The CREATE MODEL statement for ARIMA_PLUS_XREG models

This document describes the CREATE MODEL statement for creating multivariate time series models in BigQuery. You can use a multivariate time series model to forecast the future value for a given column based on the analysis of multiple variables.

You can use multivariate time series models with the ML.FORECAST to forecast future values for a given metric based on multiple variables, and use the ML.EXPLAIN_FORECAST function to retrieve the forecasting values and compute the prediction intervals. Forecasting takes place when you create the model. You can also use multivariate time series models with the ML.DETECT_ANOMALIES function to perform anomaly detection.

For information about the supported SQL statements and functions for each model type, see End-to-end user journey for each model.

Time series modeling pipeline

The multivariate ARIMA_PLUS_XREG time series model is an ARIMA_PLUS model with linear external regressors. The following diagram shows the model pipeline:

For a diagram that shows the details of the ARIMA_PLUS Pipeline section in the preceding diagram, see Time series modeling pipeline.

The modeling pipeline for the ARIMA_PLUS time series models performs the following functions:

• Infer the data frequency of the time series.
• Handle irregular time intervals.
• Handle duplicated timestamps by taking the mean value.
• Interpolate missing data using local linear interpolation.
• Detect and clean spike and dip outliers.
• Detect and adjust abrupt step (level) changes.
• Detect and adjust holiday effect.
• Detect multiple seasonal patterns within a single time series by using Seasonal and Trend decomposition using Loess (STL), and extrapolate seasonality by using double exponential smoothing (ETS).
• Detect and model the trend using the ARIMA model and the auto.ARIMA algorithm for automatic hyperparameter tuning. In auto.ARIMA, dozens of candidate models are trained and evaluated in parallel. The model with the lowest Akaike information criterion (AIC) is selected as the best model.

CREATE MODEL syntax

{CREATE MODEL | CREATE MODEL IF NOT EXISTS | CREATE OR REPLACE MODEL}
model_name
OPTIONS(model_option_list)
AS { query_statement |
  (
    training_data AS (query_statement),
    custom_holiday AS (holiday_statement)
  )
}

model_option_list:
MODEL_TYPE = 'ARIMA_PLUS_XREG'
    [, TIME_SERIES_TIMESTAMP_COL = string_value ]
    [, TIME_SERIES_DATA_COL = string_value ]
    [, HORIZON = int64_value ]
    [, AUTO_ARIMA = { TRUE | FALSE } ]
    [, AUTO_ARIMA_MAX_ORDER = int64_value ]
    [, AUTO_ARIMA_MIN_ORDER = int64_value ]
    [, NON_SEASONAL_ORDER = (int64_value, int64_value, int64_value) ]
    [, DATA_FREQUENCY = { 'AUTO_FREQUENCY' | 'PER_MINUTE' | 'HOURLY' | 'DAILY' | 'WEEKLY' | 'MONTHLY' | 'QUARTERLY' | 'YEARLY' } ]
    [, INCLUDE_DRIFT = { TRUE | FALSE } ]
    [, HOLIDAY_REGION = string_value | string_array ]
    [, CLEAN_SPIKES_AND_DIPS = { TRUE | FALSE } ]
    [, ADJUST_STEP_CHANGES = { TRUE | FALSE } ]
    [, TIME_SERIES_LENGTH_FRACTION = float64_value ]
    [, MIN_TIME_SERIES_LENGTH = int64_value ]
    [, MAX_TIME_SERIES_LENGTH = int64_value ]
    [, TREND_SMOOTHING_WINDOW_SIZE = int64_value ]
    [, L2_REG = float64_value ]
    [, MODEL_REGISTRY = { 'VERTEX_AI' } ]
    [, VERTEX_AI_MODEL_ID = string_value ]
    [, VERTEX_AI_MODEL_VERSION_ALIASES = string_array ]
    [, KMS_KEY_NAME = string_value ]

CREATE MODEL

Creates and trains a new model in the specified dataset. If the model name exists, CREATE MODEL returns an error.

CREATE MODEL IF NOT EXISTS

Creates and trains a new model only if the model doesn't exist in the specified dataset.

