In Oracle 11g how do you time weight average data hourly between two dates?

1.5k views Asked by At

I have replaced my original question with this final answer. With the help from Mr. MTO and Mr. Ponder Stibbons and four months of playing around with my oracle 11G instance, I finally have what you see here. This query is Designed for SCADA systems primarily and will do the following...

This query will perform a Time Weighted Average hourly between two date times as TWA, Minimum and Maximum Values during that Interval as Vmin and Vmax. It will also return Time of Minimum and Time of Maximum as Hmin and Hmax. (These are the date times of the minimum value occurrence and maximum value occurrence ).Starting and Ending Interval values as VSTART and VEND. This query will not fail on daylight savings in March or August. (This is why I am using TO_TIMESTAMP_TZ)

Note: this query is setup for 1 hour intervals and any desired interval is possible by replacing and adding just a few items. So Enjoy!!!

This Query works in my Oracle 11g instance and after writing this post i copy-ed the exact text below and pasted into my SQL Developer. So it works!! I am having trouble running this in sqlfiddle but soon i will figure this out and have a running test for you.

SQL Fiddle

 -- Lets Begin the Query
 WITH INPUTS AS ( 
    SELECT RECNM, 
          TO_TIMESTAMP_TZ ( '01-JAN-15 00:00:00 AMERICA/LOS_ANGELES','DD-MON-RR HH24:MI:SS TZR' ) AS START_TIME,
          TO_TIMESTAMP_TZ ( '06-NOV-15 23:59:59 AMERICA/LOS_ANGELES','DD-MON-RR HH24:MI:SS TZR' ) AS END_TIME
    FROM POINTS
  WHERE ACRONYM = 'WELL32-PSI'  
) ,
ALL_INTERVALS AS ( 
    SELECT RECNM,
         START_TIME + NUMTODSINTERVAL ( ( LEVEL-1 ) , 'HOUR' ) AS TIME
    FROM INPUTS
    CONNECT BY
    LEVEL-1 <=
               EXTRACT ( DAY FROM END_TIME - START_TIME ) * 24 +
               EXTRACT ( HOUR FROM END_TIME - START_TIME ) 
) ,
ALL_TIMES AS ( 
    SELECT 
       TIME, 
       VALUE, 
       1 AS HAS_VALUE
    FROM HST H
    INNER JOIN INPUTS I
        ON ( H.RECNM = I.RECNM
        AND H.TIME BETWEEN CAST ( I.START_TIME AS TIMESTAMP ) 
        AND  CAST ( I.END_TIME AS TIMESTAMP ) ) 
    UNION ALL
    SELECT 
       TIME, 
       NULL, 
       0
    FROM ALL_INTERVALS
    ORDER BY TIME,1, 2 NULLS FIRST 
) ,
LEAD_LAG_TIMES AS ( 
    SELECT 
         TIME,
         LAST_VALUE ( VALUE IGNORE NULLS ) OVER ( ORDER BY TIME ASC, VALUE ASC ) AS VALUE,
         24 * 60 * 60 * EXTRACT ( DAY FROM LEAD ( TIME ) OVER ( ORDER BY TIME ASC,VALUE ASC ) -TIME ) +
              60 * 60 * EXTRACT ( HOUR FROM LEAD ( TIME ) OVER ( ORDER BY TIME ASC,VALUE ASC ) -TIME ) +
                   60 * EXTRACT ( MINUTE FROM LEAD ( TIME ) OVER ( ORDER BY TIME ASC,VALUE ASC ) -TIME ) + 
                        EXTRACT ( SECOND FROM LEAD ( TIME ) OVER ( ORDER BY TIME ASC,VALUE ASC ) -TIME ) AS DURATION
    FROM ALL_TIMES 
) 
SELECT CAST ( TRUNC ( TIME,'HH24' ) AS TIMESTAMP WITH TIME ZONE ) AS TIME,
    SUM ( VALUE * DURATION ) / SUM ( DURATION ) AS TWA,
    MIN ( VALUE ) AS VMIN, 
    MAX ( TIME ) KEEP ( DENSE_RANK LAST ORDER BY VALUE DESC ) AS TMIN,
    MAX ( VALUE ) AS VMAX, 
    MAX ( TIME ) KEEP ( DENSE_RANK LAST ORDER BY VALUE ASC ) AS TMAX,
    SUM ( VALUE ) AS TOTAL,
    MAX ( VALUE ) KEEP (DENSE_RANK FIRST ORDER BY TIME ASC) as VSTART,
    MAX ( VALUE ) KEEP (DENSE_RANK LAST ORDER BY TIME ASC) as VEND,
    SUM ( DURATION ) AS TOTAL_DURATION 
FROM LEAD_LAG_TIMES
GROUP BY CAST ( TRUNC ( TIME,'HH24' ) AS TIMESTAMP WITH TIME ZONE ) 
ORDER BY TIME ASC

