AUTOREGRESSOR

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

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

Autoregressive models predict future values of a time series based on the preceding values. More specifically, the user-specified lag determines how many previous timesteps it takes into account during computation, and predicted values are linear combinations of the values at each lag.

Since its input data must be sorted by timestamp, this algorithm is single-threaded.

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

Behavior type

Volatile

Syntax

AUTOREGRESSOR ('model-name', 'input-relation', 'data-column', 'timestamp-column'
        [ USING PARAMETERS
              [ p = lags ]
              [, method = 'training-algorithm' ]
              [, missing = 'imputation-method' ]
              [, regularization = 'regularization-method' ]
              [, lambda = regularization-value ]
              [, compute_mse = boolean ]
        ] )

Arguments

model-name
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.
input-relation
The table or view containing the timestamp-column.

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.

data-column
An input column of type NUMERIC that contains the dependent variables or outcomes.
timestamp-column
One INTEGER, FLOAT, or TIMESTAMP column that represents the timestamp variable. Timesteps must be consistent.

Parameters

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

Default: 3

method
One of the following algorithms for training the model:

  • 'OLS' (Ordinary Least Squares)

  • 'Yule-Walker'

Default: 'OLS'

missing
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.

Default: ' linear_interpolation'

regularization
One of the following regularization methods used when fitting the data:

  • None

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

Default: None

lambda
FLOAT in the range [0, 100000], the regularization value, lambda.

Default: 1.0

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

Default: False

Examples

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');
                   AUTOREGRESSOR
---------------------------------------------------------
Finished. 3650 elements accepted, 0 elements rejected.

(1 row)

See Autoregressive model example for a walk-through of how to train and make predictions with an autoregression model.

See also