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Moving Function Aggregation

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Moving Function Aggregation

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Given an ordered series of data, the Moving Function aggregation will slide a window across the data and allow the user to specify a custom script that is executed on each window of data. For convenience, a number of common functions are predefined such as min/max, moving averages, etc.

This is conceptually very similar to the Moving Average pipeline aggregation, except it provides more functionality.

Syntax

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A moving_fn aggregation looks like this in isolation:

{
    "moving_fn": {
        "buckets_path": "the_sum",
        "window": 10,
        "script": "MovingFunctions.min(values)"
    }
}

Table 13. moving_avg Parameters

Parameter Name	Description	Required
`buckets_path`	Path to the metric of interest (see `buckets_path` Syntax for more details	Required
`window`	The size of window to "slide" across the histogram.	Required
`script`	The script that should be executed on each window of data	Required

moving_fn aggregations must be embedded inside of a histogram or date_histogram aggregation. They can be embedded like any other metric aggregation:

POST /_search
{
    "size": 0,
    "aggs": {
        "my_date_histo":{                
            "date_histogram":{
                "field":"date",
                "interval":"1M"
            },
            "aggs":{
                "the_sum":{
                    "sum":{ "field": "price" } 
                },
                "the_movfn": {
                    "moving_fn": {
                        "buckets_path": "the_sum", 
                        "window": 10,
                        "script": "MovingFunctions.unweightedAvg(values)"
                    }
                }
            }
        }
    }
}

	A `date_histogram` named "my_date_histo" is constructed on the "timestamp" field, with one-day intervals
	A `sum` metric is used to calculate the sum of a field. This could be any numeric metric (sum, min, max, etc)
	Finally, we specify a `moving_fn` aggregation which uses "the_sum" metric as its input.

Moving averages are built by first specifying a histogram or date_histogram over a field. You can then optionally add numeric metrics, such as a sum, inside of that histogram. Finally, the moving_fn is embedded inside the histogram. The buckets_path parameter is then used to "point" at one of the sibling metrics inside of the histogram (see buckets_path Syntax for a description of the syntax for buckets_path.

An example response from the above aggregation may look like:

{
   "took": 11,
   "timed_out": false,
   "_shards": ...,
   "hits": ...,
   "aggregations": {
      "my_date_histo": {
         "buckets": [
             {
                 "key_as_string": "2015/01/01 00:00:00",
                 "key": 1420070400000,
                 "doc_count": 3,
                 "the_sum": {
                    "value": 550.0
                 },
                 "the_movfn": {
                    "value": null
                 }
             },
             {
                 "key_as_string": "2015/02/01 00:00:00",
                 "key": 1422748800000,
                 "doc_count": 2,
                 "the_sum": {
                    "value": 60.0
                 },
                 "the_movfn": {
                    "value": 550.0
                 }
             },
             {
                 "key_as_string": "2015/03/01 00:00:00",
                 "key": 1425168000000,
                 "doc_count": 2,
                 "the_sum": {
                    "value": 375.0
                 },
                 "the_movfn": {
                    "value": 305.0
                 }
             }
         ]
      }
   }
}

Custom user scripting

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The Moving Function aggregation allows the user to specify any arbitrary script to define custom logic. The script is invoked each time a new window of data is collected. These values are provided to the script in the values variable. The script should then perform some kind of calculation and emit a single double as the result. Emitting null is not permitted, although NaN and +/- Inf are allowed.

For example, this script will simply return the first value from the window, or NaN if no values are available:

POST /_search
{
    "size": 0,
    "aggs": {
        "my_date_histo":{
            "date_histogram":{
                "field":"date",
                "interval":"1M"
            },
            "aggs":{
                "the_sum":{
                    "sum":{ "field": "price" }
                },
                "the_movavg": {
                    "moving_fn": {
                        "buckets_path": "the_sum",
                        "window": 10,
                        "script": "return values.length > 0 ? values[0] : Double.NaN"
                    }
                }
            }
        }
    }
}

Pre-built Functions

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For convenience, a number of functions have been prebuilt and are available inside the moving_fn script context:

max()
min()
sum()
stdDev()
unweightedAvg()
linearWeightedAvg()
ewma()
holt()
holtWinters()

The functions are available from the MovingFunctions namespace. E.g. MovingFunctions.max()

max Function

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This function accepts a collection of doubles and returns the maximum value in that window. null and NaN values are ignored; the maximum is only calculated over the real values. If the window is empty, or all values are null/NaN, NaN is returned as the result.

Table 14. max(double[] values) Parameters

Parameter Name	Description
`values`	The window of values to find the maximum

POST /_search
{
    "size": 0,
    "aggs": {
        "my_date_histo":{
            "date_histogram":{
                "field":"date",
                "interval":"1M"
            },
            "aggs":{
                "the_sum":{
                    "sum":{ "field": "price" }
                },
                "the_moving_max": {
                    "moving_fn": {
                        "buckets_path": "the_sum",
                        "window": 10,
                        "script": "MovingFunctions.max(values)"
                    }
                }
            }
        }
    }
}

min Function

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This function accepts a collection of doubles and returns the minimum value in that window. null and NaN values are ignored; the minimum is only calculated over the real values. If the window is empty, or all values are null/NaN, NaN is returned as the result.

