Label  Explanation  Data Type 
Input Space Time Cube
 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.  File 
Analysis Variable

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

The output feature class of all locations in the spacetime cube with forecasted values stored as fields. The layer displays the forecast for the final time step and contains popup charts showing the time series, forecasts, and 90 percent confidence bounds for each location.  Feature Class 
Output Space Time Cube
(Optional) 
A new spacetime cube (.nc file) containing the values of the input spacetime 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.  File 
Number of Time Steps to Forecast
(Optional) 
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 spacetime cube. The default value is one time step.  Long 
Time Step Window
(Optional)  The number of previous time steps that will be used when training the model. If the data displays seasonality (repeating cycles), provide the number of time steps corresponding to one season. This value cannot be larger than onethird of the number of time steps in the input spacetime cube. If no value is provided, a time window is estimated for each location using a spectral density function.  Long 
Number of Time Steps to Exclude for Validation
(Optional)  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.  Long 
Number of Trees
(Optional)  The number of trees that will be created in the forest model. More trees generally result in more accurate model prediction, but the model will take longer to calculate. The default number of trees is 100, and the value must be at least 1 and not greater than 1,000.  Long 
Minimum Leaf Size
(Optional)  The minimum number of observations that are required to keep a leaf (that is, the terminal node on a tree without further splits). For very large data, increasing this number will decrease the run time of the tool.  Long 
Maximum Tree Depth
(Optional) 
The maximum number of splits that will be made down a tree. Using a large maximum depth, more splits will be created, which may increase the chances of overfitting the model. If no value is provided, a value will be identified by the tool based on the number of trees created by the model and the size of the time step window.  Long 
Percentage of Training Available per Tree (%)
(Optional)  The percent of training data that will be used to fit the forecast model. The training data consists of associated explanatory and dependent variables constructed using time windows. All remaining training data will be used to optimize the parameters of the forecast model. The default is 100 percent.  Long 
Forecast Approach
(Optional)  Specifies how the explanatory and dependent variables will be represented when training the forest model at each location. To train the forest model that will be used to forecast, sets of explanatory and dependent variables must be created using time windows. Use this parameter to specify whether these variables will be linearly detrended and whether the dependent variable will be represented by its raw value or by the residual of a linear regression model. This linear regression model uses all time steps within a time window as explanatory variables and uses the following time step as the dependent variable. The residual is calculated by subtracting the predicted value based on linear regression from the raw value of the dependent variable.
 String 
Outlier Option
(Optional)  Specifies whether statistically significant time series outliers will be identified.
 String 
Level of Confidence (Optional)  Specifies the confidence level for the test for time series outliers.
 String 
Maximum Number of Outliers
 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 spacetime cube (a value of at least 1 will always be used). This value cannot exceed 20 percent of the number of time steps.  Long 
Other Variables
(Optional)  Other variables of the input spacetime cube that will be used as explanatory variables to improve the forecasts.  String 
Importance Threshold (%)
(Optional)  The percent of factors deemed most important for forecasting the analysis variable. For example, if the value is 20, the top 20 percent of factors for each location will be included in the importance table. Each variable (the analysis variable and each explanatory variable) is represented as a factor once for each time step in the time step window, so the number of factors at each location is the length of the time window multiplied by the number of variables. The number of factors is multiplied by the importance threshold to determine the number of important factors at each location. The default is 10, and the value must be an integer between 1 and 100.  Long 
Output Importance Table
(Optional)  The output table that will contain the most important factors at each location. Each location of the spacetime cube will be represented as a row in the table with fields containing the name of the variable and associated time lag of each important factor for the location. The table will include a chart displaying the count of most important factors across all locations broken down by time lag. The chart allows you to visualize lagged effects between the explanatory variables and the variable being forecasted.  Table 
Summary
Forecasts the values of each location of a spacetime cube using an adaptation of Leo Breiman's random forest algorithm. The forest regression model is trained using time windows on each location of the spacetime cube.
Illustration
Usage
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 the most complex but includes the fewest assumptions about the data. It is recommended for time series with complicated shapes and trends that are difficult to model with simple mathematical functions or when the assumptions of other methods are not satisfied. It is also recommended if your spacetime cube has other variables that are related to the variable being forecasted. These variables can be included as explanatory variables to improve the forecast.
