Creates an autoregressive (AR) model from a stationary time series with consistent timesteps that can then be used for prediction via PREDICT_AR.

Creates and trains an autoregression (AR) or vector autoregression (VAR) model, depending on the number of provided value columns:

  • One value column: the function executes autoregression and returns a trained AR model. AR is a univariate autoregressive time series algorithm that predicts a variable's future values based on its preceding values. The user specifies the number of lagged timesteps taken into account during computation, and the model then predicts future values as a linear combination of the values at each lag.
  • Multiple value columns: the function executes vector autoregression and returns a trained VAR model. VAR is a multivariate autoregressive time series algorithm that captures the relationship between multiple time series variables over time. Unlike AR, which only considers a single variable, VAR models incorporate feedback between different variables in the model, enabling the model to analyze how variables interact across lagged time steps. For example, with two variables—atmospheric pressure and rain accumulation—a VAR model could determine whether a drop in pressure tends to result in rain at a future date.

To make predictions with a VAR or AR model, use the PREDICT_AUTOREGRESSOR function.

Because the input data must be sorted by timestamp, this function is single-threaded.

This is a meta-function. You must call meta-functions in a top-level SELECT statement.

Behavior type



AUTOREGRESSOR ('model-name', 'input-relation', 'value-columns', 'timestamp-column'
        [ USING PARAMETERS param=value[,...] ] )


Identifies the model to create, where model-name conforms to conventions described in Identifiers. It must also be unique among all names of sequences, tables, projections, views, and models within the same schema.
The table or view containing timestamp-column and value-columns.

This algorithm expects a stationary time series as input; using a time series with a mean that shifts over time may lead to weaker results.

Comma-separated list of one or more NUMERIC input columns that contain the dependent variables or outcomes.

The number of value columns determines whether the function performs the autoregression (AR) or vector autoregression (VAR) algorithm. If only one input column is provided, the function executes autoregression. For multiple input columns, the function performs the VAR algorithm.

Name of an INTEGER, FLOAT, or TIMESTAMP column in input-relation that represents the timestamp variable. The timestep between consecutive entries must be consistent throughout the timestamp-column.


INTEGER in the range [1, 1999], the number of lags to consider in the computation. Larger values for p weaken the correlation.

Default: 3

One of the following algorithms for training the model:
  • 'OLS' (Ordinary Least Squares): default for AR models; not supported for VAR models.

  • 'Yule-Walker': default for VAR models. Sets the alpha constant in the trained model to 0.0.

One of the following methods for handling missing values:
  • 'drop': Missing values are ignored.

  • 'error': Missing values raise an error.

  • 'zero': Missing values are replaced with 0.

  • 'linear_interpolation': Missing values are replaced by linearly-interpolated values based on the nearest valid entries before and after the missing value. This means that in cases where the first or last values in a dataset are missing, they will simply be dropped. The VAR algorithm does not support linear interpolation.

The default method depends on the model type:

  • AR: 'linear_interpolation'
  • VAR: 'error'
For the OLS training method only, one of the following regularization methods used when fitting the data:
  • None

  • 'L2': Weight regularization term which penalizes the squared weight value

Default: None

For the OLS training method only, FLOAT in the range [0, 100000], the regularization value, lambda.

Default: 1.0

BOOLEAN, whether to calculate and output the mean squared error (MSE).

Default: False

BOOLEAN, whether the mean of each column in value-columns is subtracted from its column values before calculating the model coefficients. This parameter only applies if method is set to 'Yule-Walker'. If set to False, the model saves the column means as zero.

Default: False


The following example creates and trains an autoregression model using the Yule-Walker training algorithm and a lag of 3:

=> SELECT AUTOREGRESSOR('AR_temperature_yw', 'temp_data', 'Temperature', 'time' USING PARAMETERS p=3, method='yule-walker');
Finished. 3650 elements accepted, 0 elements rejected.

(1 row)

The following example creates and trains a VAR model with a lag of 2:

=> SELECT AUTOREGRESSOR('VAR_temperature', 'temp_data_VAR', 'temp_location1, temp_location2', 'time' USING PARAMETERS p=2);
WARNING 0:  Only the Yule Walker method is currently supported for Vector Autoregression, setting method to Yule Walker
Finished. 3650 elements accepted, 0 elements rejected.

(1 row)

See Autoregressive model example and VAR model example for extended examples that train and make predictions with AR and VAR models.

See also