指數移動平均線(Exponential Moving Average, EMA)

計算方式

Today EMA = (Today CP * K) + Yesterday EMA * (1 - K)

Today EMA: 今日 EMA
Today CP: 今日收盤價
K: 加權指數 (Something / N + 1)
N: 時間週期
Something: 平滑因子，通常預設為 2

舉例陽明(2609) 111/02/18 的 5 EMA

加權指數
K = 平滑因子 / (時間週期 + 1)
= Something / (N + 1)
= 2 / (5 + 1)
= 2 / 6
= 0.333333333

今日 EMA
Today EMA = (今日收盤價 * 加權指數) + 昨日 EMA * (1 - 加權指數)
= (Today CP * K) + Yesterday EMA * (1 - K)
= (116.50 * 0.333333333) + 111.53 * (1 - 0.333333333)
= 38.833332945 + 111.53 * 0.666666667
= 38.833332945 + 74.35333337051
= 113.18666631551 約等於 133.19

舉例陽明(2609) 111/02/18 的 10 EMA

加權指數
K = 平滑因子 / (時間週期 + 1)
= Something / (N + 1)
= 2 / (10 + 1)
= 2 / 11
= 0.181818182

今日 EMA
Today EMA = (今日收盤價 * 加權指數) + 昨日 EMA * (1 - 加權指數)
= (Today CP * K) + Yesterday EMA * (1 - K)
= (116.50 * 0.181818182) + 110.24 * (1 - 0.181818182)
= 21.181818203 + 110.24 * 0.818181818
= 21.181818203 + 90.19636361632
= 111.37818181932 約等於 111.38

舉例陽明(2609) 111/02/18 的 20 EMA

加權指數
K = 平滑因子 / (時間週期 + 1)
= Something / (N + 1)
= 2 / (20 + 1)
= 2 / 21
= 0.095238095

今日 EMA
Today EMA = (今日收盤價 * 加權指數) + 昨日 EMA * (1 - 加權指數)
= (Today CP * K) + Yesterday EMA * (1 - K)
= (116.50 * 0.095238095) + 109.94 * (1 - 0.095238095)
= 11.0952380675 + 109.94 * 0.904761905
= 11.0952380675 + 99.4695238357
= 110.5647619032 約等於 110.57

範例資料

日期	開盤價	最高價	最低價	收盤價	成交量	5EMA	10EMA	20EMA
111/02/18	112.00	118.00	111.00	116.50	103,926	113.19	111.38	110.57
111/02/17	113.00	114.50	111.50	112.00	39,731	111.53	110.24	109.94
111/02/16	113.50	113.50	112.00	112.50	30,104	111.30	109.85	109.73
111/02/15	112.00	112.50	110.50	111.00	31,536	110.70	109.26	109.43
111/02/14	111.50	115.50	110.50	110.50	71,168	110.55	108.88	109.27
111/02/11	114.00	115.00	112.00	112.00	55,575	110.57	108.52	109.14
111/02/10	113.50	114.50	111.50	114.00	42,037	109.86	107.74	108.84
111/02/09	114.00	115.50	111.00	112.00	62,258	107.79	106.35	108.30
111/02/08	109.00	116.50	108.50	112.50	155,773	105.68	105.10	107.91
111/02/07	100.50	108.00	100.00	108.00	59,599	102.27	103.45	107.42
111/01/26	96.10	99.90	96.10	98.60	51,052	99.41	102.44	107.36
111/01/25	99.00	99.10	95.10	95.10	48,479	99.81	103.30	108.28
111/01/24	97.00	101.00	96.50	99.90	48,844	102.17	105.12	109.67
111/01/21	103.00	103.50	99.00	99.00	65,444	103.31	106.28	110.70
111/01/20	104.00	105.50	103.50	104.00	28,239	105.46	107.90	111.93
111/01/19	105.00	107.50	103.00	104.00	51,633	106.19	108.76	112.77
111/01/18	104.50	108.00	104.00	106.50	31,750	107.29	109.82	113.69
111/01/17	106.00	106.50	104.50	105.50	30,165	107.68	110.56	114.44
111/01/14	105.00	107.50	103.00	107.50	55,764	108.77	111.68	115.39
111/01/13	108.50	109.50	105.00	105.00	47,851	109.41	112.61	116.22
111/01/12	113.50	114.00	107.50	108.00	54,098	111.61	114.31	117.40
111/01/11	112.00	115.00	110.50	112.00	41,157	113.42	115.71	118.39
111/01/10	111.50	114.50	109.00	111.50	47,052	114.13	116.53	119.06
111/01/07	115.50	116.00	111.00	113.50	37,537	115.45	117.65	119.85
111/01/06	113.50	117.00	113.50	114.50	35,949	116.42	118.57	120.52
111/01/05	115.00	117.00	113.50	115.00	35,370	117.39	119.48	121.16
111/01/04	115.00	116.00	113.50	115.50	36,842	118.58	120.47	121.80
111/01/03	120.00	120.50	113.00	114.50	106,847	120.12	121.58	122.47