Forecast multiple time series with an ARIMA_PLUS univariate model

This tutorial teaches you how to use an ARIMA_PLUS univariate time series model to forecast the future value of a given column, based on the historical values for that column.

This tutorial forecasts for multiple time series. Forecasted values are calculated for each time point, for each value in one or more specified columns. For example, if you wanted to forecast weather and specified a column containing city data, the forecasted data would contain forecasts for all time points for City A, then forecasted values for all time points for City B, and so forth.

This tutorial uses data from the public bigquery-public-data.new_york.citibike_trips table. This table contains information about Citi Bike trips in New York City.

Before reading this tutorial, we highly recommend that you read Forecast a single time series with a univariate model.

Create a dataset

Create a BigQuery dataset to store your ML model.

Console

In the Google Cloud console, go to the BigQuery page.

Go to the BigQuery page
In the Explorer pane, click your project name.
Click View actions > Create dataset
On the Create dataset page, do the following:
- For Dataset ID, enter bqml_tutorial.
- For Location type, select Multi-region, and then select US (multiple regions in United States).
- Leave the remaining default settings as they are, and click Create dataset.

bq

To create a new dataset, use the bq mk command with the --location flag. For a full list of possible parameters, see the bq mk --dataset command reference.

Create a dataset named bqml_tutorial with the data location set to US and a description of BigQuery ML tutorial dataset:
```
bq --location=US mk -d \
 --description "BigQuery ML tutorial dataset." \
 bqml_tutorial
```
Instead of using the --dataset flag, the command uses the -d shortcut. If you omit -d and --dataset, the command defaults to creating a dataset.
Confirm that the dataset was created:
```
bq ls
```

API

Call the datasets.insert method with a defined dataset resource.

{
  "datasetReference": {
     "datasetId": "bqml_tutorial"
  }
}

BigQuery DataFrames

Before trying this sample, follow the BigQuery DataFrames setup instructions in the BigQuery quickstart using BigQuery DataFrames. For more information, see the BigQuery DataFrames reference documentation.

To authenticate to BigQuery, set up Application Default Credentials. For more information, see Set up ADC for a local development environment.

import google.cloud.bigquery

bqclient = google.cloud.bigquery.Client()
bqclient.create_dataset("bqml_tutorial", exists_ok=True)

Visualize the input data

Before creating the model, you can optionally visualize your input time series data to get a sense of the distribution. You can do this by using Looker Studio.

SQL

The SELECT statement of the following query uses the EXTRACT function to extract the date information from the starttime column. The query uses the COUNT(*) clause to get the daily total number of Citi Bike trips.

Follow these steps to visualize the time series data:

In the Google Cloud console, go to the BigQuery page.

Go to BigQuery

In the query editor, paste in the following query and click Run:

SELECT
 EXTRACT(DATE from starttime) AS date,
 COUNT(*) AS num_trips
FROM
`bigquery-public-data.new_york.citibike_trips`
GROUP BY date;

When the query completes, click Explore data > Explore with Looker Studio. Looker Studio opens in a new tab. Complete the following steps in the new tab.
In the Looker Studio, click Insert > Time series chart.
In the Chart pane, choose the Setup tab.
In the Metric section, add the num_trips field, and remove the default Record Count metric. The resulting chart looks similar to the following:

BigQuery DataFrames

To authenticate to BigQuery, set up Application Default Credentials. For more information, see Set up ADC for a local development environment.


import bigframes.pandas as bpd

df = bpd.read_gbq("bigquery-public-data.new_york.citibike_trips")

features = bpd.DataFrame(
    {
        "num_trips": df.starttime,
        "date": df["starttime"].dt.date,
    }
)
date = df["starttime"].dt.date
df.groupby([date])
num_trips = features.groupby(["date"]).count()

# Results from running "print(num_trips)"

#                num_trips
# date
# 2013-07-01      16650
# 2013-07-02      22745
# 2013-07-03      21864
# 2013-07-04      22326
# 2013-07-05      21842
# 2013-07-06      20467
# 2013-07-07      20477
# 2013-07-08      21615
# 2013-07-09      26641
# 2013-07-10      25732
# 2013-07-11      24417
# 2013-07-12      19006
# 2013-07-13      26119
# 2013-07-14      29287
# 2013-07-15      28069
# 2013-07-16      29842
# 2013-07-17      30550
# 2013-07-18      28869
# 2013-07-19      26591
# 2013-07-20      25278
# 2013-07-21      30297
# 2013-07-22      25979
# 2013-07-23      32376
# 2013-07-24      35271
# 2013-07-25      31084

num_trips.plot.line(
    # Rotate the x labels so they are more visible.
    rot=45,
)

Create the time series model

You want to forecast the number of bike trips for each Citi Bike station, which requires many time series models; one for each Citi Bike station that is included in the input data. You can create multiple models to do this, but that can be a tedious and time consuming process, especially when you have a large number of time series. Instead, you can use a single query to create and fit a set of time series models in order to forecast multiple time series at once.