CREATE OR REPLACE MODEL

Creates and trains a model and replaces an existing model with the same name in the specified dataset.

model_name

The name of the model you're creating or replacing. The model name must be unique in the dataset: no other model or table can have the same name. The model name must follow the same naming rules as a BigQuery table. A model name can:

• Contain up to 1,024 characters
• Contain letters (upper or lower case), numbers, and underscores

model_name is not case-sensitive.

If you don't have a default project configured, then you must prepend the project ID to the model name in the following format, including backticks:

`[PROJECT_ID].[DATASET].[MODEL]`

For example, `myproject.mydataset.mymodel`.

MODEL_TYPE

Syntax

MODEL_TYPE = 'ARIMA_PLUS_XREG'

Description

Specifies the model type. This option is required.

TIME_SERIES_TIMESTAMP_COL

Syntax

TIME_SERIES_TIMESTAMP_COL = string_value

Description

The name of the column that provides the time points used in training the model. The column must be of one of the following data types:

• TIMESTAMP
• DATE
• DATETIME

Arguments

A STRING value.

TIME_SERIES_DATA_COL

Syntax

TIME_SERIES_DATA_COL = string_value

Description

The name of the column that contains the data to forecast. The column must be of one of the following data types:

• INT64
• NUMERIC
• BIGNUMERIC
• FLOAT64

Arguments

A STRING value.

HORIZON

Syntax

HORIZON = int64_value

Description

The number of time points to forecast.

Arguments

An INT64 value. The default value is 1,000. The maximum value is 10,000.

AUTO_ARIMA

Syntax

AUTO_ARIMA = { TRUE | FALSE }

Description

Determines whether the training process uses auto.ARIMA or not. If TRUE, training automatically finds the best non-seasonal order (that is, the p, d, q tuple) and decides whether or not to include a linear drift term when d is 1. If FALSE, you must specify the NON_SEASONAL_ORDER option.

Arguments

A BOOL value. The default value is TRUE.

AUTO_ARIMA_MAX_ORDER

Syntax

AUTO_ARIMA_MAX_ORDER = int64_value

Description

The maximum value for the sum of non-seasonal p and q. This value determines the parameter search space in the auto.ARIMA algorithm, in combination with the AUTO_ARIMA_MIN_ORDER value. This option is disabled when the AUTO_ARIMA value is FALSE.

Arguments

An INT64 value between 1 and 5, inclusive. The default value is 5.

If non-seasonal d is determined to be 0 or 2, the number of candidate models evaluated for each supported value is as follows:

• 1: 3 candidate models
• 2: 6 candidate models
• 3: 10 candidate models
• 4: 15 candidate models
• 5: 21 candidate models

If non-seasonal d is determined to be 1, the number of candidate models to evaluate is doubled, because there's an additional drift term to consider for all of the existing candidate models.

AUTO_ARIMA_MIN_ORDER

Syntax

AUTO_ARIMA_MIN_ORDER = int64_value

Description

The minimum value for the sum of non-seasonal p and q. This value determines the parameter search space in the auto.ARIMA algorithm, in combination with the AUTO_ARIMA_MAX_ORDER value. Setting this option to 1 or greater lets the model exclude some flat forecasting results. This option is disabled when AUTO_ARIMA is FALSE.

Arguments

The value is a INT64. The default value is 0.

NON_SEASONAL_ORDER

Syntax

NON_SEASONAL_ORDER = (p_value, d_value, q_value)

Description

The tuple of non-seasonal p, d, q for the ARIMA_PLUS model. There are no default values, and you must specify all three values. p and q must be a value between 0 and 5, inclusive. d must be a value between 0 and 2, inclusive.

The AUTO_ARIMA value must be FALSE to use this option.

Arguments

A tuple of three INT64 values. For example, (1, 2, 1).

DATA_FREQUENCY

Syntax

DATA_FREQUENCY = { 'AUTO_FREQUENCY' | 'PER_MINUTE' | 'HOURLY' | 'DAILY' | 'WEEKLY' | 'MONTHLY' | 'QUARTERLY' | 'YEARLY' }

Description

The data frequency of the input time series. The finest supported granularity is PER_MINUTE.

