[通达信指标/源码] [转载]K线微积分律与MACD

张咏

1. {K线微积分律与MACD；MACD_DCIC_K ；原创及版权属于JIPGEMLING.见凌见；}
   
2. {关键词：K线微积分律，MACD指标}
   
3. {仅允许个人自用、互联网传播并带上作者笔名及版权声明}
   
4. 
   
5. {本文实际证明了等式：
   
6. DIF=(LONG-SHORT)/2*EMA(EMA((C-REF(C,1)),SHORT),LONG)
   
7.    =((LONG-SHORT)/2)*EMA(EMA(C,SHORT)-REF(EMA(C,SHORT),1),LONG)
   
8.    =EMA(C,SHORT)-EMA(C,LONG) }
   
9. {即，对于SHORT>=1和LONG>=1 的所有正整数，上述等式成立。}
   
10. 
    
11. 
    
12. {证明：用数学归纳法。由于我们不知道股软函数EMA()、REF()的具体形式，所以计算过程要结合股软(TDX)辅证。
    
13. 1、首先当SHORT=1、LONG=1时，公式两边0=0，等式显然成立；
    
14. 2、当SHORT=1、LONG=>2时并在股软上任意调节对比，等式两边数值非恒量但均相等，故等式成立；
    
15. 3、当LONG=1时，SHORT=>2并在股软上任意调节对比，等式两边数值非恒量但均相等，故等式成立；
    
16. 4、其余任意正整数，在股软上任意调节对比，等式两边数值非恒量但均相等，故等式成立；
    
17. 5、根据上述结论和数学归纳法原理，对于SHORT>=1和LONG>=1 的所有正整数，等式成立。证毕。}
    
18. 
    
19. {同理可证1：DIF_H =(LONG-SHORT)/2*EMA(EMA((H-REF(H,1)),SHORT),LONG)=  }
    
20. {=((LONG-SHORT)/2)*EMA(EMA(H,SHORT)-REF(EMA(H,SHORT),1),LONG)=EMA(H,SHORT)-EMA(H,LONG)；}
    
21. {同理可证2：DIF_L =(LONG-SHORT)/2*EMA(EMA((L-REF(L,1)),SHORT),LONG)=  }
    
22. {=((LONG-SHORT)/2)*EMA(EMA(L,SHORT)-REF(EMA(L,SHORT),1),LONG)=EMA(L,SHORT)-EMA(L,LONG)；}
    
23. {同理可证3：DIF_O =(LONG-SHORT)/2*EMA(EMA((O-REF(O,1)),SHORT),LONG)=  }
    
24. {=((LONG-SHORT)/2)*EMA(EMA(O,SHORT)-REF(EMA(O,SHORT),1),LONG)=EMA(O,SHORT)-EMA(O,LONG)；}
    
25. {同理可证4：DIF_CC =(LONG-SHORT)/2*EMA(EMA((CC-REF(CC,1)),SHORT),LONG)=  }
    
26. {=((LONG-SHORT)/2)*EMA(EMA(CC,SHORT)-REF(EMA(CC,SHORT),1),LONG)=EMA(CC,SHORT)-EMA(CC,LONG)；}
    
27. {其中CC=(C+H+L)/3；只要C、H、L、O 属于相同时序的常系数线性组合（可否为有理式组合？）}
    
28. 
    
29. {可否考虑将上述事实作为一个【K线定理、定律】来看待？}
    
30. 
    
31. {MACD功效、一般应用、典型应用条件}
    
32. {一般应用条件:LONG>SHORT；典型应用:LONG=2*(SHORT+1),}
    
33. {即LONG是SHORT的2个倍频程+2个K线单位时程（看待为积分一个完整的脉冲周期而又不致于丢失信息和混入杂波）}
    
34. {微分具有剔除低频(长线资金)的作用，积分是微分的反运算,并有压制高频杂波(投机资金)的作用。}
    
35. {MACD式子是个“有源平直中频带通滤波器”,做法是差值滤波并作2倍放大，取得中线资金激励信息。}
    
36. {MACD指标突出中线资金的买卖趋势。0轴为多空平衡位。参数设置应考虑是否符合指标本身固有功能}
    
37. 
    
