Moving function aggregation
editMoving function aggregation
editGiven 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.
Syntax
editA moving_fn
aggregation looks like this in isolation:
{ "moving_fn": { "buckets_path": "the_sum", "window": 10, "script": "MovingFunctions.min(values)" } }
Table 59. moving_fn
Parameters
Parameter Name  Description  Required  Default Value 


Path to the metric of interest (see 
Required 


The size of window to "slide" across the histogram. 
Required 


The script that should be executed on each window of data 
Required 


The policy to apply when gaps are found in the data. See Dealing with gaps in the data. 
Optional 


Shift of window position. 
Optional 
0 
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", "calendar_interval": "1M" }, "aggs": { "the_sum": { "sum": { "field": "price" } }, "the_movfn": { "moving_fn": { "buckets_path": "the_sum", "window": 10, "script": "MovingFunctions.unweightedAvg(values)" } } } } } }
A 

A 

Finally, we specify a 
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
editThe 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", "calendar_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" } } } } } }
shift parameter
editBy default (with shift = 0
), the window that is offered for calculation is the last n
values excluding the current bucket.
Increasing shift
by 1 moves starting window position by 1
to the right.

To include current bucket to the window, use
shift = 1
. 
For center alignment (
n / 2
values before and after the current bucket), useshift = window / 2
. 
For right alignment (
n
values after the current bucket), useshift = window
.
If either of window edges moves outside the borders of data series, the window shrinks to include available values only.
Prebuilt Functions
editFor 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
editThis 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 60. max(double[] values)
Parameters
Parameter Name  Description 


The window of values to find the maximum 
POST /_search { "size": 0, "aggs": { "my_date_histo": { "date_histogram": { "field": "date", "calendar_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
editThis 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 61. min(double[] values)
Parameters
Parameter Name  Description 


The window of values to find the minimum 
POST /_search { "size": 0, "aggs": { "my_date_histo": { "date_histogram": { "field": "date", "calendar_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
editThis 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 62. sum(double[] values)
Parameters
Parameter Name  Description 


The window of values to find the sum of 
POST /_search { "size": 0, "aggs": { "my_date_histo": { "date_histogram": { "field": "date", "calendar_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
editThis 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 63. stdDev(double[] values)
Parameters
Parameter Name  Description 


The window of values to find the standard deviation of 

The average of the window 
POST /_search { "size": 0, "aggs": { "my_date_histo": { "date_histogram": { "field": "date", "calendar_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
editThe 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 timedependent 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 nonnull
,nonNaN
values.
Table 64. unweightedAvg(double[] values)
Parameters
Parameter Name  Description 


The window of values to find the sum of 
POST /_search { "size": 0, "aggs": { "my_date_histo": { "date_histogram": { "field": "date", "calendar_interval": "1M" }, "aggs": { "the_sum": { "sum": { "field": "price" } }, "the_movavg": { "moving_fn": { "buckets_path": "the_sum", "window": 10, "script": "MovingFunctions.unweightedAvg(values)" } } } } } }
linearWeightedAvg Function
editThe 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 65. linearWeightedAvg(double[] values)
Parameters
Parameter Name  Description 


The window of values to find the sum of 
POST /_search { "size": 0, "aggs": { "my_date_histo": { "date_histogram": { "field": "date", "calendar_interval": "1M" }, "aggs": { "the_sum": { "sum": { "field": "price" } }, "the_movavg": { "moving_fn": { "buckets_path": "the_sum", "window": 10, "script": "MovingFunctions.linearWeightedAvg(values)" } } } } } }
ewma Function
editThe ewma
function (aka "singleexponential") is similar to the linearMovAvg
function,
except older datapoints 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.
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 nonnull
,nonNaN
values.
Table 66. ewma(double[] values, double alpha)
Parameters
Parameter Name  Description 


The window of values to find the sum of 

Exponential decay 
POST /_search { "size": 0, "aggs": { "my_date_histo": { "date_histogram": { "field": "date", "calendar_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
editThe 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.
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 nonnull
,nonNaN
values.
Table 67. holt(double[] values, double alpha)
Parameters
Parameter Name  Description 


The window of values to find the sum of 

Level decay value 

Trend decay value 
POST /_search { "size": 0, "aggs": { "my_date_histo": { "date_histogram": { "field": "date", "calendar_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 longterm trends (such as a constant linear trend in the whole series), while larger
values emphasize shortterm trends.
holtWinters Function
editThe 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.
HoltWinters 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.
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 nonnull
,nonNaN
values.
Table 68. holtWinters(double[] values, double alpha)
Parameters
Parameter Name  Description 


The window of values to find the sum of 

Level decay value 

Trend decay value 

Seasonality decay value 

The periodicity of the data 

True if you wish to use multiplicative holtwinters, false to use additive 
POST /_search { "size": 0, "aggs": { "my_date_histo": { "date_histogram": { "field": "date", "calendar_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 HoltWinters 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 dividbyzero). To combat this, the
mult
HoltWinters pads all values by a very small amount (1*10^{10}) so that all values are nonzero. This affects
the result, but only minimally. If your data is nonzero, or you prefer to see NaN
when zero’s are encountered,
you can disable this behavior with pad: false
"Cold Start"
editUnfortunately, due to the nature of HoltWinters, 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 HoltWinters 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 holtwinters function.