Arguments

This option accepts the following values:

• AUTO_FREQUENCY: This is the default. The training process automatically infers the data frequency, which can be any of the other supported values for this option.
• PER_MINUTE
• HOURLY
• DAILY
• WEEKLY
• MONTHLY
• QUARTERLY
• YEARLY

INCLUDE_DRIFT

Syntax

INCLUDE_DRIFT = { TRUE | FALSE }

Description

Determines whether the ARIMA_PLUS model should include a linear drift term or not. The drift term is applicable when non-seasonal d is 1.

• When the AUTO_ARIMA value is FALSE , this argument defaults to FALSE. You can set it to TRUE only when non-seasonal d is 1. Otherwise the CREATE MODEL statement returns an invalid query error.
• When the AUTO_ARIMA value is TRUE, BigQuery ML automatically determines whether or not to include a linear drift term, so you can't use this option.

Arguments

A BOOL value. The default value is FALSE.

HOLIDAY_REGION

Syntax

HOLIDAY_REGION = string_value | string_array

Description

The geographical region based on which the holiday effect is applied in modeling. By default, holiday effect modeling isn't used. To use it, specify one or more holiday regions using this option. If you include more than one region string, the union of the holidays in all the provided regions are taken into account when modeling.

Holiday effect modeling is only applicable when the time series is daily or weekly, and longer than a year. If the input time series doesn't meet these requirements, holiday effect modeling isn't used even if you specify this option.

For more information about the holidays included in each region, see Holiday data.

Arguments

A STRING or ARRAY<STRING> value.

Use a single string value to identify one region. For example:

HOLIDAY_REGION = 'GLOBAL'

Use an array of string values to identify multiple regions. For example:

HOLIDAY_REGION = ['US', 'GB']

This option accepts the following values:

Global

• GLOBAL

Continental regions

• NA: North America
• JAPAC: Japan and Asia Pacific
• EMEA: Europe, the Middle East and Africa
• LAC: Latin America and the Caribbean

Countries

• AE: United Arab Emirates
• AR: Argentina
• AT: Austria
• AU: Australia
• BE: Belgium
• BR: Brazil
• CA: Canada
• CH: Switzerland
• CL: Chile
• CN: China
• CO: Colombia
• CZ: Czechia
• DE: Germany
• DK: Denmark
• DZ: Algeria
• EC: Ecuador
• EE: Estonia
• EG: Egypt
• ES: Spain
• FI: Finland
• FR: France
• GB: United Kingdom
• GR: Greece
• HK: Hong Kong
• HU: Hungary
• ID: Indonesia
• IE: Ireland
• IL: Israel
• IN: India
• IR: Iran
• IT: Italy
• JP: Japan
• KR: South Korea
• LV: Latvia
• MA: Morocco
• MX: Mexico
• MY: Malaysia
• NG: Nigeria
• NL: Netherlands
• NO: Norway
• NZ: New Zealand
• PE: Peru
• PH: Philippines
• PK: Pakistan
• PL: Poland
• PT: Portugal
• RO: Romania
• RS: Serbia
• RU: Russia
• SA: Saudi Arabia
• SE: Sweden
• SG: Singapore
• SI: Slovenia
• SK: Slovakia
• TH: Thailand
• TR: Turkey
• TW: Taiwan
• UA: Ukraine
• US: United States
• VE: Venezuela
• VN: Vietnam
• ZA: South Africa

CLEAN_SPIKES_AND_DIPS

Syntax

CLEAN_SPIKES_AND_DIPS = { TRUE | FALSE }

Description

Determines whether or not to perform automatic spikes and dips detection and cleanup in the ARIMA_PLUS model training pipeline. The spikes and dips are replaced with local linear interpolated values when they're detected.

Arguments

A BOOL value. The default value is TRUE.

ADJUST_STEP_CHANGES

Syntax

ADJUST_STEP_CHANGES = { TRUE | FALSE }

Description

Determines whether or not to perform automatic step change detection and adjustment in the ARIMA_PLUS model training pipeline.

Arguments

A BOOL value. The default value is TRUE.

