SQL Server MovingEWMA Function

Updated 2023-11-13 21:13:25.817000

Description

Use MovingEWMA to calculate the exponentially weighted moving average of column values in an ordered resultant table, without the need for a self-join. The exponentially weighted moving average value is calculated for each value from the first value in the window to the last value in the window. If the column values are presented to the functions out of order, an error message will be generated.

Syntax

SELECT [westclintech].[wct].[MovingEWMA](
  <@Val, float,>
 ,<@Alpha, float,>
 ,<@Offset, int,>
 ,<@Lag, int,>
 ,<@RowNum, int,>
 ,<@Id, tinyint,>)

Arguments

@Val

the value passed into the function. @Val is an expression of type float or of a type that can be implicitly converted to float.

@Alpha

the degree of weighting decrease. A higher @Alpha discounts older observations faster. @Alpha is an expression of type float or of a type that can be implicitly converted to float.

@Offset

specifies the window size. @Offset is an expression of type int or of a type that can be implicitly converted to int.

@Lag

permits the exponentially weighted moving average to by returned with the current row (@Lag = 0) or the subsequent row (@Lag = 1). @Lag is an expression of type int or of a type that can be implicitly converted to int.

@RowNum

the number of the row within the group for which the sum is being calculated. If @RowNum for the current row in a set is less than or equal to the previous @RowNum and @RowNum is not equal to 1, an error message will be generated. @RowNum is an expression of type int or of a type that can be implicitly converted to int.

@Id

a unique identifier for the RunningEWMA calculation. @Id allows you to specify multiple RunningEWMA calculation s within a resultant table. @Id is an expression of type tinyint or of a type that can be implicitly converted to tinyint.

Return Type

float

Remarks

If @Id is NULL then @Id = 0.

To calculate daily weighted moving averages, use the DWMA function.

To calculate a daily exponentially weighted moving average, use the DEMA function,

0 < @Alpha < 1.

@Lag must be 0 or 1.

@RowNum must be in ascending order.

There may be cases where the order in which the data are returned to the function and the order in which the results are returned are different, generally due to parallelism. You can use OPTION(MAXDOP 1) or OPTION(MAXDOP 1,FORCE ORDER) to help eliminate this problem.

Examples

In this example, we put a couple of months of price history for stock indices into a table and then calculate the 10-day exponentially weighted moving average for one of the indices with a = .05.