EDIT: You can Include this in the final select statement for a 1 hour Rolling Average that is Time Weighted! I find this very useful in the waste water industry as state regulations/reporting require 24 hour rolling averages and 72 minute rolling averages. If you need a 24 rolling average change ROWS 1 PROCECDING to ROWS 24 PROCEDING

ROUND( AVG ( SUM ( value * DURATION ) / sum ( DURATION ) ) OVER (ORDER BY CAST ( TRUNC ( TIME,'hh24' ) AS TIMESTAMP WITH TIME ZONE ), CAST ( TRUNC ( TIME,'hh24' ) AS TIMESTAMP WITH TIME ZONE ) ROWS 1 PRECEDING),2) AS ROLLING_1H_VAVG,

Standard deviation is fun, so add this as well.

ROUND( STDDEV ( VALUE ) , 2 ) as VDEV,

If you need the value prior to your start time and after your stop time you can place this with the other union all's.

UNION ALL
SELECT
   MAX(H.TIME) KEEP (DENSE_RANK FIRST ORDER BY H.TIME DESC) AS TIME, 
   MAX(H.VALUE) KEEP (DENSE_RANK FIRST ORDER BY H.TIME DESC),
   1
FROM INPUTS I
INNER JOIN HST H
    ON H.TIME < I.START_TIME
UNION ALL
SELECT
   MIN(H.TIME) KEEP (DENSE_RANK FIRST ORDER BY H.TIME) AS TIME, 
   MIN(H.VALUE) KEEP (DENSE_RANK FIRST ORDER BY H.TIME),
   1
FROM INPUTS I
INNER JOIN HST H
    ON H.TIME > I.END_TIME
2

There are 2 answers

4
MT0 On BEST ANSWER

Using your sample data - it didn't have a full hour's data so I've done a weighted average per minute.

You haven't specified what you want to do at the boundaries so I've taken the weighted average of the immediately preceding and succeeding values.

SQL Fiddle

Oracle 11g R2 Schema Setup:

CREATE TABLE TEST ( Acronym, Date_Time, Value ) AS
          SELECT '32-PRESS', TIMESTAMP '15-01-01 00:00:07.120000000', 63.7363 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:00:17.088000000', 64.5604 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:00:27.864000000', 66.3004 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:00:45.080000000', 66.804 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:00:55.056000000', 67.4908 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:01:11.384000000', 66.9872 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:01:30.424000000', 67.4451 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:01:40.408000000', 67.9487 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:01:50.408000000', 68.6813 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:02:01.304000000', 68.1777 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:02:11.304000000', 67.1245 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:02:21.264000000', 66.5293 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:02:31.232000000', 65.4762 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:02:45.736000000', 65.0183 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:02:59.312000000', 64.5604 FROM DUAL
UNION ALL SELECT '32-PRESS', TIMESTAMP '15-01-01 00:03:14.712000000', 64.1026 FROM DUAL;

Query 1:

