Exponential Smoothing Forecast (Space Time Pattern Mining)


Forecasts the values of each location of a space-time cube using the Holt-Winters exponential smoothing method by decomposing the time series at each location cube into seasonal and trend components.

Learn more about how Exponential Smoothed Forecasting works


Exponential Smoothing Forecast tool illustration
The Exponential Smoothing Forecast tool is used to predict the values of future time steps.


  • This tool accepts netCDF files created by the Create Space Time Cube By Aggregating Points, Create Space Time Cube From Defined Features, and Create Space Time Cube from Multidimensional Raster Layer tools.

  • Compared to other forecasting tools in the Time Series Forecasting toolset, this tool is recommended for data that has moderate trends and strong seasonal behavior. When using the exponential smoothing model, it is assumed that the seasonal behavior and the trend can be separated, so the model is most effective for data with a trend that changes gradually and follows consistent seasonal patterns over time.

  • Multiple forecasted space-time cubes can be compared and merged using the Evaluate Forecasts By Location tool. This allows you to create multiple forecast cubes using different forecasting tools and parameters, and the tool will identify the best forecast for each location using either Forecast root mean square error (RMSE) or Validation RMSE.

  • For each location in the Input Space Time Cube parameter, the tool builds two models that serve different purposes.

    • Forecast model—This model is used to forecast values of the space-time cube by performing exponential smoothing to the values of the time series and extending this smoothing to future time steps. The fit of the forecast model to the values of the space-time cube is measured by the Forecast RMSE value.
    • Validation model—This model is used to validate the forecast model and test how accurately it can forecast values. If a number greater than 0 is specified for the Number of Time Steps to Exclude for Validation parameter, this model is fitted to the time steps that were included and is used to forecast the values of the time steps that were excluded. This allows you to see how well the model can forecast values. The fit of the forecasted values to the excluded values is measured by the Validation RMSE value.

    Learn more about the forecast model, validation model, and RMSE statistics

  • The Output Features parameter values will be added to the Contents pane with rendering based on the final forecasted time step.

  • This tool creates geoprocessing messages and pop-up charts to help you understand and visualize the forecast results. The messages contain information about the structure of the space-time cube and summary statistics of the RMSE values and season lengths. Clicking a feature using the Explore navigation tool displays a line chart in the Pop-up pane showing the values of the space-time cube, fitted forest values, forecasted values, and confidence bounds for that location.

  • The Outlier Option parameter can be used to detect statistically significant outliers in the time series values at each location.

    Learn more about detecting time series outliers

  • Deciding how many time steps to exclude for validation is an important choice. The more time steps are excluded, the fewer time steps remain to estimate the validation model. However, if too few time steps are excluded, the Validation RMSE will be estimated using a small amount of data and may be misleading. It is recommended that you exclude as many time steps as possible while maintaining sufficient time steps to estimate the validation model. It is also suggested that you withhold at least as many time steps for validation as the number of time steps you intend to forecast, if your space-time cube has enough time steps to allow this.

  • The exponential smoothing model assumes that all components are additive and linear. Damped trend is always used, and additive seasonality is supported but not required. Confidence intervals are constructed under the assumption that the residuals are additive and normally distributed.

    Learn more about the components of the exponential smoothing model


arcpy.stpm.ExponentialSmoothingForecast(in_cube, analysis_variable, output_features, {output_cube}, {number_of_time_steps_to_forecast}, season_length, {number_for_validation}, {outlier_option}, {level_of_confidence}, maximum_number_of_outliers)
ParameterExplanationData Type

The netCDF cube containing the variable to forecast to future time steps. This file must have an .nc file extension and must have been created using the Create Space Time Cube By Aggregating Points, Create Space Time Cube From Defined Locations, or Create Space Time Cube From Multidimensional Raster Layer tool.


The numeric variable in the netCDF file that will be forecasted to future time steps.


The output feature class of all locations in the space-time cube with forecasted values stored as fields. The layer displays the forecast for the final time step and contains pop-up charts showing the time series, forecasts, and 90 percent confidence bounds for each location.

Feature Class

A new space-time cube (.nc file) containing the values of the input space-time cube with the forecasted time steps appended. The Visualize Space Time Cube in 3D tool can be used to see all of the observed and forecasted values simultaneously.


A positive integer specifying the number of time steps to forecast. This value cannot be larger than 50 percent of the total time steps in the input space-time cube. The default value is one time step.


The number of time steps corresponding to one season at each location. If there are multiple seasons in the data, it is recommended that you use the longest season to produce the most reliable result. If no value is specified, a season length will be estimated by the tool at each location using a spectral density function.


The number of time steps at the end of each time series to exclude for validation. The default value is 10 percent (rounded down) of the number of input time steps, and this value cannot be larger than 25 percent of the number of time steps. Provide the value 0 to not exclude any time steps.


Specifies whether statistically significant time series outliers will be identified.

  • NONEOutliers will not be identified. This is the default.
  • IDENTIFYOutliers will be identified using the Generalized ESD test.

Specifies the confidence level for the test for time series outliers.

  • 90%The confidence level for the test is 90 percent. This is the default.
  • 95%The confidence level for the test is 95 percent.
  • 99%The confidence level for the test is 99 percent.

The maximum number of time steps that can be declared outliers for each location. The default value corresponds to 5 percent (rounded down) of the number of time steps of the input space-time cube (a value of at least 1 will always be used). This value cannot exceed 20 percent of the number of time steps.


Code sample

ExponentialSmoothingForecast example 1 (Python window)

The following Python script demonstrates how to use the ExponentialSmoothingForecast tool.

import arcpy
arcpy.env.workspace = "C:/Analysis"

# Forecast four time steps using exponential smoothing.
                                        "outForecastCube.nc", 4, 2, 5)
ExponentialSmoothingForecast example 2 (stand-alone script)

The following Python script demonstrates how to use the ExponentialSmoothingForecast tool to forecast temperature.

# Forecast temperature using exponential smoothing.

# Import system modules.
import arcpy

# Set property to overwrite existing output.
arcpy.env.overwriteOutput = True

# Set workspace.
workspace = r"C:\Analysis"
arcpy.env.workspace = workspace

# Forecast three time steps.
                                        "outForecastCube.nc", 3, 2, 5,
                                        "IDENTIFY", "90%", 4)

# Create a feature class visualizing the forecasts.
arcpy.stpm.VisualizeSpaceTimeCube3D("outForecastCube.nc", "Temp_NONE_ZEROS", 
                                    "VALUE", "Analysis.gdb/ForecastsFC")

Licensing information

  • Basic: Yes
  • Standard: Yes
  • Advanced: Yes

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