Cumulative sum + serial differencing

input.txt

POST t/type_name
{
  "d": "2016-01-01T01:01:01",
  "foo": 1
}

POST t/type_name
{
  "d": "2016-01-02T01:01:01",
  "foo": 2
}

POST t/type_name
{
  "d": "2016-01-03T01:01:01",
  "foo": 3
}

POST t/type_name
{
  "d": "2016-01-04T01:01:01",
  "foo": 4
}

POST t/type_name
{
  "d": "2016-01-05T01:01:01",
  "foo": 5
}

POST t/type_name
{
  "d": "2016-01-06T01:01:01",
  "foo": 6
}

GET t/_search
{
  "query": {
    "match_all": {}
  },
  "aggs": {
    "hist": {
      "date_histogram" : {
        "field" : "d",
        "interval" : "day"
      },
      "aggs": {
          "v": {
              "sum": {
                  "field": "foo"
              }
          },
          "sum_foo": {
              "cumulative_sum": {
                  "buckets_path": "v"
              }
          },
          "diff": {
            "serial_diff": {
                "buckets_path": "sum_foo",
                "lag": 2
            }
          }
      }
    }
  }, 
  "size": 0
}

output.txt

{
  "took": 7,
  "timed_out": false,
  "_shards": {
    "total": 5,
    "successful": 5,
    "failed": 0
  },
  "hits": {
    "total": 6,
    "max_score": 0,
    "hits": []
  },
  "aggregations": {
    "hist": {
      "buckets": [
        {
          "key_as_string": "2016-01-01T00:00:00.000Z",
          "key": 1451606400000,
          "doc_count": 1,
          "v": {
            "value": 1
          },
          "sum_foo": {
            "value": 1
          }
        },
        {
          "key_as_string": "2016-01-02T00:00:00.000Z",
          "key": 1451692800000,
          "doc_count": 1,
          "v": {
            "value": 2
          },
          "sum_foo": {
            "value": 3
          }
        },
        {
          "key_as_string": "2016-01-03T00:00:00.000Z",
          "key": 1451779200000,
          "doc_count": 1,
          "v": {
            "value": 3
          },
          "sum_foo": {
            "value": 6
          },
          "diff": {
            "value": 5
          }
        },
        {
          "key_as_string": "2016-01-04T00:00:00.000Z",
          "key": 1451865600000,
          "doc_count": 1,
          "v": {
            "value": 4
          },
          "sum_foo": {
            "value": 10
          },
          "diff": {
            "value": 7
          }
        },
        {
          "key_as_string": "2016-01-05T00:00:00.000Z",
          "key": 1451952000000,
          "doc_count": 1,
          "v": {
            "value": 5
          },
          "sum_foo": {
            "value": 15
          },
          "diff": {
            "value": 9
          }
        },
        {
          "key_as_string": "2016-01-06T00:00:00.000Z",
          "key": 1452038400000,
          "doc_count": 1,
          "v": {
            "value": 6
          },
          "sum_foo": {
            "value": 21
          },
          "diff": {
            "value": 11
          }
        }
      ]
    }
  }
}