Multiple forecasted spacetime 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 value, the tool builds two models that serve different purposes.
 Forecast model—This model is used to forecast values of the spacetime cube by building a forest using the values of the time series and using this forest to forecast the values of future time steps. The fit of the forecast model to the values of the spacetime 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 built using 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 popup charts to help you understand and visualize the forecast results. The messages contain information about the structure of the spacetime cube and summary statistics of the RMSE values and season lengths. Click a feature using the Explore navigation tool to display a line chart in the Popup pane showing the values of the spacetime cube, fitted forest values, forecasted values, and confidence bounds for that location.
You can include explanatory variables to improve the forecasts using the Other Variables parameter. If any other variables are provided, the forecast model is a multivariate forestbased forecast. Each explanatory variables is converted to timelagged factors within each time window that are used to train the forest model. This allows you to estimate any lagged (delayed) effect between the explanatory variables and the analysis variable. For example, a rise in the number of hospitalizations during a pandemic may predict the number of deaths 14 days later, whereas the number of hospitalizations may poorly predict the number of deaths in the next 3 days. The number of time lags is equal to the value of the Time Step Window parameter, so the time window must be wider than any lagged effect you want to capture.
The Output Importance Table parameter creates a table displaying the most important factors at each location and includes a Time Lag Importance bar chart that displays counts of the most important factors across all locations, broken down by time lag within the time window. This allows you to see which variables were important in predicting the value of the analysis variable, as well as to visualize the associated lag when the factor was most important. For example, if the number of hospitalizations is associated with the number of deaths 14 days later, the time step window should be at least 14 days, and you should observe a large count of hospitalizations being important approximately 14 days before the end of the time window.
The number of factors deemed important at each location depends on the Importance Threshold parameter. For example, if a value of 15 is used, the top 15 percent of factors for each location will be included in the table and chart.
The Outlier Option parameter can be used to detect statistically significant outliers in the time series values at each location.
If you choose the Identify outliers option for the Outlier Option parameter, it is recommended that you provide a value for the Time Step Window parameter rather than leaving the parameter empty and estimating a different time step window at each location. For each location, the forest model uses the time steps in the first time step window to train the forecast model, and outliers are only detected for the remaining time steps. If different locations exclude different numbers of time steps for training, summary statistics such as the mean, minimum, and maximum number of outliers per time step or per location may be misleading.
If any explanatory variables are included in the Other Variables parameter, only the Build model by value option is available for the Forecast Approach parameter. Additionally, the processing time will increase for every explanatory variable that is included.
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 spacetime cube has enough time steps to allow this.
Parameters
arcpy.stpm.ForestBasedForecast(in_cube, analysis_variable, output_features, {output_cube}, {number_of_time_steps_to_forecast}, {time_window}, {number_for_validation}, {number_of_trees}, {minimum_leaf_size}, {maximum_depth}, {sample_size}, {forecast_approach}, {outlier_option}, {level_of_confidence}, maximum_number_of_outliers, {other_variables}, {importance_threshold}, {output_importance_table})
Name  Explanation  Data Type 
in_cube  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.  File 
analysis_variable 
The numeric variable in the netCDF file that will be forecasted to future time steps.  String 
output_features 
The output feature class of all locations in the spacetime cube with forecasted values stored as fields. The layer displays the forecast for the final time step and contains popup charts showing the time series, forecasts, and 90 percent confidence bounds for each location.  Feature Class 
output_cube (Optional) 
A new spacetime cube (.nc file) containing the values of the input spacetime 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.  File 
number_of_time_steps_to_forecast (Optional) 
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 spacetime cube. The default value is one time step.  Long 
time_window (Optional)  The number of previous time steps that will be used when training the model. If the data displays seasonality (repeating cycles), provide the number of time steps corresponding to one season. This value cannot be larger than onethird of the number of time steps in the input spacetime cube. If no value is provided, a time window is estimated for each location using a spectral density function.  Long 
number_for_validation (Optional)  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.  Long 
number_of_trees (Optional)  The number of trees that will be created in the forest model. More trees generally result in more accurate model prediction, but the model will take longer to calculate. The default number of trees is 100, and the value must be at least 1 and not greater than 1,000.  Long 
minimum_leaf_size (Optional)  The minimum number of observations that are required to keep a leaf (that is, the terminal node on a tree without further splits). For very large data, increasing this number will decrease the run time of the tool.  Long 
maximum_depth (Optional) 
The maximum number of splits that will be made down a tree. Using a large maximum depth, more splits will be created, which may increase the chances of overfitting the model. If no value is provided, a value will be identified by the tool based on the number of trees created by the model and the size of the time step window.  Long 
sample_size (Optional)  The percent of training data that will be used to fit the forecast model. The training data consists of associated explanatory and dependent variables constructed using time windows. All remaining training data will be used to optimize the parameters of the forecast model. The default is 100 percent.  Long 
forecast_approach (Optional)  Specifies how the explanatory and dependent variables will be represented when training the forest model at each location. To train the forest model that will be used to forecast, sets of explanatory and dependent variables must be created using time windows. Use this parameter to specify whether these variables will be linearly detrended and whether the dependent variable will be represented by its raw value or by the residual of a linear regression model. This linear regression model uses all time steps within a time window as explanatory variables and uses the following time step as the dependent variable. The residual is calculated by subtracting the predicted value based on linear regression from the raw value of the dependent variable. Learn more about the Forecast Approach parameter
 String 
outlier_option (Optional)  Specifies whether statistically significant time series outliers will be identified.