TIME_SERIES_LENGTH_FRACTION

Syntax

TIME_SERIES_LENGTH_FRACTION = float64_value

Description

The fraction of the interpolated length of the time series that's used to model the time series trend component. All of the time points of the time series are used to model the non-trend component. For example, if the time series has 100 time points, then specifying a TIME_SERIES_LENGTH_FRACTION of 0.5 uses the most recent 50 time points for trend modeling. This training option accelerates modeling training without sacrificing much forecasting accuracy.

You can use the TIME_SERIES_LENGTH_FRACTION option with the MIN_TIME_SERIES_LENGTH option, but not with the MAX_TIME_SERIES_LENGTH option.

Arguments

A FLOAT64 value in the range (0, 1). The default behavior is to use all the points in the time series.

MIN_TIME_SERIES_LENGTH

Syntax

MIN_TIME_SERIES_LENGTH = int64_value

Description

The minimum number of time points that are used in modeling the trend component of the time series. If you use this option, you must also specify a value for the TIME_SERIES_LENGTH_FRACTION option, and you can't specify a value for the MAX_TIME_SERIES_LENGTH option.

Arguments

An INT64 value greater than or equal to 4. The default value is 20.

MAX_TIME_SERIES_LENGTH

Syntax

MAX_TIME_SERIES_LENGTH = int64_value

Description

The maximum number of time points in a time series that can be used in modeling the trend component of the time series.

You can't use theMAX_TIME_SERIES_LENGTH with the TIME_SERIES_LENGTH_FRACTION or MIN_TIME_SERIES_LENGTH options.

Arguments

An INT64 value greater than or equal to 4. There is no default value. We recommend trying 30 as a starting value.

TREND_SMOOTHING_WINDOW_SIZE

Syntax

TREND_SMOOTHING_WINDOW_SIZE = int64_value

Description

The smoothing window size for the trend component. When you specify a value, a center moving average smoothing is applied on the history trend. When the smoothing window is out of the boundary at the beginning or the end of the trend, the first element or the last element is padded to fill the smoothing window before the average is applied.

Specifying a value for TREND_SMOOTHING_WINDOW_SIZE doesn't affect forecasting results. It only affects the smoothness of the trend component, which you can see by using the ML.EXPLAIN_FORECAST function.

Arguments

An INT64 value. There is no default value. You must specify a positive value to smooth the trend.

L2_REG

Syntax

L2_REG = float64_value

Description

The amount of L2 regularization applied in the linear regression.

Arguments

A FLOAT64 value.

MODEL_REGISTRY

The MODEL_REGISTRY option specifies the model registry destination. VERTEX_AI is the only supported model registry destination. To learn more, see Register a BigQuery ML model.

VERTEX_AI_MODEL_ID

The VERTEX_AI_MODEL_ID option specifies the Vertex AI model ID to register the model with.

You can only set the VERTEX_AI_MODEL_ID option when the MODEL_REGISTRY option is set to VERTEX_AI. To learn more, see Add a Vertex AI model ID.

VERTEX_AI_MODEL_VERSION_ALIASES

The VERTEX_AI_MODEL_VERSION_ALIASES option specifies the Vertex AI model alias to register the model with.

You can only set the VERTEX_AI_MODEL_VERSION_ALIASES option when the MODEL_REGISTRY option is set to VERTEX_AI. To learn more, see Add a Vertex AI model ID.

KMS_KEY_NAME

Syntax

KMS_KEY_NAME = string_value

Description

The Cloud Key Management Service customer-managed encryption key (CMEK) to use to encrypt the model.