--Create the temporary table
CREATE TABLE #p
(
    ticker varchar(4),
    date_trade datetime,
    price_open money,
    price_high money,
    price_low money,
    price_close money,
    volume bigint,
    price_adj_close money,
    PRIMARY KEY (
                    ticker,
                    date_trade
                )
);
--Populate the table with some data
INSERT INTO #p
VALUES
('GSPC', '2012-10-26', 1412.97, 1417.09, 1403.28, 1411.94, 3284910000, 1411.94);
INSERT INTO #p
VALUES
('GSPC', '2012-10-25', 1409.74, 1421.12, 1405.14, 1412.97, 3512640000, 1412.97);
INSERT INTO #p
VALUES
('GSPC', '2012-10-24', 1413.2, 1420.04, 1407.1, 1408.75, 3385970000, 1408.75);
INSERT INTO #p
VALUES
('GSPC', '2012-10-23', 1433.74, 1433.74, 1407.56, 1413.11, 3587670000, 1413.11);
INSERT INTO #p
VALUES
('GSPC', '2012-10-22', 1433.21, 1435.46, 1422.06, 1433.81, 3216220000, 1433.81);
INSERT INTO #p
VALUES
('GSPC', '2012-10-19', 1457.34, 1457.34, 1429.85, 1433.19, 3875170000, 1433.19);
INSERT INTO #p
VALUES
('GSPC', '2012-10-18', 1460.94, 1464.02, 1452.63, 1457.34, 3880030000, 1457.34);
INSERT INTO #p
VALUES
('GSPC', '2012-10-17', 1454.22, 1462.2, 1453.35, 1460.91, 3655320000, 1460.91);
INSERT INTO #p
VALUES
('GSPC', '2012-10-16', 1440.31, 1455.51, 1440.31, 1454.92, 3568770000, 1454.92);
INSERT INTO #p
VALUES
('GSPC', '2012-10-15', 1428.75, 1441.31, 1427.24, 1440.13, 3483810000, 1440.13);
INSERT INTO #p
VALUES
('GSPC', '2012-10-12', 1432.84, 1438.43, 1425.53, 1428.59, 3134750000, 1428.59);
INSERT INTO #p
VALUES
('GSPC', '2012-10-11', 1432.82, 1443.9, 1432.82, 1432.84, 3672540000, 1432.84);
INSERT INTO #p
VALUES
('GSPC', '2012-10-10', 1441.48, 1442.52, 1430.64, 1432.56, 3225060000, 1432.56);
INSERT INTO #p
VALUES
('GSPC', '2012-10-09', 1455.9, 1455.9, 1441.18, 1441.48, 3216320000, 1441.48);
INSERT INTO #p
VALUES
('GSPC', '2012-10-08', 1460.93, 1460.93, 1453.1, 1455.88, 2328720000, 1455.88);
INSERT INTO #p
VALUES
('GSPC', '2012-10-05', 1461.4, 1470.96, 1456.89, 1460.93, 3172940000, 1460.93);
INSERT INTO #p
VALUES
('GSPC', '2012-10-04', 1451.08, 1463.14, 1451.08, 1461.4, 3615860000, 1461.4);
INSERT INTO #p
VALUES
('GSPC', '2012-10-03', 1446.05, 1454.3, 1441.99, 1450.99, 3531640000, 1450.99);
INSERT INTO #p
VALUES
('GSPC', '2012-10-02', 1444.99, 1451.52, 1439.01, 1445.75, 3321790000, 1445.75);
INSERT INTO #p
VALUES
('GSPC', '2012-10-01', 1440.9, 1457.14, 1440.9, 1444.49, 3505080000, 1444.49);
INSERT INTO #p
VALUES
('GSPC', '2012-09-28', 1447.13, 1447.13, 1435.6, 1440.67, 3509230000, 1440.67);
INSERT INTO #p
VALUES
('GSPC', '2012-09-27', 1433.36, 1450.2, 1433.36, 1447.15, 3150330000, 1447.15);
INSERT INTO #p
VALUES
('GSPC', '2012-09-26', 1441.6, 1441.6, 1430.53, 1433.32, 3565380000, 1433.32);
INSERT INTO #p
VALUES
('GSPC', '2012-09-25', 1456.94, 1463.24, 1441.59, 1441.59, 3739900000, 1441.59);
INSERT INTO #p
VALUES
('GSPC', '2012-09-24', 1459.76, 1460.72, 1452.06, 1456.89, 3008920000, 1456.89);
INSERT INTO #p
