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Model Identification of Integrated ARMA Processes.

Tetiana Stadnytska1, Simone Braun1, Joachim Werner1

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Automated methods like Smallest Canonical Correlation Method (SCAN) and Extended Sample Autocorrelation Function (ESACF) for Autoregressive Integrated Moving-Average (ARIMA) model selection show inconsistent accuracy. Combining techniques improves model identification reliability.

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Area of Science:

  • Time Series Analysis
  • Statistical Modeling
  • Econometrics

Background:

  • Autoregressive Integrated Moving-Average (ARIMA) models are crucial for time series forecasting.
  • Automated model selection methods aim to simplify ARIMA identification.
  • Existing methods like SCAN and ESACF are available in statistical software (e.g., SAS).

Purpose of the Study:

  • To evaluate the performance of Smallest Canonical Correlation Method (SCAN) and Extended Sample Autocorrelation Function (ESACF) for identifying integrated ARIMA models.
  • To compare the effectiveness of SCAN and ESACF on both untransformed and differenced time series data.
  • To develop an improved strategy for ARIMA model selection by integrating various techniques.

Main Methods:

  • The study applied SCAN and ESACF to identify integrated ARIMA models.
  • Performance was assessed by comparing automated identifications with known model structures.
  • A novel model selection strategy was proposed, combining different identification approaches.

Main Results:

  • SCAN achieved 79% correct identifications, while ESACF reached 80% accuracy.
  • Both methods demonstrated disappointing accuracy for certain ARIMA models and parameterizations.
  • Inconsistent model identifications were observed for both automated tools and human experts.

Conclusions:

  • Automated ARIMA model selection tools (SCAN, ESACF) exhibit limitations in accuracy and consistency.
  • Human expertise alone does not guarantee reliable ARIMA model identification.
  • An integrated strategy combining multiple identification techniques is recommended for robust ARIMA model selection.