Generating Moving Average Trading Rules on the Oil Futures Market with Genetic Algorithms

Table 1

Details of the six moving average indicators.

Indicator	Calculation method (𝑝 denotes price)
SMA	SMA(𝑘)= 1𝑛^𝑛−1𝑖∑=0𝑝𝑘−𝑖.
WMA	∑WMA(𝑘)=^𝑛−1𝑖=0(𝑛−𝑖)𝑝𝑘−𝑖∑^𝑛−1𝑖=0(𝑛−𝑖).
EMA	EMA(𝑘)=EMA(𝑘−1)+SC𝑝𝑘−EMA(𝑘−1),; where 2SC=(1+𝑛).
AMA	AMA(𝑘)=AMA(𝑘−1)+SSC𝑘^2𝑝𝑘−AMA(𝑘−1),; where SSC𝑘=ER𝑘(fastSC−slowSC)+slowSC,; 2fastSC=(1+2),  2slowSC=(1+30),; ER𝑘=𝑝𝑘−𝑝𝑘−𝑛∑^𝑘𝑖=𝑘−𝑛+1𝑝𝑖−𝑝𝑖−1.
TPMA	TPMA(𝑘)=(high+low+close)3,; where high=max(𝑝𝑚,𝑝𝑚−1,…,𝑝𝑚−𝑛+1), low=min(𝑝𝑚,𝑝𝑚−1,…,𝑝𝑚−𝑛+1), close=𝑝𝑚.
TMA	1TMA(𝑘)=𝑛^𝑛−1𝑖∑=0SAM(𝑘−𝑖).