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The ML.ARIMA_COEFFICIENTS functionThis document describes the ML.ARIMA_COEFFICIENTS function, which lets you see the ARIMA coefficients and the weights of the external regressors for ARIMA_PLUS and ARIMA_PLUS_XREG time series models.
ML.ARIMA_COEFFICIENTS( MODEL `PROJECT_ID.DATASET.MODEL` )Arguments
ML.ARIMA_COEFFICIENTS takes the following arguments:
PROJECT_ID: your project ID.DATASET: the BigQuery dataset that contains the model.MODEL: the name of the model.ML.ARIMA_COEFFICIENTS returns the following columns:
time_series_id_col or time_series_id_cols: a value that contains the identifiers of a time series. time_series_id_col can be an INT64 or STRING value. time_series_id_cols can be an ARRAY<INT64> or ARRAY<STRING> value. Only present when forecasting multiple time series simultaneously. The column names and types are inherited from the TIME_SERIES_ID_COL option as specified in the model creation query.ar_coefficients: an ARRAY<FLOAT64> value that contains the autoregressive coefficients, which corresponds to non-seasonal p.ma_coefficients: an ARRAY<FLOAT64> value that contains the moving-average coefficients, which corresponds to non-seasonal q.intercept_or_drift: a FLOAT64 value that contains the constant term of the ARIMA model. By definition, the constant term is called intercept when non-seasonal d is 0, and drift when non-seasonal d is 1. intercept_or_drift is always 0 when non-seasonal d is 2.processed_input: a STRING value that contains the name of the model feature input column. The value of this column matches the name of the feature column provided in the query_statement clause that was used when the model was trained.weight: when the processed_input value is numerical, weight contains a FLOAT64 value and the category_weights column contains NULL values. When the processed_input value is non-numerical and has been converted to dummy encoding, the weight column is NULL and the category_weights column contains the category names and weights for each category.category_weights.category: a STRING value that contains the category name if the processed_input value is non-numeric.category_weights.weight: a FLOAT64 that contains the category's weight if the processed_input value is non-numeric.ARIMA_PLUS models, this function returns the ARIMA coefficients for all time series, in ascending order of the time_series_id_col or time_series_id_cols value. Example
The following example retrieves the model coefficients information from the model mydataset.mymodel in your default project:
SELECT * FROM ML.ARIMA_COEFFICIENTS(MODEL `mydataset.mymodel`)What's next
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Last updated 2025-08-07 UTC.
[[["Easy to understand","easyToUnderstand","thumb-up"],["Solved my problem","solvedMyProblem","thumb-up"],["Other","otherUp","thumb-up"]],[["Hard to understand","hardToUnderstand","thumb-down"],["Incorrect information or sample code","incorrectInformationOrSampleCode","thumb-down"],["Missing the information/samples I need","missingTheInformationSamplesINeed","thumb-down"],["Other","otherDown","thumb-down"]],["Last updated 2025-08-07 UTC."],[[["The `ML.ARIMA_COEFFICIENTS` function in BigQuery allows users to retrieve the coefficients and external regressor weights from `ARIMA_PLUS` and `ARIMA_PLUS_XREG` time series models."],["This function requires the model's project ID, dataset, and name as arguments in its syntax: `ML.ARIMA_COEFFICIENTS(MODEL project_id.dataset.model)`."],["The function's output includes columns such as `ar_coefficients`, `ma_coefficients`, `intercept_or_drift`, `processed_input`, and `weight`, which provide details about the model's structure and coefficients."],["When a processed_input value is non-numerical, a `category_weights` field is provided instead of the `weight` field, which contains the category name and weight for each category."],["For `ARIMA_PLUS` models, this function returns the ARIMA coefficients for each time series, in ascending order of the `time_series_id_col` or `time_series_id_cols` value."]]],[]]
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