 String 
level_of_confidence (Optional)  Specifies the confidence level for the test for time series outliers.
 String 
maximum_number_of_outliers  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 spacetime cube (a value of at least 1 will always be used). This value cannot exceed 20 percent of the number of time steps.  Long 
other_variables [other_variables,...] (Optional)  Other variables of the input spacetime cube that will be used as explanatory variables to improve the forecasts.  String 
importance_threshold (Optional)  The percent of factors deemed most important for forecasting the analysis variable. For example, if the value is 20, the top 20 percent of factors for each location will be included in the importance table. Each variable (the analysis variable and each explanatory variable) is represented as a factor once for each time step in the time step window, so the number of factors at each location is the length of the time window multiplied by the number of variables. The number of factors is multiplied by the importance threshold to determine the number of important factors at each location. The default is 10, and the value must be an integer between 1 and 100.  Long 
output_importance_table (Optional)  The output table that will contain the most important factors at each location. Each location of the spacetime cube will be represented as a row in the table with fields containing the name of the variable and associated time lag of each important factor for the location. The table will include a chart displaying the count of most important factors across all locations broken down by time lag. The chart allows you to visualize lagged effects between the explanatory variables and the variable being forecasted.  Table 
Code sample
The following Python script demonstrates how to use the ForestBasedForecast function.
import arcpy
arcpy.env.workspace = "C:/Analysis"
# Forecast four time steps using a random forest with detrending.
arcpy.stpm.ForestBasedForecast("CarTheft.nc","Cars_NONE_ZEROS",
"Analysis.gdb/Forecasts", "outForecastCube.nc"
4, 3, 5, 100, "", "", 100, "VALUE_DETREND")
The following Python script demonstrates how to use the ForestBasedForecast function to forecast counts of car theft.
# Forecast change in car thefts using a random forest.
# Import system modules.
import arcpy
# Set property to overwrite existing output, by default.
arcpy.env.overwriteOutput = True
# Set workspace.
workspace = r"C:\Analysis"
arcpy.env.workspace = workspace
# Forecast three time steps using a random forest based on change.
arcpy.stpm.ForestBasedForecast("CarTheft.nc","Cars_NONE_ZEROS",
"Analysis.gdb/Forecasts", "outForecastCube.nc"
4, 3, 5, 100, "", "", 100, "CHANGE",
"IDENTIFY", "90%", 4)
# Create a feature class visualizing the forecasts.
arcpy.stpm.VisualizeSpaceTimeCube3D("outForecastCube.nc", "Cars_NONE_ZEROS",
"VALUE", "Analysis.gdb/ForecastsFC")
Licensing information
 Basic: Yes
 Standard: Yes
 Advanced: Yes
Related topics
 An overview of the Space Time Pattern Mining toolbox
 An overview of the Time Series Forecasting toolset
 Curve Fit Forecast
 Exponential Smoothing Forecast
 Evaluate Forecasts By Location
 Understanding outliers in time series analysis
 How Forestbased Forecast works
 Forestbased Classification and Regression
 How Forestbased Classification and Regression works
 Find a geoprocessing tool