VALUES
('GSPC', '2012-09-21', 1460.34, 1467.07, 1459.51, 1460.15, 4833870000, 1460.15);
INSERT INTO #p
VALUES
('GSPC', '2012-09-20', 1461.05, 1461.23, 1449.98, 1460.26, 3382520000, 1460.26);
INSERT INTO #p
VALUES
('GSPC', '2012-09-19', 1459.5, 1465.15, 1457.88, 1461.05, 3451360000, 1461.05);
INSERT INTO #p
VALUES
('GSPC', '2012-09-18', 1461.19, 1461.47, 1456.13, 1459.32, 3377390000, 1459.32);
INSERT INTO #p
VALUES
('GSPC', '2012-09-17', 1465.42, 1465.63, 1457.55, 1461.19, 3482430000, 1461.19);
INSERT INTO #p
VALUES
('GSPC', '2012-09-14', 1460.07, 1474.51, 1460.07, 1465.77, 5041990000, 1465.77);
INSERT INTO #p
VALUES
('GSPC', '2012-09-13', 1436.56, 1463.76, 1435.34, 1459.99, 4606550000, 1459.99);
INSERT INTO #p
VALUES
('GSPC', '2012-09-12', 1433.56, 1439.15, 1432.99, 1436.56, 3641200000, 1436.56);
INSERT INTO #p
VALUES
('GSPC', '2012-09-11', 1429.13, 1437.76, 1429.13, 1433.56, 3509630000, 1433.56);
INSERT INTO #p
VALUES
('GSPC', '2012-09-10', 1437.92, 1438.74, 1428.98, 1429.08, 3223670000, 1429.08);
INSERT INTO #p
VALUES
('GSPC', '2012-09-07', 1432.12, 1437.92, 1431.45, 1437.92, 3717620000, 1437.92);
INSERT INTO #p
VALUES
('GSPC', '2012-09-06', 1403.74, 1432.12, 1403.74, 1432.12, 3952870000, 1432.12);
INSERT INTO #p
VALUES
('GSPC', '2012-09-05', 1404.94, 1408.81, 1401.25, 1403.44, 3389110000, 1403.44);
INSERT INTO #p
VALUES
('GSPC', '2012-09-04', 1406.54, 1409.31, 1396.56, 1404.94, 3200310000, 1404.94);
INSERT INTO #p
VALUES
('GSPC', '2012-08-31', 1400.07, 1413.09, 1398.96, 1406.58, 2938250000, 1406.58);
INSERT INTO #p
VALUES
('GSPC', '2012-08-30', 1410.08, 1410.08, 1397.01, 1399.48, 2530280000, 1399.48);
INSERT INTO #p
VALUES
('GSPC', '2012-08-29', 1409.32, 1413.95, 1406.57, 1410.49, 2571220000, 1410.49);
INSERT INTO #p
VALUES
('GSPC', '2012-08-28', 1410.44, 1413.63, 1405.59, 1409.3, 2629090000, 1409.3);
INSERT INTO #p
VALUES
('GSPC', '2012-08-27', 1411.13, 1416.17, 1409.11, 1410.44, 2472500000, 1410.44);
INSERT INTO #p
VALUES
('GSPC', '2012-08-24', 1401.99, 1413.46, 1398.04, 1411.13, 2598790000, 1411.13);
INSERT INTO #p
VALUES
('DJI', '2012-10-26', 13104.22, 13151.72, 13040.17, 13107.21, 1346400, 13107.21);
INSERT INTO #p
VALUES
('DJI', '2012-10-25', 13079.64, 13214.11, 13017.37, 13103.68, 1145900, 13103.68);
INSERT INTO #p
VALUES
('DJI', '2012-10-24', 13103.53, 13155.21, 13063.63, 13077.34, 1106700, 13077.34);
INSERT INTO #p
VALUES
('DJI', '2012-10-23', 13344.9, 13344.9, 13083.28, 13102.53, 1222200, 13102.53);
INSERT INTO #p
VALUES
('DJI', '2012-10-22', 13344.28, 13368.55, 13235.15, 13345.89, 1218800, 13345.89);
INSERT INTO #p
VALUES
('DJI', '2012-10-19', 13545.33, 13545.49, 13312.22, 13343.51, 2390800, 13343.51);
INSERT INTO #p
VALUES
('DJI', '2012-10-18', 13553.24, 13588.73, 13510.93, 13548.94, 1284100, 13548.94);
INSERT INTO #p
VALUES
('DJI', '2012-10-17', 13539.63, 13561.65, 13468.9, 13557, 1355700, 13557);
INSERT INTO #p
VALUES
