# ============================================================================
# T20 — Benchmarking classical time-series forecasters on synthetic seasonal series
# ----------------------------------------------------------------------------
# Unlike paper_replication's P01-P07, the "synthesis" here frames a research
# QUESTION rather than a known paper's method. The model must design the
# experiment (conditions, metrics, datasets) — we only commit to what a
# competent study of this topic would include and what the rubric expects.
# ============================================================================

id: ML20
title: "Classical forecaster robustness on synthetic seasonal time series"
arxiv_id: null
venue: "ARC-Bench 2026"
paper_asset: null

# The "synthesis" plays the role of the upstream briefing: research question,
# background, why the question matters, what "a reasonable experiment" looks
# like. It deliberately does NOT pre-specify a single method to reproduce.
synthesis: |
  Classical univariate forecasting methods remain widely used because they are
  interpretable and lightweight, yet their comparative behavior can flip under
  different data-generating regimes. AR models often perform well when dynamics
  are mostly autoregressive and weakly seasonal; ARIMA can absorb trend and
  differencing structure; SARIMAX can explicitly represent seasonal lag effects;
  ETS captures error-trend-seasonal decomposition; and Theta is often a strong
  low-variance baseline. In small CPU-constrained settings, practitioners need
  practical guidance about which method is robust to changing signal-to-noise
  and seasonality strength.

  A synthetic benchmark is appropriate here because we can precisely control
  trend slope, seasonal amplitude, and observation noise while keeping compute
  modest. By generating multiple families of monthly-like series with known
  periodicity (e.g., period 12), we can evaluate whether model rankings are
  stable or regime-dependent. This avoids overfitting conclusions to one
  real-world dataset and enables direct stress testing under high-noise versus
  high-seasonality conditions.

  A credible study should compare at least four of {AR, ARIMA, SARIMAX, ETS,
  Theta} on 2–3 synthetic dataset families, using rolling-origin or holdout
  forecasts with a fixed horizon. It should report scale-robust error metrics
  (especially sMAPE), include at least one baseline (e.g., seasonal naive), and
  aggregate over multiple random seeds. The analysis should explicitly test
  whether one method is consistently best overall or whether the best choice
  depends on data regime.

  The key outcome is actionable selection logic: if seasonal structure is strong
  and noise is low, do seasonal/state-space methods dominate; and if noise is
  high, do simpler methods become competitive? These are concrete decisions an
  autonomous forecasting pipeline can apply when only limited data and CPU are
  available.

  *How do AR, ARIMA, SARIMAX, ETS, and Theta compare in sMAPE robustness across synthetic seasonal series with controlled trend, seasonality amplitude, and noise levels?*

hypotheses:
  - id: H1
    statement: "SARIMAX or ETS achieves the lowest mean sMAPE on at least 2 of 3 synthetic dataset families when seasonality amplitude is high (amplitude >= 8) and noise is low (sigma <= 1.0), averaged over >=5 seeds."
    measurable: true
  - id: H2
    statement: "Under high-noise settings (sigma >= 3.0), the sMAPE gap between the best advanced method (ARIMA/SARIMAX/ETS/Theta) and a seasonal_naive baseline is <= 5 percentage points on at least 2 of 3 dataset families."
    measurable: true
  - id: H3
    statement: "No single method among {AR, ARIMA, SARIMAX, ETS, Theta} ranks first in mean sMAPE on all evaluated dataset families, indicating regime-dependent winners."
    measurable: true

experiment_design:
  research_question: "Which classical forecasting method is most robust in sMAPE across controlled synthetic regimes of trend, seasonality amplitude, and noise?"
  conditions:
    - name: "ar_lag12"
      description: "Autoregressive model with lag order selected from {3,6,12} by AIC on training split."
    - name: "arima_auto_small"
      description: "Non-seasonal ARIMA with (p,d,q) searched over small grid p,q in [0,2], d in [0,1], selected by AIC."
    - name: "sarimax_seasonal12"
      description: "Seasonal ARIMA/SARIMAX with seasonal period 12 and small grid over (p,d,q)x(P,D,Q), selected by AIC."
    - name: "ets_additive"
      description: "Exponential smoothing with additive trend/seasonality (period 12), damped trend optional by AIC."
    - name: "theta"
      description: "ThetaModel forecast with default theta decomposition for univariate series."
  baselines:
    - "seasonal_naive (forecast y_t = y_{t-12}) as a simple seasonal baseline"
    - "naive_last (random walk) as a non-seasonal baseline"
  metrics:
    - name: "smape"
      direction: "minimize"
      description: "Symmetric Mean Absolute Percentage Error on forecast horizon, averaged over seeds and series instances."
    - name: "mae"
      direction: "minimize"
      description: "Mean Absolute Error on forecast horizon."
    - name: "fit_time_sec"
      direction: "minimize"
      description: "Per-method wall-clock fit+forecast runtime in seconds."
  datasets:
    - name: "syn_low_noise_high_season"
      source: "Synthetic monthly series: length 180, period 12, trend slope in [0.0,0.2], season amplitude in [8,12], gaussian noise sigma in [0.5,1.0]."
    - name: "syn_medium_noise_medium_season"
      source: "Synthetic monthly series: length 180, period 12, trend slope in [0.1,0.4], season amplitude in [4,8], gaussian noise sigma in [1.5,2.5]."
    - name: "syn_high_noise_low_season"
      source: "Synthetic monthly series: length 180, period 12, trend slope in [0.0,0.3], season amplitude in [1,4], gaussian noise sigma in [3.0,4.0]."
  compute_requirements:
    gpu_required: false
    estimated_wall_clock_sec: 720

rubric_path: "experiments/arc_bench/config/ml/rubrics/ML20.json"