Forecast a single time series with a univariate model

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

This tutorial forecasts a single time series. Forecasted values are calculated once for each time point in the input data.

This tutorial uses data from the public bigquery-public-data.google_analytics_sample.ga_sessions sample table. This table contains obfuscated ecommerce data from the Google Merchandise Store.

Objectives

This tutorial guides you through completing the following tasks:

• Creating a time series model to forecast site traffic by using the CREATE MODEL statement.
• Evaluating the autoregressive integrated moving average (ARIMA) information in the model by using the ML.ARIMA_EVALUATE function.
• Inspecting the model coefficients by using the ML.ARIMA_COEFFICIENTS function.
• Retrieving the forecasted site traffic information from the model by using the ML.FORECAST function.
• Retrieving components of the time series, such as seasonality and trend, by using the ML.EXPLAIN_FORECAST function. You can inspect these time series components in order to explain the forecasted values.

Costs

This tutorial uses billable components of Google Cloud, including the following:

• BigQuery
• BigQuery ML

For more information about BigQuery costs, see the BigQuery pricing page.

For more information about BigQuery ML costs, see BigQuery ML pricing.

Before you begin

1. Sign in to your Google Cloud account. If you're new to Google Cloud, create an account to evaluate how our products perform in real-world scenarios. New customers also get $300 in free credits to run, test, and deploy workloads.

2. In the Google Cloud console, on the project selector page, select or create a Google Cloud project.

   Note: If you don't plan to keep the resources that you create in this procedure, create a project instead of selecting an existing project. After you finish these steps, you can delete the project, removing all resources associated with the project.

   Go to project selector

3. Make sure that billing is enabled for your Google Cloud project.

4. In the Google Cloud console, on the project selector page, select or create a Google Cloud project.

   Note: If you don't plan to keep the resources that you create in this procedure, create a project instead of selecting an existing project. After you finish these steps, you can delete the project, removing all resources associated with the project.

   Go to project selector

5. Make sure that billing is enabled for your Google Cloud project.

6. BigQuery is automatically enabled in new projects. To activate BigQuery in a pre-existing project, go to

   Enable the BigQuery API.

   Enable the API

Required Permissions

• To create the dataset, you need the bigquery.datasets.create IAM permission.

• To create the connection resource, you need the following permissions:

  • bigquery.connections.create
  • bigquery.connections.get

• To create the model, you need the following permissions:

  • bigquery.jobs.create
  • bigquery.models.create
  • bigquery.models.getData
  • bigquery.models.updateData
  • bigquery.connections.delegate

• To run inference, you need the following permissions:

  • bigquery.models.getData
  • bigquery.jobs.create

For more information about IAM roles and permissions in BigQuery, see Introduction to IAM.

Create a dataset

Create a BigQuery dataset to store your ML model:

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

   Go to the BigQuery page

2. In the Explorer pane, click your project name.

3. Click View actions > Create dataset.

   

4. 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).

     The public datasets are stored in the US multi-region. For simplicity, store your dataset in the same location.

   • Leave the remaining default settings as they are, and click Create dataset.

     

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.

Follow these steps to visualize the time series data:

SQL

In the following GoogleSQL query, the SELECT statement parses the date column from the input table to the TIMESTAMP type and renames it to parsed_date, and uses the SUM(...) clause and the GROUP BY date clause to create a daily totals.visits value.

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

   Go to BigQuery

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

   SELECT
   PARSE_TIMESTAMP("%Y%m%d", date) AS parsed_date,
   SUM(totals.visits) AS total_visits
   FROM
   `bigquery-public-data.google_analytics_sample.ga_sessions_*`
   GROUP BY date;

   1. 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.

   2. In the Looker Studio, click Insert > Time series chart.

   3. In the Chart pane, choose the Setup tab.

   4. In the Metric section, add the total_visits field, and remove the default Record Count metric. The resulting chart looks similar to the following:

      

      Looking at the chart, you can see that the input time series has a weekly seasonal pattern.