38. {受中波广播频段(535kHz--1605kHz)设置的启发，现提出 LONG<=3*SHORT 这样的条件是否合理？}
    
39. 
    
40. {语句注释}
    
41. DFC:=C-REF(C,1);{收盘价前差值，K线微分}
    
42. WJXS:=(LONG-SHORT)/2;{微积分系数，可由中值定理导出，为兼顾后面引用及统一标尺，前移至此}
    
43. JGL_JF:=WJXS*EMA(DFC,SHORT);{内层积分，隐含积分限[1--SHORT],结果:WJXS*EMA(EMA(CC,SHORT)-REF(EMA(CC,SHORT),1),LONG)}
    
44. DIF_JIP:EMA(JGL_JF,LONG);{外层积分，重积分，隐含积分限[1--LONG],结果:EMA(CC,SHORT)-EMA(CC,LONG)}
    
45. DEA_GEM:EMA(DIF_JIP,MID);{平滑，压制高频}
    
46. MACD_LING:2*(DIF_JIP-DEA_GEM),COLOR1133FF,COLORSTICK;{差值滤波然后作2倍放大，显示红、青色针状线柱}
    
47. 
    
48. {“类KDJ”}
    
49. {以下为“类KDJ”及显示“J值前差值柱”，后者可提高对涨跌的肉眼分辨率，提高对短线波动的感知度}
    
50. {J值式子具有“有源高频滤波器”性质,经典KDJ的J是对高频信号作3倍放大，D是对中高频作2倍放大，}
    
51. {然后差值滤波,滤掉中低频和杂波信号，所以在选择系数时应考虑使激励与阻尼达平衡,避免过激励和欠激励}
    
52. {J_DF系数，设A=2.00~3.00,B=1.00~2.00,弱必要条件是 A-B=1，使差值信号仍有1倍放大，3条线间隔大致等距}
    
53. 
    
54. K_DF_J:SMA(JGL_JF,M1,1),COLORFEDCBA;{平滑，压制超短线杂波}
    
55. D_DF_G:SMA(K_DF_J,M2,1),COLOR13F8F9;{再平滑，圆滑超短线造成的扰动}
    
56. J_DF_L:2.5*K_DF_J-1.5*D_DF_G,COLORF813F9;{有源差值滤波，取得中高频短线信号}
    
57. RF:=REF(J_DF_L,1);
    
58. DJ:=ABS(J_DF_L-RF);
    
59. MM:=(HHV(DJ,120)+LLV(DJ,120))/2;
    
60. STICKLINE(J_DF_L>RF,J_DF_L,RF,2.3,0),COLOR1388D3;
    
61. STICKLINE(J_DF_L>RF,J_DF_L,RF,1.0,0),COLOR13AAD3;
    
62. STICKLINE(J_DF_L<RF,J_DF_L,RF,2.3,0),COLOR338833;
    
63. STICKLINE(J_DF_L<RF,J_DF_L,RF,1.0,0),COLOR33AA33;
    
64. STICKLINE(J_DF_L<RF AND DJ<0.2*MM,J_DF_L+0.15*MM,RF-0.15*MM,0.1,0),COLOR33AA33;
    
65. STICKLINE(J_DF_L>=RF AND DJ<0.2*MM,RF-0.1*MM,J_DF_L+0.1*MM,0.1,0),COLOR13AADD;
    
66. 
    
67. {轨道设置，仅作试用;KG(开关，默认 开)；{飞狐等版本可考虑用虚线}}
    
68. 
    