WITH temp AS (
  SELECT  ACRONYM,
          DATE_TIME,
          VALUE
  FROM    TEST
  UNION
  SELECT  ACRONYM,
          TO_TIMESTAMP( TO_CHAR( DATE_TIME, 'YYYY-MM-DD HH24:MI' ), 'YYYY-MM-DD HH24:MI' ),
          NULL
  FROM    TEST
  GROUP BY
          ACRONYM,
          TO_TIMESTAMP( TO_CHAR( DATE_TIME, 'YYYY-MM-DD HH24:MI' ), 'YYYY-MM-DD HH24:MI' )
  UNION
  SELECT  ACRONYM,
          TO_TIMESTAMP( TO_CHAR( DATE_TIME, 'YYYY-MM-DD HH24:MI' ), 'YYYY-MM-DD HH24:MI' ) + INTERVAL '1' MINUTE,
          NULL
  FROM    TEST
  GROUP BY
          ACRONYM,
          TO_TIMESTAMP( TO_CHAR( DATE_TIME, 'YYYY-MM-DD HH24:MI' ), 'YYYY-MM-DD HH24:MI' )
  ORDER BY
          1,2
),
temp2 AS (
  SELECT  ACRONYM,
          DATE_TIME,
          COALESCE(
            VALUE,
            COALESCE(
              LAG( VALUE ) OVER ( PARTITION BY ACRONYM ORDER BY DATE_TIME ),
              LEAD( VALUE ) OVER ( PARTITION BY ACRONYM ORDER BY DATE_TIME )
            )
            +
            (
              COALESCE(
                LEAD( VALUE ) OVER ( PARTITION BY ACRONYM ORDER BY DATE_TIME ),
                LAG( VALUE ) OVER ( PARTITION BY ACRONYM ORDER BY DATE_TIME )
              )
              -
              COALESCE(
                LAG( VALUE ) OVER ( PARTITION BY ACRONYM ORDER BY DATE_TIME ),
                LEAD( VALUE ) OVER ( PARTITION BY ACRONYM ORDER BY DATE_TIME )
              )
            )
            *
            EXTRACT( SECOND FROM ( DATE_TIME - LAG( DATE_TIME, 1, DATE_TIME ) OVER ( PARTITION BY ACRONYM ORDER BY DATE_TIME ) ) )
            /
            EXTRACT( SECOND FROM (
              LEAD( DATE_TIME, 1, DATE_TIME ) OVER ( PARTITION BY ACRONYM ORDER BY DATE_TIME )
              -
              LAG( DATE_TIME, 1, DATE_TIME ) OVER ( PARTITION BY ACRONYM ORDER BY DATE_TIME )
            ) )
          ) AS VALUE,
          LEAD( DATE_TIME ) OVER ( PARTITION BY ACRONYM ORDER BY DATE_TIME ) AS NEXT_DATE_TIME
  FROM    temp
)
SELECT  ACRONYM,
        TO_DATE( TO_CHAR( DATE_TIME, 'YYYY-MM-DD HH24:MI' ), 'YYYY-MM-DD HH24:MI' ) AS DATE_TIME,
        SUM( VALUE * EXTRACT( SECOND FROM ( NEXT_DATE_TIME - DATE_TIME ) ) ) / 60 AS VALUE
FROM    temp2
WHERE   NEXT_DATE_TIME IS NOT NULL
GROUP BY
        ACRONYM,
        TO_DATE( TO_CHAR( DATE_TIME, 'YYYY-MM-DD HH24:MI' ), 'YYYY-MM-DD HH24:MI' )
ORDER BY
        1,2

Results:

|  ACRONYM |                 DATE_TIME |             VALUE |
|----------|---------------------------|-------------------|
| 32-PRESS | January, 01 0015 00:00:00 | 65.43946117333333 |
| 32-PRESS | January, 01 0015 00:01:00 | 67.56109262835211 |
| 32-PRESS | January, 01 0015 00:02:00 | 66.32093658633383 |
| 32-PRESS | January, 01 0015 00:03:00 | 64.20983764043636 |

EDIT

SQL Fiddle

Oracle 11g R2 Schema Setup:

