What is a worked example of Tema?

Direct answer

A worked example of TEMA (Triple Exponential Moving Average) shows the full calculation process on a small set of numbers using stated assumptions (period, starting EMA method, and smoothing constant). The goal is to let you reproduce the same TEMA values independently, without treating TEMA as a standalone buy or sell signal.

Mechanism or definition

TEMA is a moving average that applies exponential smoothing multiple times and combines the results to reduce lag compared with a single EMA.

To compute TEMA, first choose a period length n and a price series (for example, a closing price each time step). The exponential smoothing constant is:

α = 2 / (n + 1)

Then compute:

EMA1(t) from the raw prices
EMA2(t) as an EMA of EMA1(t)
EMA3(t) as an EMA of EMA2(t)

Finally, combine them (a common form) as:

TEMA(t) = 3·EMA1(t) − 3·EMA2(t) + EMA3(t)

Key assumption: you must define how you initialize EMA values at the start. Different platforms use different conventions (for example, using the first price as the initial EMA, or using a simple average over the first n points). That choice affects early TEMA values.

Evidence or example

Below is one transparent numeric scenario. This is not live data; it is a self-contained demonstration.

Assumptions (state these so you can verify):

Period length n = 3.
Smoothing constant α = 2 / (3 + 1) = 0.5.
Price series (time steps t1–t6):
- t1=100, t2=102, t3=101, t4=103, t5=104, t6=103.
Initialization method: EMA1(t1) = price(t1), and EMA2(t1) = EMA1(t1), EMA3(t1) = EMA2(t1).

Step 1: EMA1 Rule: EMA1(t) = α·Price(t) + (1−α)·EMA1(t−1).

EMA1(t1)=100
EMA1(t2)=0.5·102 + 0.5·100 = 101
EMA1(t3)=0.5·101 + 0.5·101 = 101
EMA1(t4)=0.5·103 + 0.5·101 = 102
EMA1(t5)=0.5·104 + 0.5·102 = 103
EMA1(t6)=0.5·103 + 0.5·103 = 103

Step 2: EMA2 (EMA of EMA1) Rule: EMA2(t) = α·EMA1(t) + (1−α)·EMA2(t−1).

EMA2(t1)=EMA1(t1)=100
EMA2(t2)=0.5·101 + 0.5·100 = 100.5
EMA2(t3)=0.5·101 + 0.5·100.5 = 100.75
EMA2(t4)=0.5·102 + 0.5·100.75 = 101.375
EMA2(t5)=0.5·103 + 0.5·101.375 = 102.1875
EMA2(t6)=0.5·103 + 0.5·102.1875 = 102.59375

Step 3: EMA3 (EMA of EMA2) Rule: EMA3(t) = α·EMA2(t) + (1−α)·EMA3(t−1).

EMA3(t1)=EMA2(t1)=100
EMA3(t2)=0.5·100.5 + 0.5·100 = 100.25
EMA3(t3)=0.5·100.75 + 0.5·100.25 = 100.5
EMA3(t4)=0.5·101.375 + 0.5·100.5 = 100.9375
EMA3(t5)=0.5·102.1875 + 0.5·100.9375 = 101.5625
EMA3(t6)=0.5·102.59375 + 0.5·101.5625 = 102.078125

Step 4: Combine to get TEMA TEMA(t) = 3·EMA1(t) − 3·EMA2(t) + EMA3(t).

TEMA(t1)=3·100 − 3·100 + 100 = 100
TEMA(t2)=3·101 − 3·100.5 + 100.25 = 100.75
TEMA(t3)=3·101 − 3·100.75 + 100.5 = 101.25
TEMA(t4)=3·102 − 3·101.375 + 100.9375 = 101.875
TEMA(t5)=3·103 − 3·102.1875 + 101.5625 = 102.9375
TEMA(t6)=3·103 − 3·102.59375 + 102.078125 = 102.96875

What you can independently verify: If you use the same n, the same α, the same input prices, and the same EMA initialization rule, you should reproduce the same EMA1/EMA2/EMA3 values and thus the same TEMA outputs (within rounding).

Limitations and risks

**Initialization changes early values. ** If your data tool initializes EMAs differently, the first several TEMA points can differ even if the later points converge. 2. **Lag reduction is not elimination. ** TEMA may react faster than a single EMA, but it still smooths and therefore can lag during abrupt moves. 3. **Data handling matters. ** Using different timeframes, inconsistent sampling intervals, or different price fields (close vs. typical price) produces different TEMA curves. 4. **Interpreting it as a standalone signal is a failure mode.