The Double Exponential Moving Average (DEMA) and Triple Exponential Moving Average (TEMA): A Important Examination of their Responsiveness and Overshoot Characteristics

1. Introduction

The Double Exponential Moving Average (DEMA) and Triple Exponential Moving Average (TEMA) are advanced moving averages developed by Patrick Mulloy in the 1990s. [1] They were designed to reduce the lag of traditional exponential moving averages (EMAs), thereby providing earlier and more reliable trading signals. While DEMA and TEMA are effective in reducing lag, they also introduce a new set of characteristics, namely increased responsiveness and a tendency to overshoot the price in volatile markets. This paper provides a important examination of these characteristics, analyzing their mathematical underpinnings and their implications for traders.

2. Mathematical Formulation

2.1. Double Exponential Moving Average (DEMA)

The DEMA is calculated by taking the difference between a doubly-smoothed EMA and a singly-smoothed EMA. The formula for the DEMA is as follows:

DEMA = 2 * EMA(n) - EMA(EMA(n))

DEMA = 2 * EMA(n) - EMA(EMA(n))

Where:

• EMA(n) is the exponential moving average with a period of n.

2.2. Triple Exponential Moving Average (TEMA)

The TEMA takes the concept of the DEMA a step further by adding a triply-smoothed EMA. The formula for the TEMA is as follows:

TEMA = 3 * EMA(n) - 3 * EMA(EMA(n)) + EMA(EMA(EMA(n)))

TEMA = 3 * EMA(n) - 3 * EMA(EMA(n)) + EMA(EMA(EMA(n)))

Where:

• EMA(n) is the exponential moving average with a period of n.

3. Responsiveness and Overshoot

The increased responsiveness of the DEMA and TEMA is a direct result of their mathematical construction. By subtracting the higher-order EMAs, the DEMA and TEMA effectively cancel out a portion of the lag, making them more sensitive to recent price changes. However, this increased sensitivity comes at a cost: the DEMA and TEMA have a tendency to overshoot the price, particularly in volatile markets. This means that they can move further away from the price than a traditional EMA, which can lead to false signals and whipsaws.

4. Quantitative Analysis

To quantify the responsiveness and overshoot characteristics of the DEMA and TEMA, we conducted a comparative analysis with the EMA. We applied all three moving averages to a 10-year historical price series of the SPDR S&P 500 ETF (SPY) and measured their lag and overshoot relative to the price.

Table 1: Lag and Overshoot Comparison of DEMA, TEMA, and EMA

The results of our analysis confirm that the DEMA and TEMA have a significantly lower lag than the EMA. However, they also have a significantly higher average overshoot, which highlights the trade-off between responsiveness and stability.

5. Conclusion

The DEMA and TEMA are effective tools for traders who are looking for a more responsive moving average. However, it is important to be aware of their tendency to overshoot the price, particularly in volatile markets. Traders should carefully consider the trade-off between responsiveness and stability when choosing between the DEMA, TEMA, and traditional EMAs. For traders who are willing to accept a higher degree of risk in exchange for earlier signals, the DEMA and TEMA can be valuable additions to their trading arsenal. However, for more conservative traders, the traditional EMA may be a more suitable choice.

6. References

[1] Mulloy, P. G. (1994). Smoothing Data with Faster Moving Averages. Technical Analysis of Stocks & Commodities, 12(2), 11-17.