Table 15. min(double[] values) Parameters

Parameter Name	Description
`values`	The window of values to find the minimum

POST /_search
{
    "size": 0,
    "aggs": {
        "my_date_histo":{
            "date_histogram":{
                "field":"date",
                "interval":"1M"
            },
            "aggs":{
                "the_sum":{
                    "sum":{ "field": "price" }
                },
                "the_moving_min": {
                    "moving_fn": {
                        "buckets_path": "the_sum",
                        "window": 10,
                        "script": "MovingFunctions.min(values)"
                    }
                }
            }
        }
    }
}

sum Function

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This function accepts a collection of doubles and returns the sum of the values in that window. null and NaN values are ignored; the sum is only calculated over the real values. If the window is empty, or all values are null/NaN, 0.0 is returned as the result.

Table 16. sum(double[] values) Parameters

Parameter Name	Description
`values`	The window of values to find the sum of

POST /_search
{
    "size": 0,
    "aggs": {
        "my_date_histo":{
            "date_histogram":{
                "field":"date",
                "interval":"1M"
            },
            "aggs":{
                "the_sum":{
                    "sum":{ "field": "price" }
                },
                "the_moving_sum": {
                    "moving_fn": {
                        "buckets_path": "the_sum",
                        "window": 10,
                        "script": "MovingFunctions.sum(values)"
                    }
                }
            }
        }
    }
}

stdDev Function

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This function accepts a collection of doubles and average, then returns the standard deviation of the values in that window. null and NaN values are ignored; the sum is only calculated over the real values. If the window is empty, or all values are null/NaN, 0.0 is returned as the result.

Table 17. stdDev(double[] values) Parameters

Parameter Name	Description
`values`	The window of values to find the standard deviation of
`avg`	The average of the window

POST /_search
{
    "size": 0,
    "aggs": {
        "my_date_histo":{
            "date_histogram":{
                "field":"date",
                "interval":"1M"
            },
            "aggs":{
                "the_sum":{
                    "sum":{ "field": "price" }
                },
                "the_moving_sum": {
                    "moving_fn": {
                        "buckets_path": "the_sum",
                        "window": 10,
                        "script": "MovingFunctions.stdDev(values, MovingFunctions.unweightedAvg(values))"
                    }
                }
            }
        }
    }
}

The avg parameter must be provided to the standard deviation function because different styles of averages can be computed on the window (simple, linearly weighted, etc). The various moving averages that are detailed below can be used to calculate the average for the standard deviation function.

unweightedAvg Function

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The unweightedAvg function calculates the sum of all values in the window, then divides by the size of the window. It is effectively a simple arithmetic mean of the window. The simple moving average does not perform any time-dependent weighting, which means the values from a simple moving average tend to "lag" behind the real data.

null and NaN values are ignored; the average is only calculated over the real values. If the window is empty, or all values are null/NaN, NaN is returned as the result. This means that the count used in the average calculation is count of non-null,non-NaN values.

Table 18. unweightedAvg(double[] values) Parameters

Parameter Name	Description
`values`	The window of values to find the sum of

POST /_search
{
    "size": 0,
    "aggs": {
        "my_date_histo":{
            "date_histogram":{
                "field":"date",
                "interval":"1M"
            },
            "aggs":{
                "the_sum":{
                    "sum":{ "field": "price" }
                },
                "the_movavg": {
                    "moving_fn": {
                        "buckets_path": "the_sum",
                        "window": 10,
                        "script": "MovingFunctions.unweightedAvg(values)"
                    }
                }
            }
        }
    }
}

linearWeightedAvg Function

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The linearWeightedAvg function assigns a linear weighting to points in the series, such that "older" datapoints (e.g. those at the beginning of the window) contribute a linearly less amount to the total average. The linear weighting helps reduce the "lag" behind the data’s mean, since older points have less influence.

If the window is empty, or all values are null/NaN, NaN is returned as the result.

Table 19. linearWeightedAvg(double[] values) Parameters

Parameter Name	Description
`values`	The window of values to find the sum of

POST /_search
{
    "size": 0,
    "aggs": {
        "my_date_histo":{
            "date_histogram":{
                "field":"date",
                "interval":"1M"
            },
            "aggs":{
                "the_sum":{
                    "sum":{ "field": "price" }
                },
                "the_movavg": {
                    "moving_fn": {
                        "buckets_path": "the_sum",
                        "window": 10,
                        "script": "MovingFunctions.linearWeightedAvg(values)"
                    }
                }
            }
        }
    }
}

ewma Function

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The ewma function (aka "single-exponential") is similar to the linearMovAvg function, except older data-points become exponentially less important, rather than linearly less important. The speed at which the importance decays can be controlled with an alpha setting. Small values make the weight decay slowly, which provides greater smoothing and takes into account a larger portion of the window. Larger values make the weight decay quickly, which reduces the impact of older values on the moving average. This tends to make the moving average track the data more closely but with less smoothing.