SQL

In the following query, the OPTIONS(model_type='ARIMA_PLUS', time_series_timestamp_col='date', ...) clause indicates that you are creating an ARIMA-based time series model. You use the time_series_id_col option of the CREATE MODEL statement to specify one or more columns in the input data that you want to get forecasts for, in this case the Citi Bike station, as represented by the start_station_name column. You use the WHERE clause to limit the start stations to those with Central Park in their names. The auto_arima_max_order option of the CREATE MODEL statement controls the search space for hyperparameter tuning in the auto.ARIMA algorithm. The decompose_time_series option of the CREATE MODEL statement defaults to TRUE, so that information about the time series data is returned when you evaluate the model in the next step.

Follow these steps to create the model:

In the Google Cloud console, go to the BigQuery page.

Go to BigQuery

In the query editor, paste in the following query and click Run:

CREATE OR REPLACE MODEL `bqml_tutorial.nyc_citibike_arima_model_group`
OPTIONS
(model_type = 'ARIMA_PLUS',
 time_series_timestamp_col = 'date',
 time_series_data_col = 'num_trips',
 time_series_id_col = 'start_station_name',
 auto_arima_max_order = 5
) AS
SELECT
 start_station_name,
 EXTRACT(DATE from starttime) AS date,
 COUNT(*) AS num_trips
FROM
`bigquery-public-data.new_york.citibike_trips`
WHERE start_station_name LIKE '%Central Park%'
GROUP BY start_station_name, date;

The query takes approximately 24 seconds to complete, after which you can access the nyc_citibike_arima_model_group model. Because the query uses a CREATE MODEL statement, you don't see query results.

This query creates twelve time series models, one for each of the twelve Citi Bike start stations in the input data. The time cost, approximately 24 seconds, is only 1.4 times more than that of creating a single time series model because of the parallelism. However, if you remove the WHERE ... LIKE ... clause, there would be 600+ time series to forecast, and they wouldn't be forecast completely in parallel because of slot capacity limitations. In that case, the query would take approximately 15 minutes to finish. To reduce the query runtime with the compromise of a potential slight drop in model quality, you could decrease the value of the auto_arima_max_order. This shrinks the search space of hyperparameter tuning in the auto.ARIMA algorithm. For more information, see Large-scale time series forecasting best practices.

BigQuery DataFrames

In the following snippet, you are creating an ARIMA-based time series model.

To authenticate to BigQuery, set up Application Default Credentials. For more information, see Set up ADC for a local development environment.

from bigframes.ml import forecasting
import bigframes.pandas as bpd

model = forecasting.ARIMAPlus(
    # To reduce the query runtime with the compromise of a potential slight
    # drop in model quality, you could decrease the value of the
    # auto_arima_max_order. This shrinks the search space of hyperparameter
    # tuning in the auto.ARIMA algorithm.
    auto_arima_max_order=5,
)

df = bpd.read_gbq("bigquery-public-data.new_york.citibike_trips")

# This query creates twelve time series models, one for each of the twelve
# Citi Bike start stations in the input data. If you remove this row
# filter, there would be 600+ time series to forecast.
df = df[df["start_station_name"].str.contains("Central Park")]

features = bpd.DataFrame(
    {
        "start_station_name": df["start_station_name"],
        "num_trips": df["starttime"],
        "date": df["starttime"].dt.date,
    }
)
num_trips = features.groupby(
    ["start_station_name", "date"],
    as_index=False,
).count()

X = num_trips["date"].to_frame()
y = num_trips["num_trips"].to_frame()

model.fit(
    X,
    y,
    # The input data that you want to get forecasts for,
    # in this case the Citi Bike station, as represented by the
    # start_station_name column.
    id_col=num_trips["start_station_name"].to_frame(),
)

# The model.fit() call above created a temporary model.
# Use the to_gbq() method to write to a permanent location.
model.to_gbq(
    your_model_id,  # For example: "bqml_tutorial.nyc_citibike_arima_model",
    replace=True,
)

This creates twelve time series models, one for each of the twelve Citi Bike start stations in the input data. The time cost, approximately 24 seconds, is only 1.4 times more than that of creating a single time series model because of the parallelism.