Arguments

A STRING value containing the fully-qualified name of the CMEK. For example,

'projects/my_project/locations/my_location/keyRings/my_ring/cryptoKeys/my_key'

AS

AS query_statement

For time series forecasting models that have a DATA_FREQUENCY value of either DAILY or AUTO_FREQUENCY, you can optionally use the following AS clause syntax to perform custom holiday modeling in addition to specifying the training data:

AS (
  training_data AS (query_statement),
  custom_holiday AS (holiday_statement)
)

query_statement

The query_statement argument specifies the query that is used to generate the training data. For information about the supported SQL syntax of the query_statement clause, see GoogleSQL query syntax.

holiday_statement

The holiday_statement argument specifies the query that provides custom holiday modeling information for time series forecast models. This query must return 50,000 rows or less and must contain the following columns:

• region: Required. A STRING value that identifies the region to target for holiday modeling. Use one of the following options:

  • An upper-case holiday region code. Use this option to overwrite or supplement the holidays for the specified region. You can see the holidays for a region by running SELECT * FROM bigquery-public-data.ml_datasets.holidays_and_events_for_forecasting WHERE region = region.
  • An arbitrary string. Use this option to specify a custom region that you want to model holidays for. For example, you could specify London if you are only modeling holidays for that city.

  Be sure not to use an existing holiday region code when you are trying to model for a custom region. For example, if you want to model a holiday in California, and specify CA as the region value, the service recognizes that as the holiday region code for Canada and targets that region. Because the argument is case-sensitive, you could specify ca, California, or some other value that isn't a holiday region code.

• holiday_name: Required. A STRING value that identifies the holiday to target for holiday modeling. Use one of the following options:

  • The holiday name as it is represented in the bigquery-public-data.ml_datasets.holidays_and_events_for_forecasting public table, including case. Use this option to overwrite or supplement the specified holiday.
  • A string that represents a custom holiday. The string must be a valid column name so that it can be used in ML.EXPLAIN_FORECAST output. For example, it cannot contain space. For more information on column naming, see Column names.

• primary_date: Required. A DATE value that specifies the date the holiday falls on.

• preholiday_days: Optional. An INT64 value that specifies the start of the holiday window around the holiday that is taken into account when modeling. Must be greater than or equal to 1. Defaults to 1.

• postholiday_days: Optional. An INT64 value that specifies the end of the holiday window around the holiday that is taken into account when modeling. Must be greater than or equal to 1. Defaults to 1.

The preholiday_days and postholiday_days arguments together describe the holiday window around the holiday that is taken into account when modeling. The holiday window is defined as [primary_date - preholiday_days, primary_date + postholiday_days] and is inclusive of the pre- and post-holiday days. The value for each holiday window must be less than or equal to 30 and must be the same across the given holiday. For example, if you are modeling Arbor Day for several different years, you must specify the same holiday window for all of those years.

To achieve the best holiday modeling result, provide as much historical and forecast information about the occurrences of each included holiday as possible. For example, if you have time series data from 2018 to 2022 and would like to forecast for 2023, you get the best result by providing the custom holiday information for all of those years, similar to the following:

CREATE OR REPLACE MODEL mydataset.arima_model
  OPTIONS (
    model_type = 'ARIMA_PLUS_XREG',
    holiday_region = 'US',...) AS (
        training_data AS (SELECT * FROM mydataset.timeseries_data),
        custom_holiday AS (
            SELECT
              'US' AS region,
              'Halloween' AS holiday_name,
              primary_date,
              5 AS preholiday_days,
              1 AS postholiday_days
            FROM
              UNNEST(
                [
                  DATE('2018-10-31'),
                  DATE('2019-10-31'),
                  DATE('2020-10-31'),
                  DATE('2021-10-31'),
                  DATE('2022-10-31'),
                  DATE('2023-10-31')])
                AS primary_date
          )
      )

Holiday data

When you perform holiday modeling by specifying the HOLIDAY_REGION option, the model uses holiday data from the region or regions you specify. For example, the following table describes the holiday data used in the US region for the year 2022-2023.

• region specifies the geographic region to which the holiday applies. The supported regions are listed in HOLIDAY_REGION.
• holiday_name contains the name of the holiday.
• primary_date specifies the date of the holiday. For holidays that span multiple days, this is usually the first day of the holiday.
• preholiday_days describes the number of days the holiday effect starts before the primary_date value.
• postholiday_days describes the number of days the holiday effect ends after the primary_date value.

You can also see the holidays for a region by running SELECT * FROM bigquery-public-data.ml_datasets.holidays_and_events_for_forecasting WHERE region = region.