Table 20. ewma(double[] values, double alpha) Parameters

Parameter Name	Description
`values`	The window of values to find the sum of
`alpha`	Exponential decay

POST /_search
{
    "size": 0,
    "aggs": {
        "my_date_histo":{
            "date_histogram":{
                "field":"date",
                "interval":"1M"
            },
            "aggs":{
                "the_sum":{
                    "sum":{ "field": "price" }
                },
                "the_movavg": {
                    "moving_fn": {
                        "buckets_path": "the_sum",
                        "window": 10,
                        "script": "MovingFunctions.ewma(values, 0.3)"
                    }
                }
            }
        }
    }
}

holt Function

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The holt function (aka "double exponential") incorporates a second exponential term which tracks the data’s trend. Single exponential does not perform well when the data has an underlying linear trend. The double exponential model calculates two values internally: a "level" and a "trend".

The level calculation is similar to ewma, and is an exponentially weighted view of the data. The difference is that the previously smoothed value is used instead of the raw value, which allows it to stay close to the original series. The trend calculation looks at the difference between the current and last value (e.g. the slope, or trend, of the smoothed data). The trend value is also exponentially weighted.

Values are produced by multiplying the level and trend components.

Table 21. holt(double[] values, double alpha) Parameters

Parameter Name	Description
`values`	The window of values to find the sum of
`alpha`	Level decay value
`beta`	Trend decay value

POST /_search
{
    "size": 0,
    "aggs": {
        "my_date_histo":{
            "date_histogram":{
                "field":"date",
                "interval":"1M"
            },
            "aggs":{
                "the_sum":{
                    "sum":{ "field": "price" }
                },
                "the_movavg": {
                    "moving_fn": {
                        "buckets_path": "the_sum",
                        "window": 10,
                        "script": "MovingFunctions.holt(values, 0.3, 0.1)"
                    }
                }
            }
        }
    }
}

In practice, the alpha value behaves very similarly in holtMovAvg as ewmaMovAvg: small values produce more smoothing and more lag, while larger values produce closer tracking and less lag. The value of beta is often difficult to see. Small values emphasize long-term trends (such as a constant linear trend in the whole series), while larger values emphasize short-term trends.

holtWinters Function

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The holtWinters function (aka "triple exponential") incorporates a third exponential term which tracks the seasonal aspect of your data. This aggregation therefore smooths based on three components: "level", "trend" and "seasonality".

The level and trend calculation is identical to holt The seasonal calculation looks at the difference between the current point, and the point one period earlier.

Holt-Winters requires a little more handholding than the other moving averages. You need to specify the "periodicity" of your data: e.g. if your data has cyclic trends every 7 days, you would set period = 7. Similarly if there was a monthly trend, you would set it to 30. There is currently no periodicity detection, although that is planned for future enhancements.

Table 22. holtWinters(double[] values, double alpha) Parameters

Parameter Name	Description
`values`	The window of values to find the sum of
`alpha`	Level decay value
`beta`	Trend decay value
`gamma`	Seasonality decay value
`period`	The periodicity of the data
`multiplicative`	True if you wish to use multiplicative holt-winters, false to use additive

POST /_search
{
    "size": 0,
    "aggs": {
        "my_date_histo":{
            "date_histogram":{
                "field":"date",
                "interval":"1M"
            },
            "aggs":{
                "the_sum":{
                    "sum":{ "field": "price" }
                },
                "the_movavg": {
                    "moving_fn": {
                        "buckets_path": "the_sum",
                        "window": 10,
                        "script": "if (values.length > 5*2) {MovingFunctions.holtWinters(values, 0.3, 0.1, 0.1, 5, false)}"
                    }
                }
            }
        }
    }
}

Multiplicative Holt-Winters works by dividing each data point by the seasonal value. This is problematic if any of your data is zero, or if there are gaps in the data (since this results in a divid-by-zero). To combat this, the mult Holt-Winters pads all values by a very small amount (1*10^-10) so that all values are non-zero. This affects the result, but only minimally. If your data is non-zero, or you prefer to see NaN when zero’s are encountered, you can disable this behavior with pad: false

"Cold Start"

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Unfortunately, due to the nature of Holt-Winters, it requires two periods of data to "bootstrap" the algorithm. This means that your window must always be at least twice the size of your period. An exception will be thrown if it isn’t. It also means that Holt-Winters will not emit a value for the first 2 * period buckets; the current algorithm does not backcast.

You’ll notice in the above example we have an if () statement checking the size of values. This is checking to make sure we have two periods worth of data (5 * 2, where 5 is the period specified in the holtWintersMovAvg function) before calling the holt-winters function.

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