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Auto-Regressive Integrated Moving Average (ARIMA) model

Note: the ARIMA model here refers to the time-series model implemented in DTBase.

Theoretical background

The ARIMA model is designed to produce a forecast of a univariate (i.e. single variable) time series, e.g. temperature. It employs the SARIMAX model of the statsmodels library.

In the current implementation, the following parameters can be specified for the ARIMA model. See the SARIMAX model documentation page for more details.

  • arima_order: The (p, d, q) order of the model for the number of auto-regressive parameters, differences, and moving-average parameters, respectively.
  • seasonal_order: The (P, D, Q, s) order of the seasonal component of the model for the auto-regressive parameters, differences, moving-average parameters, and periodicity, respectively.
  • trend: The parameter controlling the trend polynomial of the time series.

Currently, support for exogenous regressors (i.e. the effect of external variables on the modelled variable) is not provided. Therefore, the ARIMA model of DTBase can be employed to fit a model to a univariate time series that:

  • Shows a changing variable that regresses on its own prior (lagged) values, i.e. is auto-regressive. The model implicitly assumes that the future will resemble the past.
  • May be non-stationary. The integrated part of the model represents the differencing of raw observations to allow the time series to become stationary.
  • May contain outliers or random, short-term fluctuations, whose influence is smoothed out by employing constantly updated moving averages.
  • May have a seasonal component, where seasonality in a time series is defined as a regular pattern of changes that repeats itself (e.g. daily temperature fluctuations between day/night).
  • May have a trend, which represents the long-term change in the level of a time-series (e.g. upward monotonic due to a constantly increasing average temperature).

Code Structure

The following figure shows relevant files in the ARIMA model directory:

image

User-specified parameters are controlled through config_arima.ini. These include specification of what data to pull from the database, parameters for data pre-processing, as well as model parameters such as arima_order, seasonal_order and trend. All user interaction with the model can be done through config_arima.ini.

The ARIMA model Python modules are:

  1. arima.get_data: employed to fetch data stored in the data base using sqlalchemy. Make sure you first source your .secrets file containing usernames, passwords, etc. in order to be able to connect to the data base.
  2. arima.clean_data: employed to clean up the data fetched from the data base before further processing.
  3. arima.prepare_data: used to pre-process the cleaned data before feeding it to the model.
  4. arima.arima_pipeline: this is the main module, which contains functions for model fitting and forecasting, as well as functions for model evaluation such as time-series cross-validation.

The script run_locally.py can be employed to run the ARIMA model locally in your machine. Just run:

python run_locally.py

in your terminal.