Evaluate the model

SQL

Evaluate the time series model by using the ML.ARIMA_EVALUATE function. The ML.ARIMA_EVALUATE function shows you the evaluation metrics that were generated for the model during the process of automatic hyperparameter tuning.

Follow these steps to evaluate the model:

In the Google Cloud console, go to the BigQuery page.

Go to BigQuery
In the query editor, paste in the following query and click Run:
```
SELECT
*
FROM
ML.ARIMA_EVALUATE(MODEL `bqml_tutorial.nyc_citibike_arima_model_group`);
```
The results should look like the following:

While auto.ARIMA evaluates dozens of candidate ARIMA models for each time series, ML.ARIMA_EVALUATE by default only outputs the information of the best model to make the output table compact. To view all the candidate models, you can set the ML.ARIMA_EVALUATE function's show_all_candidate_model argument to TRUE.

BigQuery DataFrames

To authenticate to BigQuery, set up Application Default Credentials. For more information, see Set up ADC for a local development environment.

# Evaluate the time series models by using the summary() function. The summary()
# function shows you the evaluation metrics of all the candidate models evaluated
# during the process of automatic hyperparameter tuning.
summary = model.summary()
print(summary.peek())

# Expected output:
#    start_station_name                  non_seasonal_p  non_seasonal_d   non_seasonal_q  has_drift  log_likelihood           AIC     variance ...
# 1         Central Park West & W 72 St               0               1                5      False    -1966.449243   3944.898487  1215.689281 ...
# 8            Central Park W & W 96 St               0               0                5      False     -274.459923    562.919847   655.776577 ...
# 9        Central Park West & W 102 St               0               0                0      False     -226.639918    457.279835    258.83582 ...
# 11        Central Park West & W 76 St               1               1                2      False    -1700.456924   3408.913848   383.254161 ...
# 4   Grand Army Plaza & Central Park S               0               1                5      False    -5507.553498  11027.106996   624.138741 ...

The start_station_name column identifies the input data column for which time series were created. This is the column that you specified with the time_series_id_col option when creating the model.

The non_seasonal_p, non_seasonal_d, non_seasonal_q, and has_drift output columns define an ARIMA model in the training pipeline. The log_likelihood, AIC, and varianceoutput columns are relevant to the ARIMA model fitting process.The fitting process determines the best ARIMA model by using the auto.ARIMA algorithm, one for each time series.

The auto.ARIMA algorithm uses the KPSS test to determine the best value for non_seasonal_d, which in this case is 1. When non_seasonal_d is 1, the auto.ARIMA algorithm trains 42 different candidate ARIMA models in parallel. In this example, all 42 candidate models are valid, so the output contains 42 rows, one for each candidate ARIMA model; in cases where some of the models aren't valid, they are excluded from the output. These candidate models are returned in ascending order by AIC. The model in the first row has the lowest AIC, and is considered as the best model. This best model is saved as the final model and is used when you forecast data, evaluate the model, and inspect the model's coefficients as shown in the following steps.

The seasonal_periods column contains information about the seasonal pattern identified in the time series data. Each time series can have different seasonal patterns. For example, from the figure, you can see that one time series has a yearly pattern, while others don't.

The has_holiday_effect, has_spikes_and_dips, and has_step_changes columns are only populated when decompose_time_series=TRUE. These columns also reflect information about the input time series data, and are not related to the ARIMA modeling. These columns also have the same values across all output rows.

Inspect the model's coefficients

SQL

Inspect the time series model's coefficients by using the ML.ARIMA_COEFFICIENTS function.

Follow these steps to retrieve the model's coefficients:

In the Google Cloud console, go to the BigQuery page.

Go to BigQuery
In the query editor, paste in the following query and click Run:
```
SELECT
*
FROM
ML.ARIMA_COEFFICIENTS(MODEL `bqml_tutorial.nyc_citibike_arima_model_group`);
```
The query takes less than a second to complete. The results should look similar to the following:

For more information about the output columns, see ML.ARIMA_COEFFICIENTS function.

BigQuery DataFrames

Inspect the time series model's coefficients by using the coef_ function.