CREATE TABLE POINTS ( RECNM NUMBER, ACRONYM VARCHAR2(20) );
INSERT INTO POINTS  VALUES(1136, '32-PRESS');
INSERT INTO POINTS  VALUES(1138, 'OTHER_POINT');

CREATE TABLE HST ( RECNM NUMBER, TIME TIMESTAMP, VALUE NUMBER );
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:00:00',63.3);
INSERT INTO HST  VALUES(1138, TIMESTAMP '15-01-01 00:00:00',0.0);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:00:07',63.7);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:00:17',64.6);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:00:28',66.3);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:00:45',66.8);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:00:55',67.5);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:01:11',67.0);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:01:30',67.4);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:01:40',67.9);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:01:50',68.7);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:02:01',68.2);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:02:11',67.1);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:02:21',66.5);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:02:31',65.5);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:02:46',65.0);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:02:59',64.6);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:03:15',64.1);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:03:25',63.2);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:03:35',62.7);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:04:05',62.2);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:04:32',61.8);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:05:40',61.3);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:05:55',60.8);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:10:20',60.3);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:10:38',60.9);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:10:48',61.3);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:10:58',61.8);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:11:27',62.3);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:13:54',61.8);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:14:10',61.4);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:14:41',60.9);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:15:18',61.4);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:15:51',60.9);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:16:19',60.4);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:16:32',59.9);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:17:04',59.4);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:17:27',59.9);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:17:37',59.4);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:17:58',59.0);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:18:22',59.4);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:18:50',59.9);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:19:00',60.3);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:19:25',60.8);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:19:34',61.4);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:19:45',62.1);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:19:55',62.5);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:20:30',63.0);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:20:51',63.5);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:21:03',63.9);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:22:04',64.4);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:22:28',64.8);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:23:17',64.4);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:23:27',63.9);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:24:31',63.4);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:26:06',63.0);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:27:20',62.5);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:27:30',61.9);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:28:08',62.4);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:28:37',62.0);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:29:21',62.5);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:29:38',62.9);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:31:27',62.5);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:32:01',62.0);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:32:25',62.5);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:35:07',62.9);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:35:56',62.5);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:36:06',62.0);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:36:59',61.5);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:39:31',62.0);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:40:12',61.5);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:40:22',60.9);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:40:35',60.5);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:40:55',60.0);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:41:22',60.5);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:41:46',60.1);
INSERT INTO HST  VALUES(1136, TIMESTAMP '15-01-01 00:42:31',60.6);

Query 1:

WITH inputs AS (
  SELECT RECNM,
         TIMESTAMP '15-01-01 00:00:00' AS start_time,
         TIMESTAMP '15-01-01 00:40:00' AS end_time
  FROM   POINTS
  WHERE  ACRONYM = '32-PRESS'
),
all_minutes AS (
  SELECT RECNM,
         start_time + (LEVEL-1)/24/60 AS time
  FROM   inputs
  CONNECT BY
         LEVEL - 1 <= EXTRACT( MINUTE FROM end_time - start_time )
),
all_times AS (
  SELECT  TIME,
          VALUE,
          1 AS HAS_VALUE
  FROM    HST h
          INNER JOIN inputs i
          ON (     h.RECNM = i.RECNM
               AND h.TIME BETWEEN i.start_time
                          AND     i.end_time )
  UNION ALL
  SELECT  TIME,
          NULL,
          0
  FROM    all_minutes
  ORDER BY 1, 2 NULLS FIRST
),
lag_lead_ignore_nulls AS (
  SELECT TIME,
         VALUE,
         COUNT( VALUE ) OVER ( ORDER BY TIME ASC, VALUE ASC NULLS FIRST ) AS LAG_GRP,
         COUNT( VALUE ) OVER ( ORDER BY TIME DESC, VALUE DESC NULLS LAST ) AS LEAD_GRP
  FROM   all_times
),
lag_lead_values AS (
  SELECT  TIME,
          VALUE,
          FIRST_VALUE( TIME  ) OVER ( PARTITION BY LAG_GRP  ORDER BY VALUE ASC NULLS LAST ) AS PREV_MEASURED_TIME,
          FIRST_VALUE( VALUE ) OVER ( PARTITION BY LAG_GRP  ORDER BY VALUE ASC NULLS LAST ) AS PREV_MEASURED_VALUE,
          FIRST_VALUE( TIME  ) OVER ( PARTITION BY LEAD_GRP ORDER BY VALUE ASC NULLS LAST ) AS NEXT_MEASURED_TIME,
          FIRST_VALUE( VALUE ) OVER ( PARTITION BY LEAD_GRP ORDER BY VALUE ASC NULLS LAST ) AS NEXT_MEASURED_VALUE,
          LEAD( TIME ) OVER ( ORDER BY TIME ASC ) AS NEXT_TIME
  FROM    lag_lead_ignore_nulls
),
interpolated_values AS (
  SELECT CAST( TIME AS DATE ) TIME,
         COALESCE(
           VALUE,
           PREV_MEASURED_VALUE
           + ( NEXT_MEASURED_VALUE - PREV_MEASURED_VALUE )
           * (
               60 * EXTRACT( MINUTE FROM TIME - PREV_MEASURED_TIME )
               + EXTRACT( SECOND FROM TIME - PREV_MEASURED_TIME )
             )
           / (
               60 * EXTRACT( MINUTE FROM NEXT_MEASURED_TIME - PREV_MEASURED_TIME )
               + EXTRACT( SECOND FROM NEXT_MEASURED_TIME - PREV_MEASURED_TIME )
             )
         ) AS INTERPOLATED_VALUE,
         60 * EXTRACT( MINUTE FROM NEXT_TIME - TIME )
         + EXTRACT( SECOND FROM NEXT_TIME - TIME ) AS DURATION
  FROM lag_lead_values
)
SELECT TRUNC( TIME, 'MI' ) AS TIME,
       SUM( INTERPOLATED_VALUE * DURATION ) / SUM( DURATION ) AS TWA,
       SUM( DURATION ) AS TOTAL_DURATION
FROM   interpolated_values
WHERE  INTERPOLATED_VALUE IS NOT NULL
GROUP BY TRUNC( TIME, 'MI' )
ORDER BY TIME ASC

Results:

|                      TIME |                TWA | TOTAL_DURATION |
|---------------------------|--------------------|----------------|
| January, 01 0015 00:00:00 |  65.38833333333333 |             60 |
| January, 01 0015 00:01:00 |  67.56302083333334 |             60 |
| January, 01 0015 00:02:00 |  66.30575757575758 |             60 |
| January, 01 0015 00:03:00 |  63.48385416666667 |             60 |
| January, 01 0015 00:04:00 |  62.02027777777778 |             60 |
| January, 01 0015 00:05:00 |  61.45441176470588 |             60 |
| January, 01 0015 00:06:00 |  60.79056603773585 |             60 |
| January, 01 0015 00:07:00 | 60.677358490566036 |             60 |
| January, 01 0015 00:08:00 |  60.56415094339623 |             60 |
| January, 01 0015 00:09:00 | 60.450943396226414 |             60 |
| January, 01 0015 00:10:00 |  60.62924528301887 |             60 |
| January, 01 0015 00:11:00 |  62.09051724137931 |             60 |
| January, 01 0015 00:12:00 |  62.18775510204082 |             60 |
| January, 01 0015 00:13:00 |  61.96530612244898 |             60 |
| January, 01 0015 00:14:00 |  61.28333333333333 |             60 |
| January, 01 0015 00:15:00 | 61.252027027027026 |             60 |
| January, 01 0015 00:16:00 |  60.27410714285714 |             60 |
| January, 01 0015 00:17:00 |  59.47416666666667 |             60 |
| January, 01 0015 00:18:00 |  59.34888888888889 |             60 |
| January, 01 0015 00:19:00 |              61.06 |             60 |
| January, 01 0015 00:20:00 |  62.86071428571429 |             60 |
| January, 01 0015 00:21:00 |             63.895 |             60 |
| January, 01 0015 00:22:00 |  64.61114754098361 |             60 |
| January, 01 0015 00:23:00 |  64.16431972789115 |             60 |
| January, 01 0015 00:24:00 |  63.52513020833333 |             60 |
| January, 01 0015 00:25:00 |  63.27789473684211 |             60 |
| January, 01 0015 00:26:00 | 63.002526315789474 |             60 |
| January, 01 0015 00:27:00 | 62.245045045045046 |             60 |
| January, 01 0015 00:28:00 |  62.23263157894737 |             60 |
| January, 01 0015 00:29:00 |  62.56314393939394 |             60 |
| January, 01 0015 00:30:00 |  62.81926605504587 |             60 |
| January, 01 0015 00:31:00 | 62.544587155963306 |             60 |
| January, 01 0015 00:32:00 |  62.29191176470588 |             60 |
| January, 01 0015 00:33:00 |  62.58641975308642 |             60 |
| January, 01 0015 00:34:00 |  62.73456790123457 |             60 |
| January, 01 0015 00:35:00 |  62.87131687242798 |             60 |
| January, 01 0015 00:36:00 |  62.02166666666667 |             60 |
| January, 01 0015 00:37:00 |  61.50328947368421 |             60 |
| January, 01 0015 00:38:00 |  61.70065789473684 |             60 |
| January, 01 0015 00:39:00 |  61.94731359649123 |             60 |
12
Ponder Stibbons On