      Note: For more information about Looker Studio support, see Looker Support integrations with Google Cloud.

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 authentication for a local development environment.

import bigframes.pandas as bpd

# Start by loading the historical data from BigQuerythat you want to analyze and forecast.
# This clause indicates that you are querying the ga_sessions_* tables in the google_analytics_sample dataset.
# Read and visualize the time series you want to forecast.
df = bpd.read_gbq("bigquery-public-data.google_analytics_sample.ga_sessions_*")
parsed_date = bpd.to_datetime(df.date, format="%Y%m%d", utc=True)
visits = df["totals"].struct.field("visits")
total_visits = visits.groupby(parsed_date).sum()

# Expected output: total_visits.head()
# date
# 2016-08-01 00:00:00+00:00    1711
# 2016-08-02 00:00:00+00:00    2140
# 2016-08-03 00:00:00+00:00    2890
# 2016-08-04 00:00:00+00:00    3161
# 2016-08-05 00:00:00+00:00    2702
# Name: visits, dtype: Int64

total_visits.plot.line()

The result is similar to the following:

Create the time series model

Create a time series model to forecast total site visits as represented by totals.visits column, and train it on the Google Analytics 360 data.

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. The auto_arima option of the CREATE MODEL statement defaults to TRUE, so the auto.ARIMA algorithm automatically tunes the hyperparameters in the model. The algorithm fits dozens of candidate models and chooses the best model, which is the model with the lowest Akaike information criterion (AIC). The data_frequency option of the CREATE MODEL statements defaults to AUTO_FREQUENCY, so the training process automatically infers the data frequency of the input time series. 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:

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

   Go to BigQuery

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

   CREATE OR REPLACE MODEL `bqml_tutorial.ga_arima_model`
   OPTIONS
   (model_type = 'ARIMA_PLUS',
     time_series_timestamp_col = 'parsed_date',
     time_series_data_col = 'total_visits',
     auto_arima = TRUE,
     data_frequency = 'AUTO_FREQUENCY',
     decompose_time_series = TRUE
   ) AS
   SELECT
   PARSE_TIMESTAMP("%Y%m%d", date) AS parsed_date,
   SUM(totals.visits) AS total_visits
   FROM
   `bigquery-public-data.google_analytics_sample.ga_sessions_*`
   GROUP BY date;

   The query takes about 4 seconds to complete, after which the ga_arima_model model appears in the Explorer pane. Because the query uses a CREATE MODEL statement to create a model, you don't see query results.

Note: You might wonder if United States holidays have an impact on the time series. You can try setting the holiday_region option of the CREATE MODEL statement to US. Setting this option allows a more accurate modeling on holiday time points if there are any holiday patterns in the time series.

Evaluate the candidate models

Evaluate the time series models by using the ML.ARIMA_EVALUATE function. The ML.ARIMA_EVALUATE function shows you the evaluation metrics of all the candidate models evaluated during the process of automatic hyperparameter tuning.

Follow these steps to evaluate the model:

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

   Go to BigQuery

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

   SELECT
    *
   FROM
    ML.ARIMA_EVALUATE(MODEL `bqml_tutorial.ga_arima_model`);

   The results should look similar to the following:

   

   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 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 the best model. The best model is saved as the final model and is used when you call functions such as ML.FORECAST on the model

   The seasonal_periods column contains information about the seasonal pattern identified in the time series data. It has nothing to do with the ARIMA modeling, therefore it has the same value across all output rows. It reports a weekly pattern, which agrees with the results you saw if you chose to visualize the input data.

   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.

   The error_message column shows any errors that incurred during the auto.ARIMA fitting process. One possible reason for errors is when the selected non_seasonal_p, non_seasonal_d, non_seasonal_q, and has_drift columns are not able to stabilize the time series. To retrieve the error message of all the candidate models, set the show_all_candidate_models option to TRUE when you create the model.