To authenticate to BigQuery, set up Application Default Credentials. For more information, see Set up ADC for a local development environment.

coef = model.coef_
print(coef.peek())

# Expected output:
#    start_station_name                                              ar_coefficients                                   ma_coefficients intercept_or_drift
# 5    Central Park West & W 68 St                                                [] [-0.41014089  0.21979212 -0.59854213 -0.251438...                0.0
# 6         Central Park S & 6 Ave                                                [] [-0.71488957 -0.36835772  0.61008532  0.183290...                0.0
# 0    Central Park West & W 85 St                                                [] [-0.39270166 -0.74494638  0.76432596  0.489146...                0.0
# 3    W 82 St & Central Park West                         [-0.50219511 -0.64820817]             [-0.20665325  0.67683137 -0.68108631]                0.0
# 11  W 106 St & Central Park West [-0.70442887 -0.66885553 -0.25030325 -0.34160669]                                                []                0.0

The start_station_name column identifies the input data column for which time series were created. This is the column that you specified in the time_series_id_col option when creating the model.

The ar_coefficients output column shows the model coefficients of the autoregressive (AR) part of the ARIMA model. Similarly, the ma_coefficients output column shows the model coefficients of the moving-average (MA) part of the ARIMA model. Both of these columns contain array values, whose lengths are equal to non_seasonal_p and non_seasonal_q, respectively. The intercept_or_drift value is the constant term in the ARIMA model.

Use the model to forecast data

SQL

Forecast future time series values by using the ML.FORECAST function.

In the following GoogleSQL query, the STRUCT(3 AS horizon, 0.9 AS confidence_level) clause indicates that the query forecasts 3 future time points, and generates a prediction interval with a 90% confidence level.

Follow these steps to forecast data with the model:

In the Google Cloud console, go to the BigQuery page.

Go to BigQuery

In the query editor, paste in the following query and click Run:

SELECT
*
FROM
ML.FORECAST(MODEL `bqml_tutorial.nyc_citibike_arima_model_group`,
 STRUCT(3 AS horizon, 0.9 AS confidence_level))

Click Run.

The query takes less than a second to complete. The results should look like the following:

For more information about the output columns, see ML.FORECAST function.

BigQuery DataFrames

Forecast future time series values by using the predict function.

To authenticate to BigQuery, set up Application Default Credentials. For more information, see Set up ADC for a local development environment.

prediction = model.predict(horizon=3, confidence_level=0.9)

print(prediction.peek())
# Expected output:
#            forecast_timestamp                             start_station_name  forecast_value  standard_error  confidence_level ...
# 4   2016-10-01 00:00:00+00:00                         Central Park S & 6 Ave      302.377201       32.572948               0.9 ...
# 14  2016-10-02 00:00:00+00:00  Central Park North & Adam Clayton Powell Blvd      263.917567       45.284082               0.9 ...
# 1   2016-09-25 00:00:00+00:00                    Central Park West & W 85 St      189.574706       39.874856               0.9 ...
# 20  2016-10-02 00:00:00+00:00                    Central Park West & W 72 St      175.474862       40.940794               0.9 ...
# 12  2016-10-01 00:00:00+00:00                   W 106 St & Central Park West        63.88163       18.088868               0.9 ...

The first column, start_station_name, annotates the time series that each time series model is fitted against. Each start_station_name has three rows of forecasted results, as specified by the horizon value.

For each start_station_name, the output rows are in chronological order by the forecast_timestamp column value. In time series forecasting, the prediction interval, as represented by the prediction_interval_lower_bound and prediction_interval_upper_bound column values, is as important as the forecast_value column value. The forecast_value value is the middle point of the prediction interval. The prediction interval depends on the standard_error and confidence_level column values.

Explain the forecasting results

SQL

You can get explainability metrics in addition to forecast data by using the ML.EXPLAIN_FORECAST function. The ML.EXPLAIN_FORECAST function forecasts future time series values and also returns all the separate components of the time series. If you just want to return forecast data, use the ML.FORECAST function instead, as shown in Use the model to forecast data.

The STRUCT(3 AS horizon, 0.9 AS confidence_level) clause used in the ML.EXPLAIN_FORECAST function indicates that the query forecasts 3 future time points and generates a prediction interval with 90% confidence.

Follow these steps to explain the model's results:

In the Google Cloud console, go to the BigQuery page.

