Serial Differencing Aggregationedit

Warning

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.

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(xt) - f(xt-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.

Figure 15. Dow Jones plotted and made stationary with first-differencing

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.

Figure 16. Lemmings data plotted made stationary with 1st and 30th difference

images/pipeline_serialdiff/lemmings.png

Syntaxedit

A serial_diff aggregation looks like this in isolation:

{
    "serial_diff": {
        "buckets_path": "the_sum",
        "lag": "7"
    }
}

Table 13. serial_diff Parameters

Parameter Name

Description

Required

Default Value

buckets_path

Path to the metric of interest (see 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:

POST /_search
{
   "size": 0,
   "aggs": {
      "my_date_histo": {                  
         "date_histogram": {
            "field": "timestamp",
            "interval": "day"
         },
         "aggs": {
            "the_sum": {
               "sum": {
                  "field": "lemmings"     
               }
            },
            "thirtieth_difference": {
               "serial_diff": {                
                  "buckets_path": "the_sum",
                  "lag" : 30
               }
            }
         }
      }
   }
}

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 metric (sum, min, max, etc)

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 Syntaxedit for a description of the syntax for buckets_path.