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

Inspect the model's coefficients

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

Follow these steps to retrieve the model's coefficients:

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

   Go to BigQuery

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

   SELECT
    *
   FROM
    ML.ARIMA_COEFFICIENTS(MODEL `bqml_tutorial.ga_arima_model`);

   The results should look similar to the following:

   

   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. You saw in the output of the ML.ARIMA_EVALUATE function that the best model has a non_seasonal_p value of 2 and a non_seasonal_q value of 3. Therefore, in the ML.ARIMA_COEFFICIENTS output, the ar_coefficients value is a 2-element array and the ma_coefficients value is a 3-element array. The intercept_or_drift value is the constant term in the ARIMA model.

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

Use the model to forecast data

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

In the following GoogleSQL query, the STRUCT(30 AS horizon, 0.8 AS confidence_level) clause indicates that the query forecasts 30 future time points, and generates a prediction interval with a 80% confidence level.

Follow these steps to forecast data with the model:

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

   Go to BigQuery

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

   SELECT
    *
   FROM
    ML.FORECAST(MODEL `bqml_tutorial.ga_arima_model`,
                STRUCT(30 AS horizon, 0.8 AS confidence_level));

   The results should look similar to the following:

   

   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.

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

Explain the forecasting results

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.

Similar to the ML.FORECAST function, the STRUCT(30 AS horizon, 0.8 AS confidence_level) clause used in the ML.EXPLAIN_FORECAST function indicates that the query forecasts 30 future time points and generates a prediction interval with 80% confidence.

Follow these steps to explain the model's results:

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

   Go to BigQuery

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

   SELECT
    *
   FROM
    ML.EXPLAIN_FORECAST(MODEL `bqml_tutorial.ga_arima_model`,
      STRUCT(30 AS horizon, 0.8 AS confidence_level));

   The results should look similar to the following:

   

   The output rows are ordered chronologically by the time_series_timestamp column value.

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

   If you would like to visualize the results, you can use Looker Studio as described in the Visualize the input data section to create a chart, using the following columns as metrics:

   • time_series_data
   • prediction_interval_lower_bound
   • prediction_interval_upper_bound
   • trend
   • seasonal_period_weekly
   • step_changes

Clean up

To avoid incurring charges to your Google Cloud account for the resources used in this tutorial, either delete the project that contains the resources, or keep the project and delete the individual resources.

• You can delete the project you created.
• Or you can keep the project and delete the dataset.

Delete your dataset

Deleting your project removes all datasets and all tables in the project. If you prefer to reuse the project, you can delete the dataset you created in this tutorial:

1. If necessary, open the BigQuery page in the Google Cloud console.

   Go to the BigQuery page

2. In the navigation, click the bqml_tutorial dataset you created.

3. Click Delete dataset on the right side of the window. This action deletes the dataset, the table, and all the data.

4. In the Delete dataset dialog box, confirm the delete command by typing the name of your dataset (bqml_tutorial) and then click Delete.

Delete your project

To delete the project:

Caution: Deleting a project has the following effects:

• Everything in the project is deleted. If you used an existing project for the tasks in this document, when you delete it, you also delete any other work you've done in the project.
• Custom project IDs are lost. When you created this project, you might have created a custom project ID that you want to use in the future. To preserve the URLs that use the project ID, such as an appspot.com URL, delete selected resources inside the project instead of deleting the whole project.

If you plan to explore multiple architectures, tutorials, or quickstarts, reusing projects can help you avoid exceeding project quota limits.

1. In the Google Cloud console, go to the Manage resources page.

   Go to Manage resources

2. In the project list, select the project that you want to delete, and then click Delete.
3. In the dialog, type the project ID, and then click Shut down to delete the project.

What's next

• Learn how to forecast a single time series with a multivariate model
• Learn how to forecast multiple time series with a univariate model
• Learn how to scale a univariate model when forecasting multiple time series over many rows.
• Learn how to hierarchically forecast multiple time series with a univariate model
• For an overview of BigQuery ML, see Introduction to AI and ML in BigQuery.