The bigquery-public-data.ml_datasets.holidays_and_events_for_forecasting table only contains holidays and events from the following regions:

• AU: Australia
• CA: Canada
• CH: Switzerland
• CL: Chile
• CZ: Czechia
• DE: Germany
• DK: Denmark
• EMEA: Europe, the Middle East and Africa
• ES: Spain
• FR: France
• GB: United Kingdom
• GLOBAL
• ID: Indonesia
• IN: India
• IT: Italy
• JAPAC: Japan and Asia Pacific
• JP: Japan
• KR: South Korea
• LAC: Latin America and the Caribbean
• MX: Mexico
• MY: Malaysia
• NA: North America
• NL: Netherlands
• NZ: New Zealand
• PT: Portugal
• SK: Slovakia
• US: United States
• ZA: South Africa

Custom holidays

You can combine use of the holiday_statement argument and the HOLIDAY_REGION option to enable several different custom holiday scenarios, as described in the following sections.

Supplement built-in holidays with additional custom holidays

To model one or more custom holidays in addition to a region's built-in holidays, specify the target holiday region with the HOLIDAY_REGION option, and then provide the new holiday metadata in the holiday_statement argument.

The following example models all built-in holidays for the US holiday region, and additionally models the custom holiday members_day:

CREATE OR REPLACE MODEL mydataset.arima_model
  OPTIONS (
    model_type = 'ARIMA_PLUS_XREG',
    holiday_region = 'US',...) AS (
        training_data AS (SELECT * FROM mydataset.timeseries_data),
        custom_holiday AS (
            SELECT
              'US' AS region,
              'members_day' AS holiday_name,
              primary_date,
              2 AS preholiday_days,
              2 AS postholiday_days
            FROM
              UNNEST(
                [
                  DATE('2016-06-15'),
                  DATE('2017-06-07'),
                  DATE('2018-06-06')])
                AS primary_date
          )
      );

Model only custom holidays

To model only custom holidays, don't specify a value for the HOLIDAY_REGION option, and provide the new holiday metadata in the holiday_statement argument.

The following example models only the custom holiday members_day for the US holiday region:

CREATE OR REPLACE MODEL mydataset.arima_model
  OPTIONS (
    model_type = 'ARIMA_PLUS_XREG',
    -- Don't specify HOLIDAY_REGION
    ...) AS (
        training_data AS (SELECT * FROM mydataset.timeseries_data),
        custom_holiday AS (
            SELECT
              'US' AS region,
              'members_day' AS holiday_name,
              primary_date,
              2 AS preholiday_days,
              2 AS postholiday_days
            FROM
              UNNEST(
                [
                  DATE('2016-06-15'),
                  DATE('2017-06-07'),
                  DATE('2018-06-06')])
                AS primary_date
          )
      );

Change the metadata for built-in holidays

You can change the primary date and holiday effect window used by the model for one or more built-in holidays. To do this, specify the target holiday region with the HOLIDAY_REGION option, and then provide the modified holiday metadata in the holiday_statement argument.

The following example models all built-in holidays for the US holiday region, but models 3 years of the EasterMonday holiday with a 3-day holiday effect window instead of the default 9-day holiday effect window:

  OPTIONS (
    model_type = 'ARIMA_PLUS_XREG',
    holiday_region = 'US',...) AS (
        training_data AS (SELECT * FROM mydataset.timeseries_data),
        custom_holiday AS (
            SELECT
              'US' AS region,
              'EasterMonday' AS holiday_name,
              primary_date,
              1 AS preholiday_days,
              1 AS postholiday_days
            FROM
              UNNEST(
                [
                  DATE('2016-03-28'),
                  DATE('2017-04-17'),
                  DATE('2018-04-02')])
                AS primary_date
          )
      );

Model a subset of built-in holidays

To model only a subset of built-in holidays, don't specify a value for the HOLIDAY_REGION option, and provide a query based on the bigquery-public-data.ml_datasets.holidays_and_events_for_forecasting public table to specify the set of holidays to model.

