series_dbl_exp_smoothing_fl()

Applies to: ✅ Microsoft Fabric ✅ Azure Data Explorer ✅ Azure Monitor ✅ Microsoft Sentinel

Applies a double exponential smoothing filter on a series.

The function series_dbl_exp_smoothing_fl() is a user-defined function (UDF) that takes an expression containing a dynamic numerical array as input and applies a double exponential smoothing filter. When there is trend in the series, this function is superior to the series_exp_smoothing_fl() function, which implements a basic exponential smoothing filter.

Syntax

series_dbl_exp_smoothing_fl(y_series [, alpha [, beta ]])

Learn more about syntax conventions.

Parameters

Name	Type	Required	Description
y_series	dynamic	✔️	An array of numeric values.
alpha	real		A value in the range [0-1] that specifies the weight of the last point vs. the weight of the previous points, which is 1 - alpha. The default is 0.5.
beta	real		A value in the range [0-1] that specifies the weight of the last slope vs. the weight of the previous slopes, which is 1 - beta. The default is 0.5.

Function definition

You can define the function by either embedding its code as a query-defined function, or creating it as a stored function in your database, as follows:

Query-defined

Define the function using the following let statement. No permissions are required.

Important

A let statement can't run on its own. It must be followed by a tabular expression statement. To run a working example of series_dbl_exp_smoothing_fl(), see Example.

let series_dbl_exp_smoothing_fl = (y_series:dynamic, alpha:double=0.5, beta:double=0.5)
{
    series_iir(y_series, pack_array(alpha, alpha*(beta-1)), pack_array(1, alpha*(1+beta)-2, 1-alpha))
};
// Write your query to use the function here.

Stored

Define the stored function once using the following .create function. Database User permissions are required.

Important

You must run this code to create the function before you can use the function as shown in the Example.

.create-or-alter function with (folder = "Packages\\Series", docstring = "Double exponential smoothing for a series")
series_dbl_exp_smoothing_fl(y_series:dynamic, alpha:double=0.5, beta:double=0.5)
{
    series_iir(y_series, pack_array(alpha, alpha*(beta-1)), pack_array(1, alpha*(1+beta)-2, 1-alpha))
}

Example

Query-defined

To use a query-defined function, invoke it after the embedded function definition.

Run the query

let series_dbl_exp_smoothing_fl = (y_series:dynamic, alpha:double=0.5, beta:double=0.5)
{
    series_iir(y_series, pack_array(alpha, alpha*(beta-1)), pack_array(1, alpha*(1+beta)-2, 1-alpha))
};
range x from 1 to 50 step 1
| extend y = x + rand()*10
| summarize x = make_list(x), y = make_list(y)
| extend dbl_exp_smooth_y = series_dbl_exp_smoothing_fl(y, 0.2, 0.4) 
| render linechart

Stored

Important

For this example to run successfully, you must first run the Function definition code to store the function.

range x from 1 to 50 step 1
| extend y = x + rand()*10
| summarize x = make_list(x), y = make_list(y)
| extend dbl_exp_smooth_y = series_dbl_exp_smoothing_fl(y, 0.2, 0.4) 
| render linechart

Output