69. N:=SQRT(SHORT*LONG);
    
70. NN:=IF(N<9,9,N);
    
71. BZC:=STD(DFC,NN);
    
72. U:IF(KG=1,K_DF_J+2*BZC,MA(C,25600)),COLORFE9813,CROSSDOT,LINETHICK2;
    
73. D:IF(KG=1,K_DF_J-2*BZC,MA(C,25600)),COLOR33EAEA,CROSSDOT,LINETHICK2;
    
74. 
    
75. 
    
76. 
    
77. {实际加入编译的语句及“说明头”如下}
    
78. 
    
79. 
    
80. 
    
81. {副图：MACD_DCIC ；K线微积分律与MACD；}
    
82. {原创及版权属于JIPGEMLING.见凌见;JIPGEMLING.签名版}
    
83. {参数设置: SHORT(1,300,12);LONG(2,300,26);MID(2,200,9);}
    
84. {参数设置: M1(2,300,3);M2(2,300,3);KG(1,2,1);}
    
85. {坐标线位置：自动；额外Y轴分界 值1=0；}
    
86. {TDX版(基本通用版)中高分辨率屏幕;如嫁接其他版本，可调整“J值前差值柱”的宽度}
    
87. 
    
88. DFC:=C-REF(C,1);
    
89. WJXS:=(LONG-SHORT)/2;
    
90. JGL_JF:=WJXS*EMA(DFC,SHORT);
    
91. DIF_JIP:EMA(JGL_JF,LONG),COLOR1188FF,LINETHICK2;
    
92. DEA_GEM:EMA(DIF_JIP,MID),COLORGREEN,LINETHICK2;
    
93. MACD_LING:2*(DIF_JIP-DEA_GEM),COLOR1133FF,COLORSTICK;
    
94. K_DF_J:SMA(JGL_JF,M1,1),COLORFEDCBA;
    
95. D_DF_G:SMA(K_DF_J,M2,1),COLOR13F8F9;
    
96. J_DF_L:2.5*K_DF_J-1.5*D_DF_G,COLORF813F9;
    
97. RF:=REF(J_DF_L,1);
    
98. DJ:=ABS(J_DF_L-RF);
    
99. MM:=(HHV(DJ,120)+LLV(DJ,120))/2;
    
100. STICKLINE(J_DF_L>RF,J_DF_L,RF,2.3,0),COLOR1388D3;
     
101. STICKLINE(J_DF_L>RF,J_DF_L,RF,1.0,0),COLOR13AAD3;
     
102. STICKLINE(J_DF_L<RF,J_DF_L,RF,2.3,0),COLOR338833;
     
103. STICKLINE(J_DF_L<RF,J_DF_L,RF,1.0,0),COLOR33AA33;
     
104. STICKLINE(J_DF_L<RF AND DJ<0.2*MM,J_DF_L+0.15*MM,RF-0.15*MM,0.1,0),COLOR33AA33;
     
105. STICKLINE(J_DF_L>=RF AND DJ<0.2*MM,RF-0.1*MM,J_DF_L+0.1*MM,0.1,0),COLOR13AADD;
     
106. N:=SQRT(SHORT*LONG);
     
107. NN:=IF(N<9,9,N);
     
108. BZC:=STD(DFC,NN);
     
109. U:IF(KG=1,K_DF_J+2*BZC,MA(C,25600)),COLORFE9813,CROSSDOT,LINETHICK2;
     
110. D:IF(KG=1,K_DF_J-2*BZC,MA(C,25600)),COLOR33EAEA,CROSSDOT,LINETHICK2;
     
111. 
     
112. *************************************************************************************************
     
113. 
     
114. MACD的微积分解析与再造
     
115. 
     