Go to BigQuery
In the query editor, paste in the following query and click Run:
```
SELECT
*
FROM
ML.EXPLAIN_FORECAST(MODEL `bqml_tutorial.nyc_citibike_arima_model_group`,
 STRUCT(3 AS horizon, 0.9 AS confidence_level));
```
The query takes less than a second to complete. The results should look like the following:

The first thousands rows returned are all history data. You must scroll through the results to see the forecast data.

The output rows are ordered first by start_station_name, then chronologically by the time_series_timestamp column value. In time series forecasting, the prediction interval, as represented by the prediction_interval_lower_bound and prediction_interval_upper_bound column values, is as important as the forecast_value column value. The forecast_value value is the middle point of the prediction interval. The prediction interval depends on the standard_error and confidence_level column values.

For more information about the output columns, see ML.EXPLAIN_FORECAST.

BigQuery DataFrames

You can get explainability metrics in addition to forecast data by using the predict_explain function. The predict_explain function forecasts future time series values and also returns all the separate components of the time series. If you just want to return forecast data, use the predict function instead, as shown in Use the model to forecast data.

The horizon=3, confidence_level=0.9 clause used in the predict_explain function indicates that the query forecasts 3 future time points and generates a prediction interval with 90% confidence.

To authenticate to BigQuery, set up Application Default Credentials. For more information, see Set up ADC for a local development environment.

explain = model.predict_explain(horizon=3, confidence_level=0.9)

print(explain.peek(5))
# Expected output:
#   time_series_timestamp	        start_station_name	            time_series_type	    time_series_data	    time_series_adjusted_data	    standard_error	    confidence_level	    prediction_interval_lower_bound	    prediction_interval_upper_bound	    trend	    seasonal_period_yearly	    seasonal_period_quarterly	    seasonal_period_monthly	    seasonal_period_weekly	    seasonal_period_daily	    holiday_effect	    spikes_and_dips	    step_changes	    residual
# 0	2013-07-01 00:00:00+00:00	Central Park S & 6 Ave	                history	                  69.0	                   154.168527	              32.572948	             <NA>	                        <NA>	                            <NA>	                 0.0	          35.477484	                       <NA>	                        <NA>	                  -28.402102	                 <NA>	                <NA>	               0.0	         -85.168527	        147.093145
# 1	2013-07-01 00:00:00+00:00	Grand Army Plaza & Central Park S	    history	                  79.0	                      79.0	                  24.982769	             <NA>	                        <NA>	                            <NA>	                 0.0	          43.46428	                       <NA>	                        <NA>	                  -30.01599	                     <NA>	                <NA>	               0.0	            0.0	             65.55171
# 2	2013-07-02 00:00:00+00:00	Central Park S & 6 Ave	                history	                  180.0	                   204.045651	              32.572948	             <NA>	                        <NA>	                            <NA>	              147.093045	      72.498327	                       <NA>	                        <NA>	                  -15.545721	                 <NA>	                <NA>	               0.0	         -85.168527	         61.122876
# 3	2013-07-02 00:00:00+00:00	Grand Army Plaza & Central Park S	    history	                  129.0	                    99.556269	              24.982769	             <NA>	                        <NA>	                            <NA>	               65.551665	      45.836432	                       <NA>	                        <NA>	                  -11.831828	                 <NA>	                <NA>	               0.0	            0.0	             29.443731
# 4	2013-07-03 00:00:00+00:00	Central Park S & 6 Ave	                history	                  115.0	                   205.968236	              32.572948	             <NA>	                        <NA>	                            <NA>	               191.32754	      59.220766	                       <NA>	                        <NA>	                  -44.580071	                 <NA>	                <NA>	               0.0	         -85.168527	        -5.799709

The output rows are ordered first by time_series_timestamp, then chronologically by the start_station_name column value. In time series forecasting, the prediction interval, as represented by the prediction_interval_lower_bound and prediction_interval_upper_bound column values, is as important as the forecast_value column value. The forecast_value value is the middle point of the prediction interval. The prediction interval depends on the standard_error and confidence_level column values.

Forecast multiple time series with an ARIMA_PLUS univariate model Stay organized with collections Save and categorize content based on your preferences.

Create a dataset

Console

bq

API

BigQuery DataFrames

Visualize the input data

SQL

BigQuery DataFrames

Create the time series model

SQL

BigQuery DataFrames

Evaluate the model

SQL

BigQuery DataFrames

Inspect the model's coefficients

SQL

BigQuery DataFrames

Use the model to forecast data

SQL

BigQuery DataFrames

Explain the forecasting results

SQL

BigQuery DataFrames

Forecast multiple time series with an ARIMA_PLUS univariate model