The following example models all built-in holidays for the US holiday region except for the Christmas and NewYears holidays:

CREATE OR REPLACE MODEL mydataset.arima_model
  OPTIONS (
    model_type = 'ARIMA_PLUS_XREG',
    -- Don't specify HOLIDAY_REGION
    ...) AS (
        training_data AS (SELECT * FROM mydataset.timeseries_data),
        custom_holiday AS (
            SELECT *
            FROM bigquery-public-data.ml_datasets.holiday
            WHERE
              region = 'US'
              AND (holiday_name != 'Christmas' OR holiday_name != 'NewYear')
          )
      );

Custom holiday limitations

• Custom holiday modeling only works for models that have a data_frequency value of either DAILY or AUTO_FREQUENCY. If you use AUTO_FREQUENCY, the actual frequency of the time series data needs to be daily.
• You can't use the TRANSFORM clause of the CREATE MODEL statement if you are performing custom holiday modeling.
• holiday_name column cannot have more than 500 distinct values.
• Custom holiday modeling uses an algorithm that automatically detects the significance of the holiday effect within the provided holiday effect window, and only extracts the holiday effect on the days that the algorithm classifies as significant. For example, if primary date is 01/02 with preholiday_days and postholiday_days set to 1, the algorithm analyzes the holiday effect for these three days: [01/01, 01/02, 01/03]. In the ML.EXPLAIN_FORECAST output, it is not guaranteed that all three of these days will have a holiday effect. Only those days within this window that have a significant holiday effect are associated with a non-zero holiday effect in the output.
• To get a better result from custom holiday modeling, don't specify the same holiday more than twice a year.
• If you specify the same holiday more than once, make sure its occurrences don't overlap. For example, a holiday that happens twice a year, with the first occurrence from December 1 - December 5 and the second occurrence from December 4 - December 8, won't work because these two occurrences overlap with each other on December 4 and December 5.
• Different holidays can have partial overlap with each other, but full overlap isn't allowed. For example, if holiday A has an occurrence from December 1 - December 5, then holiday B can have an occurrence from December 4 - December 8. However, holiday B can't have an occurrence from December 2 - December 4, which is fully within holiday A's occurrence, and holiday B can't have an occurrence from December 1 - December 8, which overlaps with all of holiday A's occurrence.
• In cases where holidays overlap for a period, the overlap between the holidays can't be identical in multiple years. If it is, then it isn't possible to determine each holiday's effect on the overlapped period. For example, suppose holiday A and holiday B overlap from December 2 - December 4 in 2024, and the time series has three years of data from 2022-2024. Holidays A and B can't overlap from December 2 - December 4 in 2023 and 2022 as well if you want to be able to determine the holiday effect for each.

Limitations

ARIMA_PLUS_XREG models have the following limitations:

• For the input time series, the maximum length is 1,000,000 time points and the minimum length is 3 time points.
• The maximum time points to forecast is 10,000.
• The maximum cardinality of training features is 10,000.
• Holiday effect modeling is effective only for approximately 5 years.
• You can't export ARIMA_PLUS_XREG models.

Examples

The following examples show how to create different types of ARIMA_PLUS_XREG time series models.

Forecast a single time series

This example shows how to create a time series model that forecasts a single time series:

CREATE MODEL `project_id.mydataset.mymodel`
 OPTIONS(MODEL_TYPE='ARIMA_PLUS_XREG',
         time_series_timestamp_col='date',
         time_series_data_col='transaction') AS
SELECT
  date,
  transaction,
  feature1,
  feature2
FROM
  `mydataset.mytable`

Train a time series model more quickly by using a fraction of the time points

This example shows how to create a time series model while improving training speed by using the TIME_SERIES_LENGTH_FRACTION and MIN_TIME_SERIES_LENGTH options:

CREATE MODEL `project_id.mydataset.mymodel`
 OPTIONS(MODEL_TYPE='ARIMA_PLUS_XREG',
         time_series_timestamp_col='date',
         time_series_data_col='transaction',
         time_series_length_fraction=0.5,
         min_time_series_length=30) AS
SELECT
  date,
  transaction,
  feature1,
  feature2
FROM
  `mydataset.mytable`

What's next

• Walk through our tutorials that use the multivariate time series model in BigQuery ML:
  • Performing single time-series forecasting from Seattle air quality data
  • Perform anomaly detection with a multivariate time-series forecasting model