Moving Average Aggregationedit
Given an ordered series of data, the Moving Average aggregation will slide a window across the data and emit the average
value of that window. For example, given the data [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
, we can calculate a simple moving
average with windows size of 5
as follows:
 (1 + 2 + 3 + 4 + 5) / 5 = 3
 (2 + 3 + 4 + 5 + 6) / 5 = 4
 (3 + 4 + 5 + 6 + 7) / 5 = 5
 etc
Moving averages are a simple method to smooth sequential data. Moving averages are typically applied to timebased data, such as stock prices or server metrics. The smoothing can be used to eliminate high frequency fluctuations or random noise, which allows the lower frequency trends to be more easily visualized, such as seasonality.
Syntaxedit
A moving_avg
aggregation looks like this in isolation:
{ "moving_avg": { "buckets_path": "the_sum", "model": "holt", "window": 5, "gap_policy": "insert_zeros", "settings": { "alpha": 0.8 } } }
Table 9. moving_avg
Parameters
Parameter Name  Description  Required  Default Value 
 Path to the metric of interest (see  Required  
 The moving average weighting model that we wish to use  Optional 

 Determines what should happen when a gap in the data is encountered.  Optional 

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

 If the model should be algorithmically minimized. See Minimization for more details  Optional 

 Modelspecific settings, contents which differ depending on the model specified.  Optional 
moving_avg
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_movavg":{ "moving_avg":{ "buckets_path": "the_sum" } } } } } }
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 normal metrics, such as a sum
, inside of that histogram. Finally, the moving_avg
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
Syntaxedit 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 } }, { "key_as_string": "2015/02/01 00:00:00", "key": 1422748800000, "doc_count": 2, "the_sum": { "value": 60.0 }, "the_movavg": { "value": 550.0 } }, { "key_as_string": "2015/03/01 00:00:00", "key": 1425168000000, "doc_count": 2, "the_sum": { "value": 375.0 }, "the_movavg": { "value": 305.0 } } ] } } }
Modelsedit
The moving_avg
aggregation includes four different moving average "models". The main difference is how the values in the
window are weighted. As datapoints become "older" in the window, they may be weighted differently. This will
affect the final average for that window.
Models are specified using the model
parameter. Some models may have optional configurations which are specified inside
the settings
parameter.
Simpleedit
The simple
model 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 model does not perform any timedependent weighting, which means
the values from a simple
moving average tend to "lag" behind the real data.
POST /_search { "size": 0, "aggs": { "my_date_histo":{ "date_histogram":{ "field":"date", "interval":"1M" }, "aggs":{ "the_sum":{ "sum":{ "field": "price" } }, "the_movavg":{ "moving_avg":{ "buckets_path": "the_sum", "window" : 30, "model" : "simple" } } } } } }
A simple
model has no special settings to configure
The window size can change the behavior of the moving average. For example, a small window ("window": 10
) will closely
track the data and only smooth out small scale fluctuations:
In contrast, a simple
moving average with larger window ("window": 100
) will smooth out all higherfrequency fluctuations,
leaving only lowfrequency, long term trends. It also tends to "lag" behind the actual data by a substantial amount:
Linearedit
The linear
model 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.
POST /_search { "size": 0, "aggs": { "my_date_histo":{ "date_histogram":{ "field":"date", "interval":"1M" }, "aggs":{ "the_sum":{ "sum":{ "field": "price" } }, "the_movavg": { "moving_avg":{ "buckets_path": "the_sum", "window" : 30, "model" : "linear" } } } } } }
A linear
model has no special settings to configure
Like the simple
model, window size can change the behavior of the moving average. For example, a small window ("window": 10
)
will closely track the data and only smooth out small scale fluctuations:
In contrast, a linear
moving average with larger window ("window": 100
) will smooth out all higherfrequency fluctuations,
leaving only lowfrequency, long term trends. It also tends to "lag" behind the actual data by a substantial amount,
although typically less than the simple
model:
EWMA (Exponentially Weighted)edit
The ewma
model (aka "singleexponential") is similar to the linear
model, 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 valuers 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.
The default value of alpha
is 0.3
, and the setting accepts any float from 01 inclusive.
The EWMA model can be Minimized
POST /_search { "size": 0, "aggs": { "my_date_histo":{ "date_histogram":{ "field":"date", "interval":"1M" }, "aggs":{ "the_sum":{ "sum":{ "field": "price" } }, "the_movavg": { "moving_avg":{ "buckets_path": "the_sum", "window" : 30, "model" : "ewma", "settings" : { "alpha" : 0.5 } } } } } } }
HoltLinearedit
The holt
model (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.
The default value of alpha
is 0.3
and beta
is 0.1
. The settings accept any float from 01 inclusive.
The HoltLinear model can be Minimized
POST /_search { "size": 0, "aggs": { "my_date_histo":{ "date_histogram":{ "field":"date", "interval":"1M" }, "aggs":{ "the_sum":{ "sum":{ "field": "price" } }, "the_movavg": { "moving_avg":{ "buckets_path": "the_sum", "window" : 30, "model" : "holt", "settings" : { "alpha" : 0.5, "beta" : 0.5 } } } } } } }
In practice, the alpha
value behaves very similarly in holt
as ewma
: 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. This will become more apparently when you are predicting values.
HoltWintersedit
The holt_winters
model (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.
There are two varieties of HoltWinters: additive and multiplicative.
"Cold Start"edit
Unfortunately, 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.
Because the "cold start" obscures what the moving average looks like, the rest of the HoltWinters images are truncated to not show the "cold start". Just be aware this will always be present at the beginning of your moving averages!