('DJI', '2012-10-16', 13423.84, 13556.37, 13423.76, 13551.78, 1134500, 13551.78);
INSERT INTO #p
VALUES
('DJI', '2012-10-15', 13329.54, 13437.66, 13325.93, 13424.23, 1148800, 13424.23);
INSERT INTO #p
VALUES
('DJI', '2012-10-12', 13325.62, 13401.32, 13296.43, 13328.85, 1137400, 13328.85);
INSERT INTO #p
VALUES
('DJI', '2012-10-11', 13346.28, 13428.49, 13326.12, 13326.39, 866300, 13326.39);
INSERT INTO #p
VALUES
('DJI', '2012-10-10', 13473.53, 13478.83, 13327.62, 13344.97, 1011200, 13344.97);
INSERT INTO #p
VALUES
('DJI', '2012-10-09', 13582.88, 13592.33, 13473.31, 13473.53, 1036300, 13473.53);
INSERT INTO #p
VALUES
('DJI', '2012-10-08', 13589.26, 13610.38, 13552.09, 13583.65, 713000, 13583.65);
INSERT INTO #p
VALUES
('DJI', '2012-10-05', 13569.18, 13661.87, 13568.75, 13610.15, 1155000, 13610.15);
INSERT INTO #p
VALUES
('DJI', '2012-10-04', 13495.18, 13594.33, 13495.18, 13575.36, 1063900, 13575.36);
INSERT INTO #p
VALUES
('DJI', '2012-10-03', 13479.21, 13536.27, 13439.12, 13494.61, 1038900, 13494.61);
INSERT INTO #p
VALUES
('DJI', '2012-10-02', 13515.3, 13567.06, 13424.92, 13482.36, 907300, 13482.36);
INSERT INTO #p
VALUES
('DJI', '2012-10-01', 13437.66, 13598.25, 13437.66, 13515.11, 1061200, 13515.11);
INSERT INTO #p
VALUES
('DJI', '2012-09-28', 13485.89, 13487.66, 13367.27, 13437.13, 1469500, 13437.13);
INSERT INTO #p
VALUES
('DJI', '2012-09-27', 13413.47, 13522.83, 13413.47, 13485.97, 1139900, 13485.97);
INSERT INTO #p
VALUES
('DJI', '2012-09-26', 13458.63, 13480.37, 13406.91, 13413.51, 1243500, 13413.51);
INSERT INTO #p
VALUES
('DJI', '2012-09-25', 13559.92, 13620.21, 13457.25, 13457.55, 1386300, 13457.55);
INSERT INTO #p
VALUES
('DJI', '2012-09-24', 13577.85, 13601.9, 13521.68, 13558.92, 1203700, 13558.92);
INSERT INTO #p
VALUES
('DJI', '2012-09-21', 13597.24, 13647.1, 13571.53, 13579.47, 4296100, 13579.47);
INSERT INTO #p
VALUES
('DJI', '2012-09-20', 13575.17, 13599.02, 13503, 13596.93, 1179100, 13596.93);
INSERT INTO #p
VALUES
('DJI', '2012-09-19', 13565.41, 13626.48, 13556.74, 13577.96, 1162100, 13577.96);
INSERT INTO #p
VALUES
('DJI', '2012-09-18', 13552.33, 13582.12, 13517.81, 13564.64, 1207200, 13564.64);
INSERT INTO #p
VALUES
('DJI', '2012-09-17', 13588.57, 13593.15, 13526.67, 13553.1, 1280200, 13553.1);
INSERT INTO #p
VALUES
('DJI', '2012-09-14', 13540.4, 13653.24, 13533.94, 13593.37, 1851600, 13593.37);
INSERT INTO #p
VALUES
('DJI', '2012-09-13', 13329.71, 13573.33, 13325.11, 13539.86, 1517700, 13539.86);
INSERT INTO #p
VALUES
('DJI', '2012-09-12', 13321.62, 13373.62, 13317.52, 13333.35, 1115200, 13333.35);
INSERT INTO #p
VALUES
('DJI', '2012-09-11', 13254.6, 13354.34, 13253.21, 13323.36, 1049200, 13323.36);
INSERT INTO #p
VALUES
('DJI', '2012-09-10', 13308.56, 13324.1, 13251.39, 13254.29, 1238100, 13254.29);
INSERT INTO #p
VALUES
('DJI', '2012-09-07', 13289.53, 13320.27, 13266.22, 13306.64, 1422100, 13306.64);
INSERT INTO #p
VALUES
('DJI', '2012-09-06', 13045.23, 13294.13, 13045.08, 13292, 1286500, 13292);
