QuanTAlib/docs/indicators/averages/tema/calc.md

The Math Behind TEMA

Components of TEMA

TEMA is composed of three main components:

1. Exponential Moving Average (EMA)
2. A "triple smoothing" factor

Let's break these down:

EMA Calculation

The Exponential Moving Average (EMA) is calculated as:

EMA_t = \alpha \cdot P_t + (1 - \alpha) \cdot EMA_{t-1}

Where:

• EMA_t is the EMA value at time t
• P_t is the price at time t
• \alpha is the smoothing factor, calculated as \frac{2}{n+1}
• n is the number of periods

TEMA Formula

The TEMA is then calculated using the following formula:

TEMA_t = 3 \cdot EMA_t - 3 \cdot EMA(EMA_t) + EMA(EMA(EMA_t))

Where:

• TEMA_t is the TEMA value at time t
• EMA_t is the EMA of the price
• EMA(EMA_t) is the EMA of the EMA
• EMA(EMA(EMA_t)) is the EMA of the EMA of the EMA

Calculation Process

1. Calculate the EMA of the price series (EMA1).
2. Calculate another EMA on the result of step 1 (EMA2).
3. Calculate a third EMA on the result of step 2 (EMA3).
4. Multiply EMA1 by 3.
5. Multiply EMA2 by 3.
6. Subtract EMA2 * 3 from EMA1 * 3.
7. Add EMA3 to the result.

This process effectively reduces lag while maintaining smoothness and attempting to minimize overshooting.

Parameter

TEMA uses a single parameter:

• Period (n): Determines the number of periods used in the EMA calculations. This affects the overall reactivity and smoothness of the indicator.