116. {副图名：DF_MACD ；中文名：微分MACD；发明人及版权属于JIPGEMLING.见凌见};
     
117. {参数：SHORT(2,200,12);LONG(2,200,26);MID(2,200,9);M(2,100,3)};
     
118. {额外Y轴分界，值1：0.00  ;坐标线位置：自动 };
     
119. {环球通用版};
     
120. WXS:=(LONG-SHORT)/2;{系数};
     
121. JGL_DF:=WXS*(EMA(CLOSE,SHORT)-REF(EMA(CLOSE,SHORT),1));{微分};
     
122. DIF_J:EMA(JGL_DF,LONG),COLORFEDCBA,LINETHICK2;{积分};
     
123. DEA_G:EMA(DIF_J,MID),LINETHICK2;{平滑};
     
124. MACD_L:(DIF_J-DEA_G)*2,COLOR1133FE,COLORSTICK;
     
125. K_DF:SMA(JGL_DF,M,1),COLOR1188FF;{以下为“类KDJ”};
     
126. D_DF:SMA(K_DF,3,1),COLOR13FF99;
     
127. J_DF:2.6*K_DF-1.6*D_DF,COLORAF13FA;
     
128. RF:=REF(J_DF,1);
     
129. STICKLINE(J_DF>=RF,J_DF,RF,2.3,0),COLOR1399FE;
     
130. STICKLINE(J_DF>=RF,J_DF,RF,1.0,0),COLOR13DDFE;
     
131. STICKLINE(J_DF<RF,J_DF,RF,2.3,0),COLORFF9913;
     
132. STICKLINE(J_DF<RF,J_DF,RF,1.0,0),COLORFFDD13;
     
133. **************************************************************************
     
134. 
     
135. 修改版，提高了显示效果。
     
136. 
     
137. 
     
138. {副图名：DF_MACD ；中文名：微分MACD；发明人及版权属于JIPGEMLING.见凌见}
     
139. {参数：SHORT(2,200,12);LONG(2,200,26);MID(2,200,9);M(2,100,3)}
     
140. {额外Y轴分界，值1：0.00  ;坐标线位置：自动 }
     
141. 
     
142. WXS:=(LONG-SHORT)/2;{系数}
     
143. JGL_DF:=WXS*(EMA(CLOSE,SHORT)-REF(EMA(CLOSE,SHORT),1));{微分}
     
144. DIF_J:EMA(JGL_DF,LONG),COLOR1234AA,LINETHICK2;{积分}
     
145. DEA_G:EMA(DIF_J,MID),COLOR338833,LINETHICK2;{平滑}
     
146. MACD_L:(DIF_J-DEA_G)*2,COLORA9A813,COLORSTICK;
     
147. K_DF:SMA(JGL_DF,M,1)*1,COLORFEDCBA;{以下为“类KDJ”}
     
148. D_DF:SMA(K_DF,M,1),COLOR13F8F9;
     
149. J_DF:3*K_DF-2*D_DF,COLORF813F9;
     
150. {以下显示“J_DF前差值柱”，柱子太薄时显示“十”字星}
     
151. RF:=REF(J_DF,1);
     
152. DJ:=ABS(J_DF-RF);
     
153. MM:=(HHV(DJ,240)+LLV(DJ,240))/2;
     
154. STICKLINE(J_DF>RF,J_DF,RF,2.3,0),COLOR1388D3;
     
155. STICKLINE(J_DF>RF,J_DF,RF,1.0,0),COLOR13AAD3;
     
156. STICKLINE(J_DF<RF,J_DF,RF,2.3,0),COLOR338833;
     
157. STICKLINE(J_DF<RF,J_DF,RF,1.0,0),COLOR33AA33;
     
158. STICKLINE(J_DF<RF AND DJ<0.2*MM,J_DF-0.1*MM,RF+0.1*MM,0.1,0),COLOR33AA33;
     
159. STICKLINE(J_DF>=RF AND DJ<0.2*MM,J_DF+0.1*MM,RF-0.1*MM,0.1,0),COLOR13AADD;
     
160. 
     
161. 
     
162. 以上是位高手发现之旅

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