INSERT INTO #p
VALUES
('DJI', '2012-09-05', 13036.09, 13095.91, 13018.74, 13047.48, 925500, 13047.48);
INSERT INTO #p
VALUES
('DJI', '2012-09-04', 13092.15, 13092.39, 12977.09, 13035.94, 1039200, 13035.94);
INSERT INTO #p
VALUES
('DJI', '2012-08-31', 13002.72, 13151.87, 13002.64, 13090.84, 1197800, 13090.84);
INSERT INTO #p
VALUES
('DJI', '2012-08-30', 13101.29, 13101.37, 12978.91, 13000.71, 899800, 13000.71);
INSERT INTO #p
VALUES
('DJI', '2012-08-29', 13103.46, 13144.81, 13081.27, 13107.48, 915300, 13107.48);
INSERT INTO #p
VALUES
('DJI', '2012-08-28', 13122.74, 13147.32, 13081.12, 13102.99, 816300, 13102.99);
INSERT INTO #p
VALUES
('DJI', '2012-08-27', 13157.74, 13176.17, 13115.46, 13124.67, 960700, 13124.67);
INSERT INTO #p
VALUES
('DJI', '2012-08-24', 13052.82, 13175.51, 13027.2, 13157.97, 880300, 13157.97);
INSERT INTO #p
VALUES
('IXIC', '2012-10-26', 2986.05, 2999.14, 2961.16, 2987.95, 1839700000, 2987.95);
INSERT INTO #p
VALUES
('IXIC', '2012-10-25', 3005.04, 3007.71, 2975.98, 2986.12, 1922660000, 2986.12);
INSERT INTO #p
VALUES
('IXIC', '2012-10-24', 3011.82, 3012.95, 2978.73, 2981.7, 1967000000, 2981.7);
INSERT INTO #p
VALUES
('IXIC', '2012-10-23', 2989.44, 3006.59, 2974.07, 2990.46, 1830840000, 2990.46);
INSERT INTO #p
VALUES
('IXIC', '2012-10-22', 3005.92, 3020.61, 2995.78, 3016.96, 1654130000, 3016.96);
INSERT INTO #p
VALUES
('IXIC', '2012-10-19', 3066.56, 3066.56, 3000.27, 3005.62, 2225580000, 3005.62);
INSERT INTO #p
VALUES
('IXIC', '2012-10-18', 3097.77, 3102.56, 3065.24, 3072.87, 2043290000, 3072.87);
INSERT INTO #p
VALUES
('IXIC', '2012-10-17', 3091.38, 3112.45, 3088.05, 3104.12, 1770920000, 3104.12);
INSERT INTO #p
VALUES
('IXIC', '2012-10-16', 3073.21, 3102.97, 3070.25, 3101.17, 1736930000, 3101.17);
INSERT INTO #p
VALUES
('IXIC', '2012-10-15', 3053.21, 3066.31, 3037.27, 3064.18, 1563440000, 3064.18);
INSERT INTO #p
VALUES
('IXIC', '2012-10-12', 3049.08, 3061.77, 3039.58, 3044.11, 1524840000, 3044.11);
INSERT INTO #p
VALUES
('IXIC', '2012-10-11', 3075.89, 3078.08, 3047.14, 3049.41, 1595020000, 3049.41);
INSERT INTO #p
VALUES
('IXIC', '2012-10-10', 3066.25, 3071.57, 3046.78, 3051.78, 1788970000, 3051.78);
INSERT INTO #p
VALUES
('IXIC', '2012-10-09', 3108.01, 3108.01, 3062.52, 3065.02, 1645740000, 3065.02);
INSERT INTO #p
VALUES
('IXIC', '2012-10-08', 3121.33, 3125.49, 3107.57, 3112.35, 1186260000, 3112.35);
INSERT INTO #p
VALUES
('IXIC', '2012-10-05', 3161.21, 3171.46, 3130.76, 3136.19, 1607940000, 3136.19);
INSERT INTO #p
VALUES
('IXIC', '2012-10-04', 3142.38, 3153.48, 3132.56, 3149.46, 1585190000, 3149.46);
INSERT INTO #p
VALUES
('IXIC', '2012-10-03', 3130.85, 3142.36, 3115.04, 3135.23, 1704050000, 3135.23);
INSERT INTO #p
VALUES
('IXIC', '2012-10-02', 3127.73, 3131.64, 3101.64, 3120.04, 1609570000, 3120.04);
INSERT INTO #p
VALUES
('IXIC', '2012-10-01', 3130.31, 3146.99, 3103.89, 3113.53, 1758170000, 3113.53);
INSERT INTO #p
VALUES
