Tham khảo tài liệu 'ehlers, john - cybernetics analysis for stock and futures_2', tài chính - ngân hàng, đầu tư chứng khoán phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 14 CYBERNETIC ANALYSIS FOR STOCKS AND FUTURES Trends and Cycles 15 the filtered amplitude is so small at these frequencies. The real impact of lag of all moving averages is the value of the lag at very low frequencies. With Equation we now have the capacity to construct a high-pass filter. We will subtract Equation from unity as 2-5 l- l-a Z 1- l r 1 - 1 - a z1 l- l-a z-1 Sharper attenuation can be obtained by using higher-order filters. However I have learned that higher-order filters not only have greater lag but they also have transient effects that impress false artifacts on their outputs. This is somewhat like ringing a bell The ringing is more a function of the bell itself rather than a filtered response of a driving force. A reasonable compromise is the use of a second-order Gaussian filter. A second-order Gaussian low-pass filter can be generated by taking an EMA and immediately taking another identical EMA of the first EMA. This can be represented by squaring the transfer response. We can therefore obtain a second-order Gaussian high-pass filter response by squaring Equation as f 1 1 2 z-1 z-2 KP s i _ 2 1 _ a 1 _ a 2 z 2 2 6 Equation is converted to an EasyLanguage statement as HPF 1 - a 2 2 Price - 2 Pricefl Price 2 2 1 - a HPF 1 - 1 - a 2 HPF 2 The transfer responses of Equations and they are the same are plotted in Figure . Figure shows that only frequency periods longer than 40 bars frequency cycles per day are significantly attenuated. Thus we have created a high-pass filter with a relatively sharp cutoff response. Since the output of this filter contains essentially no trending components it must be the cycle component of price. 16 CYBERNETIC ANALYSIS FOR STOCKS AND FUTURES FIGURE Transfer Response of a Second-Order High-Pass Gaussian Filter a The complementary low-pass filter that produces the Instantaneous Trendline is found by subtracting the high-pass components of Equation from unity. .
