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Choosing the Right Forecasting Model

Understand the strengths and weaknesses of different models to choose the best one for your data.

Model Categories​

AnoFox Forecast provides 31 models across 4 categories:

Category 1: Naïve & Baseline Models​

Simple, fast models that establish minimum accuracy baseline.

ModelBest ForSpeedSeasonality
NaiveTesting, baselines⚡ Very Fast❌ No
SeasonalNaiveStrongly seasonal data⚡ Very Fast✅ Yes
SeasonalWindowAverageSimple seasonal⚡ Very Fast✅ Yes
RandomWalkDriftTrending data⚡ Very Fast❌ No
SMA (Simple Moving Average)Smooth trends⚡ Very Fast❌ No

When to use: Starting point, comparison baseline

Category 2: Statistical Models​

Traditional time-series models backed by mathematical theory.

ModelBest ForSpeedSeasonality
ETSTrending + seasonal⚡ Fast✅ Yes
AutoETSAutomatic selection🟢 Medium✅ Yes
Holt-WintersClear trend + seasonality🟢 Medium✅ Yes
ARIMAComplex patterns🟢 Medium✅ Yes
AutoARIMAAuto parameter tuning🟡 Slow✅ Yes
ThetaShort-term forecasts⚡ Fast✅ Yes
GARCHVolatility modeling🟡 Slow❌ No
SESSimple data⚡ Fast❌ No

When to use: Well-structured data with clear patterns

Category 3: Advanced Models​

Specialized models for complex patterns.

ModelBest ForSpeedSeasonality
TBATSMultiple seasonality🟡 Slow✅ Multiple
MSTLVery complex seasonality🟡 Slow✅ Multiple
MFLESMessy real-world data🟢 Medium✅ Yes
DTWSimilarity-based🟡 Slow✅ Yes

When to use: Complex patterns, multiple seasonal patterns

Category 4: Intermittent Demand​

For sparse, irregular data (many zeros or gaps).

ModelBest ForSpeedSeasonality
CrostonIntermittent demand⚡ Fast✅ Yes
CrostonOptimizedOptimized Croston🟢 Medium✅ Yes
CrostonSBASyntetos-Boylan adjusted🟢 Medium✅ Yes
ADIDADemand spikes🟢 Medium✅ Yes
IMAPAIntermittent + multiple🟡 Slow✅ Yes
TSBAggregate demand🟢 Medium✅ Yes

When to use: Sparse demand, e-commerce, inventory forecasting

Decision Tree: Which Model Should I Use?​

START: Need a forecast

├─ Do I have lots of missing data or sparse demand?
│  ├─ YES → Use Croston or ADIDA
│  └─ NO ↓
│
├─ How much data do I have?
│  ├─ < 2 months → Use Naive, Theta, or SeasonalNaive
│  ├─ 2-12 months → Use ETS, ARIMA, or Theta
│  └─ > 12 months ↓
│
├─ How many seasonal patterns?
│  ├─ None → Use AutoARIMA or ETS
│  ├─ One (weekly/yearly) → Use AutoETS or ARIMA
│  └─ Multiple (hourly+daily+yearly) → Use TBATS or MSTL
│
├─ How clean is your data?
│  ├─ Lots of outliers → Use MFLES
│  ├─ Clean data → Use AutoETS or AutoARIMA
│  └─ Very complex patterns ↓
│
└─ Want to keep it simple?
   ├─ YES → Use Theta or AutoETS
   └─ NO → Use TBATS or MFLES

Model Comparison Matrix​

Quick reference for comparing models:

                     | Seasonality | Trend | Outliers | Speed   | Complexity
---------------------|-------------|-------|----------|---------|----------
Naive                | ❌          | ❌    | ❌       | ⚡⚡⚡  | ⭐
SeasonalNaive        | ✅          | ❌    | ❌       | ⚡⚡⚡  | ⭐
SimpleMA             | ❌          | ✅    | ⭐⭐    | ⚡⚡⚡  | ⭐⭐
ETS                  | ✅          | ✅    | ⭐      | ⚡⚡   | ⭐⭐⭐
AutoETS              | ✅          | ✅    | ⭐      | ⚡⚡   | ⭐⭐⭐
Theta                | ✅          | ✅    | ⭐      | ⚡⚡   | ⭐⭐
ARIMA                | ✅          | ✅    | ⭐      | 🟢     | ⭐⭐⭐⭐
AutoARIMA            | ✅          | ✅    | ⭐      | 🟡     | ⭐⭐⭐⭐
Holt-Winters         | ✅          | ✅    | ⭐      | 🟢     | ⭐⭐⭐
TBATS                | ✅✅        | ✅    | ⭐      | 🟡     | ⭐⭐⭐⭐⭐
MSTL                 | ✅✅        | ✅    | ⭐      | 🟡     | ⭐⭐⭐⭐⭐
MFLES                | ✅          | ✅    | ✅✅    | 🟢     | ⭐⭐⭐⭐
Croston              | ✅          | ❌    | ⭐      | ⚡⚡   | ⭐⭐
ADIDA                | ✅          | ⭐    | ✅      | 🟢     | ⭐⭐⭐