('IXIC', '2012-09-28', 3125.31, 3132.51, 3109.91, 3116.23, 1864640000, 3116.23);
INSERT INTO #p
VALUES
('IXIC', '2012-09-27', 3105.87, 3142.02, 3098.46, 3136.6, 1691800000, 3136.6);
INSERT INTO #p
VALUES
('IXIC', '2012-09-26', 3113.4, 3114.54, 3080.28, 3093.7, 1738010000, 3093.7);
INSERT INTO #p
VALUES
('IXIC', '2012-09-25', 3170.37, 3176.3, 3117.73, 3117.73, 1975470000, 3117.73);
INSERT INTO #p
VALUES
('IXIC', '2012-09-24', 3155.35, 3167.74, 3150.71, 3160.78, 1704860000, 3160.78);
INSERT INTO #p
VALUES
('IXIC', '2012-09-21', 3194.86, 3196.93, 3178.09, 3179.96, 2526250000, 3179.96);
INSERT INTO #p
VALUES
('IXIC', '2012-09-20', 3166.84, 3178.45, 3156.46, 3175.96, 1809130000, 3175.96);
INSERT INTO #p
VALUES
('IXIC', '2012-09-19', 3179.04, 3189.35, 3170.29, 3182.62, 1850920000, 3182.62);
INSERT INTO #p
VALUES
('IXIC', '2012-09-18', 3173.62, 3179.37, 3169.41, 3177.8, 1707200000, 3177.8);
INSERT INTO #p
VALUES
('IXIC', '2012-09-17', 3183.4, 3183.4, 3168.63, 3178.67, 1485390000, 3178.67);
INSERT INTO #p
VALUES
('IXIC', '2012-09-14', 3166.24, 3195.67, 3164.26, 3183.95, 1984720000, 3183.95);
INSERT INTO #p
VALUES
('IXIC', '2012-09-13', 3117.66, 3167.63, 3112.62, 3155.83, 1870050000, 3155.83);
INSERT INTO #p
VALUES
('IXIC', '2012-09-12', 3115.33, 3120.12, 3098.82, 3114.31, 1689140000, 3114.31);
INSERT INTO #p
VALUES
('IXIC', '2012-09-11', 3105.02, 3117.86, 3099.1, 3104.53, 1586250000, 3104.53);
INSERT INTO #p
VALUES
('IXIC', '2012-09-10', 3131.34, 3133.89, 3102.76, 3104.02, 1575370000, 3104.02);
INSERT INTO #p
VALUES
('IXIC', '2012-09-07', 3133.22, 3139.61, 3128.17, 3136.42, 1740640000, 3136.42);
INSERT INTO #p
VALUES
('IXIC', '2012-09-06', 3087.94, 3135.81, 3087.67, 3135.81, 1918900000, 3135.81);
INSERT INTO #p
VALUES
('IXIC', '2012-09-05', 3072.58, 3082.75, 3062.54, 3069.27, 1495030000, 3069.27);
INSERT INTO #p
VALUES
('IXIC', '2012-09-04', 3063.25, 3082.26, 3040.24, 3075.06, 1505960000, 3075.06);
INSERT INTO #p
VALUES
('IXIC', '2012-08-31', 3069.64, 3078.52, 3040.59, 3066.96, 1394760000, 3066.96);
INSERT INTO #p
VALUES
('IXIC', '2012-08-30', 3066.73, 3067.54, 3045.92, 3048.71, 1216640000, 3048.71);
INSERT INTO #p
VALUES
('IXIC', '2012-08-29', 3078.05, 3087.24, 3067.62, 3081.19, 1282900000, 3081.19);
INSERT INTO #p
VALUES
('IXIC', '2012-08-28', 3069.4, 3083.19, 3063.65, 3077.14, 1364740000, 3077.14);
INSERT INTO #p
VALUES
('IXIC', '2012-08-27', 3083.62, 3085.81, 3068.13, 3073.19, 1383530000, 3073.19);
INSERT INTO #p
VALUES
('IXIC', '2012-08-24', 3045.22, 3076.8, 3042.22, 3069.79, 1349740000, 3069.79);
--Calculate the 10-days EWMA for DJI with an Alpha of .182
SELECT ticker,
       cast(date_trade as date) as [trade date],
       price_close as [Closing Price],
       wct.MovingEWMA(price_close, .182, 10, 0, ROW_NUMBER() OVER (ORDER BY 
                 date_trade ASC), NULL) as [EWMA]
FROM #p
WHERE ticker = 'DJI'
ORDER BY date_trade ASC;
--Clean up
DROP TABLE #p;

This produces the following result.