Auto ARIMA

Auto ARIMA automatically selects the best ARIMA or SARIMA model by testing different combinations of (p,d,q) and seasonal (P,D,Q,m) parameters. It eliminates manual parameter tuning while finding models that balance fit and complexity.

When to Use Auto ARIMA

Auto ARIMA is best suited for:

• When you want ARIMA but don't want to manually tune parameters
• Univariate time series forecasting with or without seasonality
• Automated forecasting pipelines requiring minimal human intervention
• Exploring what ARIMA configuration works best for your data
• When you need statistically rigorous forecasts with confidence intervals
• Quick model development without domain expertise in ARIMA

Strengths

• Eliminates manual parameter tuning
• Tests many model configurations efficiently
• Uses information criteria (AIC/BIC) for model selection
• Can detect and model seasonality automatically
• Includes stationarity and unit root tests
• Provides ARIMA and SARIMA models
• Statistically principled model selection
• Good for production pipelines
• Works well with diverse time series types

Weaknesses

• Slower than fitting a single ARIMA model (searches over many models)
• Still limited to univariate forecasting
• Cannot incorporate exogenous variables (use pmdarima's auto_arima with exogenous if needed)
• May select overly complex models on noisy data
• Computational cost increases with large seasonal periods
• No guarantee of "best" model for out-of-sample forecasts
• Black box: less interpretable than manually selected models

Parameters

Common Time Series Parameters

All time series models share these parameters:

• Timestamp Column (required): Column containing dates/times
• Target Column (required): Numeric value to forecast
• Frequency (optional): Time spacing (D, H, W, M). Auto-inferred if not specified
• Forecast Steps (required, default=1): How many periods to predict

Auto ARIMA-Specific Parameters

Seasonal

• Type: Boolean
• Default: true
• Description: Whether to search for seasonal ARIMA models (SARIMA)
  • true: Searches both non-seasonal and seasonal models
  • false: Only searches non-seasonal ARIMA models
• Guidance:
  • Set to true if your data has seasonality
  • Set to false for non-seasonal data or when seasonality is pre-removed

Seasonal Period (m)

• Type: Integer
• Default: 12
• Description: Number of periods in a seasonal cycle (only used if seasonal=true)
• Common Values:
  • 7 for weekly seasonality in daily data
  • 12 for yearly seasonality in monthly data
  • 24 for daily seasonality in hourly data
  • 4 for yearly seasonality in quarterly data
• Important: Must match your data's seasonal pattern

Stepwise Search

• Type: Boolean
• Default: true
• Description: Search strategy
  • true: Stepwise algorithm (faster, explores promising areas)
  • false: Exhaustive grid search (slower, guaranteed to find best in search space)
• Guidance:
  • Use true for faster results (recommended)
  • Use false if you have time and want exhaustive search

Show Progress (Trace)

• Type: Boolean
• Default: false
• Description: Whether to print search progress and model comparisons
  • true: Shows each model tested and its AIC score
  • false: Silent mode
• Guidance: Set to true for debugging or understanding model selection

Configuration Tips

Quick Start Configuration

For most cases, use these settings:

seasonal=true
m=[your seasonal period]
stepwise=true
trace=false

Auto ARIMA will handle the rest.

Choosing Seasonal Period (m)

Match m to your data's repeating pattern:

• Daily data with weekly patterns: m=7
• Hourly data with daily patterns: m=24
• Monthly data with yearly patterns: m=12
• Quarterly data: m=4

Stepwise vs Exhaustive Search

Stepwise (stepwise=true):

• Faster (minutes vs hours)
• Intelligent search based on information criteria
• May miss global optimum but finds good models
• Recommended for most use cases

Exhaustive (stepwise=false):

• Tests all combinations in parameter space
• Guaranteed to find best model within bounds
• Very slow for large seasonal periods (m > 24)
• Use when you have time and need the absolute best

Understanding the Search Process

Auto ARIMA:

1. Tests for stationarity (unit root tests)
2. Determines d and D (differencing orders)
3. Searches over p, q (non-seasonal AR, MA)
4. Searches over P, Q (seasonal AR, MA)
5. Selects model with lowest AIC (or BIC)

Handling Large Seasonal Periods

For m > 24 (e.g., hourly data with weekly seasonality, m=168):

• Consider aggregating to lower frequency (hourly → daily)
• Use stepwise=true (exhaustive will be extremely slow)
• Or use Prophet/TBATS which handle large m more efficiently

When to Disable Seasonal Search

Set seasonal=false if:

• Your data has no seasonality (e.g., stock returns)
• Seasonality already removed via preprocessing
• Seasonal period is very large (m > 52)

Common Issues and Solutions

Issue: Search Takes Too Long

Solution:

• Ensure stepwise=true (not exhaustive)
• Reduce seasonal period by aggregating data (hourly → daily)
• Set seasonal=false if seasonality isn't critical
• Consider using simpler models like Theta or Exponential Smoothing
• Reduce the max search space (if configurable in your implementation)

Issue: Selected Model Has Poor Out-of-Sample Performance

Solution:

• Auto ARIMA optimizes in-sample AIC, which may overfit
• Use time series cross-validation to validate
• Try constraining search space (e.g., max p=3, q=3)
• Compare with simpler models (Theta, Exponential Smoothing)
• Ensure sufficient data for model complexity

Issue: Model Selection Unstable (Changes with Small Data Updates)

Solution:

• This is expected with borderline AIC differences
• Consider averaging forecasts from top models
• Use a simpler, manually selected ARIMA model for stability
• Increase data history if possible

Issue: Need External Variables (Promotions, Weather, etc.)

Solution:

• Standard Auto ARIMA doesn't support exogenous variables
• Some implementations (e.g., pmdarima) support exogenous regressors
• Alternatively, use SARIMAX with manual parameter selection
• Or use Prophet with additional regressors

Issue: Seasonal Period Unclear

Solution:

• Plot your data and look for repeating patterns
• Use autocorrelation plots (ACF) to identify lags with high correlation
• Try multiple seasonal periods and compare performance
• Use Prophet which auto-detects multiple seasonalities

Issue: Selected Model Is Too Complex

Solution:

• AIC may favor complex models on some data
• Manually specify simpler models (ARIMA(1,1,1) or SARIMA(1,1,1)(1,1,1)s)
• Use BIC instead of AIC if your implementation allows (BIC penalizes complexity more)
• Compare forecast performance vs simpler baselines

Issue: No Suitable Model Found

Solution:

• Your data may not be suitable for ARIMA
• Check for structural breaks or outliers
• Try preprocessing (outlier removal, log transformation)
• Consider non-linear models (Prophet, XGBoost)

Example Use Cases

Daily Retail Sales (Weekly Seasonality)

seasonal=true
m=7
stepwise=true

Finds best SARIMA model for day-of-week patterns.

Monthly Revenue (Yearly Seasonality)

seasonal=true
m=12
stepwise=true

Discovers optimal monthly model with yearly cycle.

Hourly Energy Consumption (Daily Cycle)

seasonal=true
m=24
stepwise=true
trace=true  # see search progress

Identifies best model for intraday patterns.

Stock Prices (No Seasonality)

seasonal=false
stepwise=true

Finds best non-seasonal ARIMA (likely random walk).

Weekly Website Traffic

seasonal=true
m=52
stepwise=true

Warning: m=52 is large; consider aggregating to monthly (m=12).

Comparison with Other Models

vs Manual ARIMA:

• Auto ARIMA: Automatic, no expertise needed, explores many models
• Manual ARIMA: Faster if you know parameters, more interpretable

vs SARIMA:

• Auto ARIMA: Automatically finds SARIMA parameters
• SARIMA: Requires manual specification of (p,d,q)(P,D,Q,s)

vs Prophet:

• Auto ARIMA: Univariate, no exogenous variables, statistical
• Prophet: Multiple seasonalities, external regressors, more flexible

vs Theta Method:

• Auto ARIMA: More complex, potentially better fit
• Theta Method: Much faster, simpler baseline

vs XGBoost/LightGBM:

• Auto ARIMA: Statistical model, confidence intervals, works with less data
• XGBoost: Non-linear, handles many features, needs more data

Technical Details

Model Selection Criteria

Auto ARIMA typically uses AIC (Akaike Information Criterion):

• AIC = -2 × log(likelihood) + 2 × (number of parameters)
• Lower AIC is better
• Balances fit (likelihood) and simplicity (parameters)

Some implementations offer BIC (Bayesian Information Criterion):

• BIC penalizes complexity more than AIC
• Tends to select simpler models

Search Bounds

Typical default search spaces:

• p: 0 to 5
• d: 0 to 2
• q: 0 to 5
• P: 0 to 2
• D: 0 to 1
• Q: 0 to 2

Stationarity Tests

Auto ARIMA performs unit root tests (e.g., KPSS, ADF) to determine d and D automatically.

Practical Recommendations

1. Start with Auto ARIMA to understand what works for your data
2. Examine the selected model: Note the (p,d,q)(P,D,Q)m parameters
3. Validate: Use time series cross-validation
4. Compare: Benchmark against simpler models (Theta, Exponential Smoothing)
5. Productionize: Consider fixing the selected model for stability

Auto ARIMA is excellent for exploration and baseline forecasts, but manual tuning or alternative models may outperform in production.