Legend:
✅ Handles well  | ⭐ Moderate  | ✅✅ Excellent | ❌ Poor
⚡⚡⚡ Very fast  | ⚡⚡ Fast  | 🟢 Medium  | 🟡 Slow

Model Descriptions & Use Cases​

1. Naive (Baseline)​

Forecast = last observation

Today: Jan 15, sales = 100
Forecast for Jan 16: 100

Use when:

  • You need a quick baseline
  • Data is highly random
  • Want to compare other models against

Pros: ⚡ Instant, simple Cons: ❌ Ignores trends, seasonality

2. Seasonal Naive​

Forecast = same period last year

Sales last Jan 15: 100
Forecast for Jan 15 this year: 100

Use when:

  • Data has strong seasonality
  • You want a simple seasonal benchmark
  • Data is stable year-over-year

Pros: ⚡ Fast, captures seasonality Cons: ❌ Ignores trends

3. ETS (Error, Trend, Seasonality)​

Exponential smoothing state-space model

Forecast = Smoothed trend + Smoothed seasonal + Error

Use when:

  • Data has trend and/or seasonality
  • Data is relatively clean
  • You want good default performance

Pros: 🟢 Good accuracy, handles seasonality, fast Cons: ❌ Can overfit to noise

4. AutoETS​

ETS with automatic parameter selection

Automatically chooses:
- Which components (trend/seasonal)
- How much smoothing
- Initial values

Use when:

  • You're unsure about data structure
  • Want automation without tuning
  • Data has clear trends/seasonality

Pros: ✅ Automatic, reliable, accurate Cons: 🟡 Slightly slower

5. ARIMA (AutoRegressive Integrated Moving Average)​

Uses past values to predict future

Forecast = f(past values) + f(past errors)

Parameters: (p, d, q)

  • p = AutoRegressive (past values)
  • d = Integrated (differencing)
  • q = Moving Average (past errors)

Use when:

  • Data has trends needing differencing
  • Complex relationships between past values
  • Data has seasonality (use SARIMA)

Pros: ✅ Flexible, mathematically sound Cons: 🟡 Slow, requires tuning

6. AutoARIMA​

ARIMA with automatic parameter selection

Automatically finds best (p,d,q) and (P,D,Q,s)

Use when:

  • You want ARIMA without parameter tuning
  • Data has complex patterns
  • You have time for slower training

Pros: ✅ Comprehensive, automatic Cons: 🟡🟡 Slow, can be overkill

7. Theta​

Simple trend + seasonal decomposition

Forecast = Theta-line 1 + Theta-line 2

Use when:

  • You want simplicity
  • Short-term forecasting (< 8 periods)
  • Data has trend and seasonality

Pros: ⚡ Fast, good for short-term, interpretable Cons: ❌ Poor for long horizons

8. TBATS (Trigonometric, Box-Cox, ARMA, Trend, Seasonality)​

Handles multiple seasonal patterns

Forecast = Trend component
         + Seasonal component 1 (hourly)
         + Seasonal component 2 (daily)
         + Seasonal component 3 (yearly)
         + Error correction

Use when:

  • Multiple overlapping seasonal patterns
  • Daily data with hourly + daily + yearly patterns
  • Complex business data (e-commerce, utilities)

Pros: ✅ Handles complexity, multiple seasonality Cons: 🟡 Slow, complex

9. MSTL (Multiple Seasonal and Trend decomposition using Loess)​

Advanced decomposition for multiple seasonality

Similar to TBATS but uses different method

Use when:

  • Very complex seasonal patterns
  • Multiple seasonal periods
  • Data with changing seasonality

Pros: ✅ Handles complexity, adaptive Cons: 🟡 Slow, requires enough data

10. MFLES (Median-based Feature-Logic-Expert System)​

Robust model combining statistical and feature-based approaches

Combines:
- Feature engineering
- Statistical methods
- Median-based robustness

Use when:

  • Real-world messy data with outliers
  • Inconsistent data quality
  • Multiple seasonal patterns
  • You need robustness

Pros: ✅ Robust, handles outliers, flexible Cons: 🟡 Medium speed, needs tuning

11. Croston (Intermittent Demand)​

Forecast non-zero occurrences separately from sizes

Forecast = P(non-zero) × Average size

Use when:

  • Sparse demand (many zeros)
  • Intermittent ordering patterns
  • Inventory forecasting

