Fit best SARIMA(X) model to univariate time series.

Returns best SARIMA(X) model according to either AIC, AICc, BIC, or HQC value. The function conducts a brute-force search over possible models within the order constraints provided.

The auto_arima has the following features:

• Support for seasonal ARIMA models with/without exogenous regressors
• GUI access through gretl menu
• Public convenience functions for result summarization and retrieving the gretl ARIMA command of the 'best' model.
• Source code is tested by means of unit-tests to minimize bugs.

Source code and test scripts: https://github.com/atecon/auto_arima

This package is an extension of gretl's built-in arima command for which the degrees of differencing in the command are not treated as subject to search:

https://gretl.sourceforge.net/gretl-help/cmdref.html#arima

Furthermore, the auto_arima package is also an alternative to the armax package written by Yi-Nung Yang which has some limitations, e.g. it does only work for ARMA type models.

Access via: Model -> Univariate time series -> Automatic ARIMA

Seasonality Settings:

If at least one of the following options is non-zero, the function will consider seasonal parameters:

• max_P: Maximum seasonal autoregressive order
• max_D: Maximum seasonal-differencing order
• max_Q: Maximum seasonal moving-average order

Non-seasonal ARIMA(X) considered if these seasonality parameters are zero or dataset is non-seasonal.

auto_arima (series y, list xlist, bundle opts)

Fit SARIMA(X) model to endogenous series y.

• y: series - Endogenous variable
• xlist: list - Exogenous variables (optional)
• opts: bundle - SARIMA parameters and options (see below)

Bundle containing model results and diagnostics. The bundle item error (int) is set to 1 if an error occurs, otherwise 0.

print_auto_arima_results (bundle model)

Print summary results for parameter combinations and information criteria. In case model estimation fails for some parameter setting (e.g. due to non-convergence), NA is returned for this setting.

• model: bundle - Result from auto_arima()

get_auto_arima_parameters (bundle model, string info_criteria, int model_rank[1::])

Retrieve SARIMA parameters for n-th best model by information criterion.

• model: bundle - Result from auto_arima()
• info_criteria: string - "aicc", "aic", "bic", or "hqc"
• model_rank: int - Ranking position (1 = best)

Vector of SARIMA parameters.

get_auto_arima_command (bundle model, string info_criteria, int model_rank[1::])

Generate hansl command for specified model.

• model: bundle - Result from auto_arima()
• info_criteria: string - "aicc", "aic", "bic", or "hqc"
• model_rank: int - Ranking position (1 = best)

String containing executable hansl command.

Supported parameters:

• verbose: bool - Enable detailed output (default 1)
• with_intercept: bool - Include intercept term (default 1)
• with_seasonality: bool - Consider seasonal parameters (default 1)
• estimation_method: string - "conditional_ml" for conditional ML or "exact_ml" for exact ML (default: "exact_ml")
• SARIMA order limits (see defaults below)

• min_p/max_p: 0/4 (AR orders)
• min_d/max_d: 0/1 (Differencing)
• min_q/max_q: 0/4 (MA orders)
• min_P/max_P: 0/1 (Seasonal AR)
• min_D/max_D: 0/1 (Seasonal diff)
• min_Q/max_Q: 0/1 (Seasonal MA)

• v0.9 (April 2025)

  • Add conditional/exact ML estimation option
  • Improve GUI documentation
  • Update help content and switch to markdown format

• v0.8 (February 2023)

  • Remove line breaks in help text
  • Fix typos

• v0.7 (September 2020)

  • Fix error handling with verbose=0
  • Set default verbose to 0

• v0.6 (August 2020)

  • Fix model ranking bugs
  • Improve error handling
  • Enhance unit tests

• v0.52 (August 2020)

  • Fix max_P handling in GUI

• v0.51 (July 2020)

  • Fix command generation bugs
  • Automate seasonality detection

• v0.5 (July 2020)

  • Initial release