# 3rd Generation Moving Average Indicator

## 3rd Generation Moving Average

Moving Averages based on the Nyquist-Shannon Signal Theorem. Mathematically suggested to have the least possible lag. Less lag than general and second generation averages like Ehler's 'zero-lag' averages.

Fig. 1. Comparison of Moving Averages. The 3rd generation average performes best with least lag in comparison to all other averages.
All averages were run with the same window size 21. The data represents 3x60 data points with a Gaussian distribution around 100 and 200 and a standard deviation of 5 points. Formulas as in Dürschner 2011. EMA implementation based on MetaTrader4 algorithm, 2nd generation uses Ehler (2001) correction, 3rd generation is based on the Nyquist-Shannon theorem as outlined in Dürschner (2011) with lambda of 4.

## Moving Averages of the 3rd Generation

Moving averages are supposed to "smooth" data and to remove noise and useless information. Multiple average variants are used widely, for example Simple Moving Average (SMA) or Exponentially Moving Average (EMA) (Wikipedia, Moving Averages, 2011). One challenge is that moving averages introduce a lag, i.e. the smoothed curve follows the trend usually later (see Fig. 1). Adaptive moving averages like VIYDA (Chande, 1992; Brown) and Kaufman`s Adaptive Moving Average (KAMA) (Kaufmann, 1995) tried to address this issue by incorporating dynamic variables. In 2001, J. Ehler introduced a general concept based on signal theory which we refer as second generation averages (Ehler, 2001). Here, the basic assumption is that the time series is composed from a limited number of overlapping signal phases which would make signal theory applicable (Ehler, 2001; Huang, et al., 1998). In 2011, M. G. Dürschner stated that –under the signal theory model- the Nyquist-Shannon theorem (Wikipedia, Nyquist, 2008) must be applied (Dürschner, 2011). In his work, Dürschner outlined that averages according to these criteria would have the least theoretically possible lag and termed them 3rd generation Moving Averages.

## Indicator Parameter

 Parameter Name Default Value Description MA_Period 21 The window size of the moving average MA_Method 1 (EMA) SMA (Simple Moving Average) = 0; EMA (Exponetially Moving Average) = 1; SMMA (Smoothed Moving Average) = 2; LWMA (Linear Weighted Moving Average) = 3; MA_priceType 6 (Weighted) Close = 0; Open = 1; High = 2; Low = 3; Median = 4; Typical = 5; Weighted = 6; MA_correction 2 (3rd Gen.) 1st Generation, no lag correction =0; 2nd Generation (correction based on Ehler 2001) = 1; 3rd Generation (correction based on Dürschner 2011) = 2;

Price calculations and basic averages implemented as in MetaTrader 4.

## References

Brown, D. (n.d.). The Variable Moving Average (VMA) aka Volatility Index Dynamic Average (VIDYA). Retrieved 09 01, 2011, from http://etfhq.com/blog/2011/02/22/variable-moving-average-vma-volatility-index-dynamic-average-vidya/

Chande, T. S. (1992, 05). Adapting Moving Averages To Market Volatility. Technical Analysis of Stocks & Commodities .

Ehler, J. F. (2001). Signal Analysis Concepts. Retrieved 09 01, 2011, from http://www.technicalanalysis.org.uk/moving-averages/Ehle.pdf

Huang, N., Shen, Z., Long, S., Mu, M., Shih, E., Zhang, Q., et al. (1998). The empirical mode decomposition and the Hilbert Spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society London , pp. A 454: 903 - 905

Kaufmann, P. J. (1995). Kaufman’s Adaptive Moving Average (KAMA). In P. J. Kaufmann, Smarter Trading. New York: McGraw-Hill.