Pros: ⚡ Fast, handles sparse data Cons: ❌ Limited to specific domain

Matching Models to Your Data Characteristics​

High-Quality, Clean Data​

✅ Recommendation: AutoETS or Theta

  • Reason: Simple, fast, accurate on clean data

✅ Recommendation: AutoETS or ARIMA

  • Reason: Both capture trends well

Seasonal Data (Single Period)​

✅ Recommendation: AutoETS or Holt-Winters

  • Reason: Designed for this, fast, accurate

Multiple Seasonal Patterns​

✅ Recommendation: TBATS or MSTL

  • Reason: Specifically designed for this

Sparse/Intermittent Data​

✅ Recommendation: Croston or ADIDA

  • Reason: Designed for intermittent demand

Noisy/Outlier-Ridden Data​

✅ Recommendation: MFLES

  • Reason: Robust to outliers

Limited Data (< 30 observations)​

✅ Recommendation: SeasonalNaive or Theta

  • Reason: Simple models need less data

Very Long Data (1000+ observations)​

✅ Recommendation: ARIMA, TBATS, MSTL, MFLES

  • Reason: Complex models benefit from more data

Model Selection Strategy​

1. Start Simple​

-- Begin with SeasonalNaive as baseline
SELECT * FROM TS_FORECAST(..., 'SeasonalNaive', ...);

2. Try Automatic Models​

-- Then try AutoETS (good default)
SELECT * FROM TS_FORECAST(..., 'AutoETS', ...);

-- And AutoARIMA for comparison
SELECT * FROM TS_FORECAST(..., 'AutoARIMA', ...);

3. Add Domain Knowledge​

-- If data has multiple seasonality, try TBATS
SELECT * FROM TS_FORECAST(..., 'TBATS', ...);

-- If data is noisy, try MFLES
SELECT * FROM TS_FORECAST(..., 'MFLES', ...);

4. Compare and Evaluate​

-- Calculate accuracy for each model
-- Use TS_MAE, TS_RMSE, TS_MAPE
-- Choose the best performer

5. Deploy Winner​

-- Use the model with lowest error metrics
-- Monitor performance over time
-- Retrain regularly as data changes

Ensemble Approach​

Combine multiple models for better accuracy:

-- Forecast with 3 models
SELECT
    forecast_step,
    date_col,
    (f1.point_forecast + f2.point_forecast + f3.point_forecast) / 3
        AS ensemble_forecast
FROM (
    SELECT * FROM TS_FORECAST(..., 'AutoETS', ...)
) f1
JOIN (
    SELECT * FROM TS_FORECAST(..., 'AutoARIMA', ...)
) f2
    ON f1.forecast_step = f2.forecast_step
JOIN (
    SELECT * FROM TS_FORECAST(..., 'Theta', ...)
) f3
    ON f1.forecast_step = f3.forecast_step;

Common Mistakes in Model Selection​

❌ Using the Most Complex Model​

Problem: TBATS on simple weekly data = overfitting

Solution: Start simple, increase complexity as needed

❌ Not Considering Data Quality​

Problem: Using ARIMA on noisy data → Poor performance

Solution: Use MFLES or clean data first

❌ Ignoring Seasonality in Model Choice​

Problem: Using Naive on strongly seasonal data

Solution: Use SeasonalNaive or AutoETS

❌ Only Trying One Model​

Problem: Assuming first model tried is best

Solution: Always compare 3-5 models

❌ Not Evaluating on Real Test Data​

Problem: Choosing model based on training error

Solution: Always backtest on held-out test data

Quick Reference: When to Use Each Model​

| Data Characteristic | Recommended Model | Alternative |
|-------------------|------------------|-------------|
| Clean, trending | AutoETS | Theta |
| Seasonal (weekly) | AutoETS | Holt-Winters |
| Multiple seasonality | TBATS | MSTL |
| Noisy, outliers | MFLES | ETS |
| Sparse demand | Croston | ADIDA |
| Very simple | SeasonalNaive | Naive |
| Very complex | MSTL | TBATS |
| Limited data | Theta | SeasonalNaive |
| Production 24/7 | AutoETS | Theta |

Next Steps​

  1. Evaluate Forecast Accuracy — Measure model performance
  2. Model Comparison Guide — Practical comparison tutorial
  3. Forecasting Models Reference — All 31 models detailed

Key Takeaways​

  • ✅ 31 models in 4 categories for different situations
  • ✅ Start simple (SeasonalNaive, Theta, AutoETS)
  • ✅ Match model to data characteristics
  • ✅ Multiple seasonality → Use TBATS/MSTL
  • ✅ Sparse data → Use Croston/ADIDA
  • ✅ Noisy data → Use MFLES
  • ✅ Always compare multiple models
  • ✅ Evaluate on test data, not training data
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