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[[search-aggregations-pipeline-serialdiff-aggregation]]
=== Serial Differencing Aggregation
experimental[]
Serial differencing is a technique where values in a time series are subtracted from itself at
different time lags or periods. For example, the datapoint f(x) = f(x~t~) - f(x~t-n~), where n is the period being used.
A period of 1 is equivalent to a derivative with no time normalization: it is simply the change from one point to the
next. Single periods are useful for removing constant, linear trends.
Single periods are also useful for transforming data into a stationary series. In this example, the Dow Jones is
plotted over ~250 days. The raw data is not stationary, which would make it difficult to use with some techniques.
By calculating the first-difference, we de-trend the data (e.g. remove a constant, linear trend). We can see that the
data becomes a stationary series (e.g. the first difference is randomly distributed around zero, and doesn't seem to
exhibit any pattern/behavior). The transformation reveals that the dataset is following a random-walk; the value is the
previous value +/- a random amount. This insight allows selection of further tools for analysis.
[[serialdiff_dow]]
.Dow Jones plotted and made stationary with first-differencing
image::images/pipeline_serialdiff/dow.png[]
Larger periods can be used to remove seasonal / cyclic behavior. In this example, a population of lemmings was
synthetically generated with a sine wave + constant linear trend + random noise. The sine wave has a period of 30 days.
The first-difference removes the constant trend, leaving just a sine wave. The 30th-difference is then applied to the
first-difference to remove the cyclic behavior, leaving a stationary series which is amenable to other analysis.
[[serialdiff_lemmings]]
.Lemmings data plotted made stationary with 1st and 30th difference
image::images/pipeline_serialdiff/lemmings.png[]
==== Syntax
A `serial_diff` aggregation looks like this in isolation:
[source,js]
--------------------------------------------------
{
"serial_diff": {
"buckets_path": "the_sum",
"lag": "7"
}
}
--------------------------------------------------
.`moving_avg` Parameters
|===
|Parameter Name |Description |Required |Default Value
|`buckets_path` |Path to the metric of interest (see <<buckets-path-syntax, `buckets_path` Syntax>> for more details |Required |
|`lag` |The historical bucket to subtract from the current value. E.g. a lag of 7 will subtract the current value from
the value 7 buckets ago. Must be a positive, non-zero integer |Optional |`1`
|`gap_policy` |Determines what should happen when a gap in the data is encountered. |Optional |`insert_zero`
|`format` |Format to apply to the output value of this aggregation |Optional | `null`
|===
`serial_diff` aggregations must be embedded inside of a `histogram` or `date_histogram` aggregation:
[source,js]
--------------------------------------------------
{
"aggs": {
"my_date_histo": { <1>
"date_histogram": {
"field": "timestamp",
"interval": "day"
},
"aggs": {
"the_sum": {
"sum": {
"field": "lemmings" <2>
}
},
"thirtieth_difference": {
"serial_diff": { <3>
"buckets_path": "the_sum",
"lag" : 30
}
}
}
}
}
}
--------------------------------------------------
<1> A `date_histogram` named "my_date_histo" is constructed on the "timestamp" field, with one-day intervals
<2> A `sum` metric is used to calculate the sum of a field. This could be any metric (sum, min, max, etc)
<3> Finally, we specify a `serial_diff` aggregation which uses "the_sum" metric as its input.
Serial differences 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 `serial_diff` 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`.