Additive HoltWintersedit
Additive seasonality is the default; it can also be specified by setting "type": "add"
. This variety is preferred
when the seasonal affect is additive to your data. E.g. you could simply subtract the seasonal effect to "deseasonalize"
your data into a flat trend.
The default values of alpha
and gamma
are 0.3
while beta
is 0.1
. The settings accept any float from 01 inclusive.
The default value of period
is 1
.
The additive HoltWinters model can be Minimized
POST /_search { "size": 0, "aggs": { "my_date_histo":{ "date_histogram":{ "field":"date", "interval":"1M" }, "aggs":{ "the_sum":{ "sum":{ "field": "price" } }, "the_movavg": { "moving_avg":{ "buckets_path": "the_sum", "window" : 30, "model" : "holt_winters", "settings" : { "type" : "add", "alpha" : 0.5, "beta" : 0.5, "gamma" : 0.5, "period" : 7 } } } } } } }
Figure 10. HoltWinters moving average with window of size 120, alpha = 0.5, beta = 0.7, gamma = 0.3, period = 30
Multiplicative HoltWintersedit
Multiplicative is specified by setting "type": "mult"
. This variety is preferred when the seasonal affect is
multiplied against your data. E.g. if the seasonal affect is x5 the data, rather than simply adding to it.
The default values of alpha
and gamma
are 0.3
while beta
is 0.1
. The settings accept any float from 01 inclusive.
The default value of period
is 1
.
The multiplicative HoltWinters model can be Minimized
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
POST /_search { "size": 0, "aggs": { "my_date_histo":{ "date_histogram":{ "field":"date", "interval":"1M" }, "aggs":{ "the_sum":{ "sum":{ "field": "price" } }, "the_movavg": { "moving_avg":{ "buckets_path": "the_sum", "window" : 30, "model" : "holt_winters", "settings" : { "type" : "mult", "alpha" : 0.5, "beta" : 0.5, "gamma" : 0.5, "period" : 7, "pad" : true } } } } } } }
Predictionedit
This functionality is experimental and may be changed or removed completely in a future release. Elastic will take a best effort approach to fix any issues, but experimental features are not subject to the support SLA of official GA features.
All the moving average model support a "prediction" mode, which will attempt to extrapolate into the future given the current smoothed, moving average. Depending on the model and parameter, these predictions may or may not be accurate.
Predictions are enabled by adding a predict
parameter to any moving average aggregation, specifying the number of
predictions you would like appended to the end of the series. These predictions will be spaced out at the same interval
as your buckets:
POST /_search { "size": 0, "aggs": { "my_date_histo":{ "date_histogram":{ "field":"date", "interval":"1M" }, "aggs":{ "the_sum":{ "sum":{ "field": "price" } }, "the_movavg": { "moving_avg":{ "buckets_path": "the_sum", "window" : 30, "model" : "simple", "predict" : 10 } } } } } }
The simple
, linear
and ewma
models all produce "flat" predictions: they essentially converge on the mean
of the last value in the series, producing a flat:
In contrast, the holt
model can extrapolate based on local or global constant trends. If we set a high beta
value, we can extrapolate based on local constant trends (in this case the predictions head down, because the data at the end
of the series was heading in a downward direction):
Figure 12. HoltLinear moving average with window of size 100, predict = 20, alpha = 0.5, beta = 0.8
In contrast, if we choose a small beta
, the predictions are based on the global constant trend. In this series, the
global trend is slightly positive, so the prediction makes a sharp uturn and begins a positive slope:
Figure 13. Double Exponential moving average with window of size 100, predict = 20, alpha = 0.5, beta = 0.1
The holt_winters
model has the potential to deliver the best predictions, since it also incorporates seasonal
fluctuations into the model:
Figure 14. HoltWinters moving average with window of size 120, predict = 25, alpha = 0.8, beta = 0.2, gamma = 0.7, period = 30
Minimizationedit
Some of the models (EWMA, HoltLinear, HoltWinters) require one or more parameters to be configured. Parameter choice can be tricky and sometimes nonintuitive. Furthermore, small deviations in these parameters can sometimes have a drastic effect on the output moving average.
For that reason, the three "tunable" models can be algorithmically minimized. Minimization is a process where parameters are tweaked until the predictions generated by the model closely match the output data. Minimization is not fullproof and can be susceptible to overfitting, but it often gives better results than handtuning.
Minimization is disabled by default for ewma
and holt_linear
, while it is enabled by default for holt_winters
.
Minimization is most useful with HoltWinters, since it helps improve the accuracy of the predictions. EWMA and
HoltLinear are not great predictors, and mostly used for smoothing data, so minimization is less useful on those
models.
Minimization is enabled/disabled via the minimize
parameter:
POST /_search { "size": 0, "aggs": { "my_date_histo":{ "date_histogram":{ "field":"date", "interval":"1M" }, "aggs":{ "the_sum":{ "sum":{ "field": "price" } }, "the_movavg": { "moving_avg":{ "buckets_path": "the_sum", "model" : "holt_winters", "window" : 30, "minimize" : true, "settings" : { "period" : 7 } } } } } } }
When enabled, minimization will find the optimal values for alpha
, beta
and gamma
. The user should still provide
appropriate values for window
, period
and type
.
Minimization works by running a stochastic process called simulated annealing. This process will usually generate a good solution, but is not guaranteed to find the global optimum. It also requires some amount of additional computational power, since the model needs to be rerun multiple times as the values are tweaked. The runtime of minimization is linear to the size of the window being processed: excessively large windows may cause latency.
Finally, minimization fits the model to the last n
values, where n = window
. This generally produces
better forecasts into the future, since the parameters are tuned around the end of the series. It can, however, generate
poorer fitting moving averages at the beginning of the series.