This query generated desired values:

with input as (
  select value, htime, to_char(htime, 'yyyy-mm-dd hh24:mi') mnt,
      extract(day from d)+extract(hour from d)/24+
      extract(minute from d)/(24*60)+extract (second from d)/(24*60*60) tm
    from (select value, htime, htime-timestamp '1899-12-30 00:00:00' d from test))
select distinct mnt, round(
    sum(tm*value) over (partition by mnt)/sum(tm) over (partition by mnt), 6) wav
  from input order by mnt

Output:

MNT               WAV
----------------  ----------
2015-01-01 12:00   65.77838
2015-01-01 12:01   67.765575
2015-01-01 12:02   66.147733
2015-01-01 12:03   64.1026

SQLFiddle

According to documentation Excel calendar starts with '1900-01-01', but I had to modify this date slightly to achieve "date zero" to get number values for time difference exactly like in spreadsheet. Rest is only the matter of substracting timestamps, casting this difference to number and summing results for each minute with function sum() in analytic version.

If you have gaps in data you need at first create periods for each minute with recursive query (connect by) and then left join this query with mine filling data for gaps with function lag(wav ignore nulls) gathering weighted average from previous minute(s).


Edit: Version filling gaps:

with input as (
    select value, htime, to_char(htime, 'yyyy-mm-dd hh24:mi') mnt,
        extract(day from d)+extract(hour from d)/24+
        extract(minute from d)/(24*60)+extract (second from d)/(24*60*60) tm
      from (select value, htime, htime-timestamp '1899-12-30 00:00:00' d from data)),
  period as (select to_date(min(mnt), 'yyyy-mm-dd hh24:mi') m1, 
                    to_date(max(mnt), 'yyyy-mm-dd hh24:mi') m2 from input),
  minutes as (
    select to_char(to_date(m1) + (level - 1)/(24*60), 'yyyy-mm-dd hh24:mi') mnt
      from period connect by level+1<(m2-m1)*24*60),
  calc as (
    select distinct mnt, 
        round(sum(tm*value) over (partition by mnt)/sum(tm) over (partition by mnt), 6) wav
      from minutes left join input using (mnt) order by mnt)
select mnt, wav, nvl(wav, lag(wav ignore nulls) over (order by mnt)) wavg from calc

SQLFiddle

Subquery input prepares data for further treatment, period selects min and max minute from table (you can insert some values by hand here instead of querying from table, for example "date '2015-01-01 13:52:00'"), minutes generates... minutes recursively for given period, calc counts weighted averages joining input and minutes, last select fills last known averages for empty minutes - you can observe it for minutes 6, 7, 12 in SQLFiddle.