35%", "v1_holdout_prior_window": "Sep 2024 to Aug 2025", "v1_holdout_prior_mape": "5.41%", "v1_holdout_prior_naive_mape": "2.74%", "v1_holdout_prior_snaive_mape": "3.85%" }, "method": [ "Data: FRED series RSAFSNA (U.S. retail trade and food services, not seasonally adjusted, millions of dollars), 416 monthly values from Jan 1992 to Aug 2026.", "Pandemic months (Mar 2020 to Jun 2021) are treated as missing whenever a model estimates anything: averages skip changes that touch them, the log-linear fit leaves them out, and the Holt smoother carries its state across them and restarts its level on the first month after. No scored forecast starts from, looks back into, or lands in that window.", "Six methods, all on the log of sales and all refit at every origin using only the data available at that point: naive, seasonal naive, drift, seasonal naive with drift, damped Holt and a log-linear trend plus month effects.", "Rolling-origin backtest: 24 origins (Sep 2023 to Aug 2025), each forecasting 1 to 12 months ahead, so 288 forecasts per method, each compared with what was later reported. Methods are ranked by MASE (error relative to a seasonal-naive yardstick); MAPE is shown beside it.", "A simple baseline won: Seasonal naive with drift beat both fitted models out of sample, so the forecast below uses it. It scored MAPE 1.27% (MASE 0.45), against seasonal naive 3.48% and naive 6.35%. The best fitted model, Damped Holt (log, deseasonalised), scored 1.65%.", "The 80% band comes from the champion's own past errors at the same horizon: the 10th and 90th percentiles of its log errors on every checkable forecast since Jan 2012, pandemic-touching ones excluded. It is not an in-sample standard error. Checked the same way in the backtest (each band built only from errors known at the time), it held 237 of 288 times (82.3%; 95% interval 77.5% to 86.3%).", "Seasonal decomposition: classical decomposition on logs (2x12 centred moving-average trend; seasonal factor = mean detrended value of each calendar month over its last 10 clean years; factors normalised to average zero on the log scale). The strongest month is Dec +12.0% and the weakest is Feb -10.9% against trend; the largest gap to the factors implied by Census's own adjustment (RSAFSNA / RSAFS) is 0.5 pp." ], "limits": [ "The backtest uses today's revised history. A planner at each origin saw the advance estimates, which Census later revises, so real-world accuracy at the time would likely have been somewhat worse.", "Trading-day and holiday effects (how many weekends a month has, when Easter falls) are not modelled; Census's seasonal adjustment accounts for them.", "Values are nominal dollars, not adjusted for inflation.", "The 24 scored origins cover one period (Sep 2023 to Aug 2025). The 288 scored forecasts overlap in time, so they are not independent: the band's misses fall in 8 of 35 target months, and resampling whole target months puts the coverage at about 68.3% to 93.8%, wider than the Wilson interval (77.5% to 86.3%).", "The champion was picked on these same origins, which flatters it: re-picked at each origin from only the errors known by then, the forecasts scored MAPE 1.51%, against 1.27% for the champion chosen on all 24 origins at once.", "The point forecast is the exponential of a log forecast, so it sits near the median rather than the mean.", "Built from a one-off download recorded in data/fred/SOURCES.json; nothing refreshes it on a schedule. Not investment advice." ], "erratum_text": [ "Correction to v1 of this page: it described FRED series RSAFS as retail sales excluding food services, not seasonally adjusted. RSAFS is retail trade and food services, seasonally adjusted, so v1's month effects were fitted to a series that had already had its seasonality removed.", "v1 fitted a straight-line trend plus month effects to dollar levels over 176 months (14 years 8 months). The 4.95% error it showed was measured on the same months it was fitted to. Re-run as a forecast on the two most recent 12-month holdouts, it missed by 4.50% (Sep 2025 to Aug 2026) and 5.41% (Sep 2024 to Aug 2025), against 2.56% and 2.74% for simply repeating the last value, so it lost to the naive baseline both times.", "Its first forecast month ($743.5B) sat -3.93% away from the last actual ($773.9B). The seasonally adjusted series typically moves 0.61% a month (median over the last 10 years), so that first step was a cliff, more than three typical months in one. The Forecast Lab replaces it." ], "reproduce": { "commands": [ "python tools/fetch_fred.py", "python build_forecast.py", "python build_forecast.py --check" ], "inputs": [ { "path": "data/fred/RSAFSNA.csv", "sha256": "2bbe15d2fc830b6bd4f69184734d4373a6d94ec3840a7621570e43e221a8a4bf" }, { "path": "data/fred/RSAFS.csv", "sha256": "c57685eed78fe9d2c961e7ed540c88c2c0161bc356672f0ebf8cf2b83cb9ed88" } ] } }