Direct answer
A worked example of Trend Intensity Index (TII) is a step-by-step calculation using a small set of assumed prices, explicit parameter choices (window length, method for direction, and normalization), and intermediate results. Because TII implementations vary, a “worked example” is most useful when every assumption is stated so you can reproduce the same number.
What Trend Intensity Index measures (definition first)
In plain terms, TII tries to convert recent price movement into an “intensity” number that reflects both:
- Direction: whether movement is mostly one way (up or down) across the lookback window.
- Distance / participation: how much the price has moved relative to an assumed scale.
A common mechanical idea behind many trend-strength metrics is: strong trend behavior means consecutive changes point in the same general direction and the net move is large compared with the typical step size. Weak trend behavior means changes alternate direction or cancel out, producing a smaller net move.
Important uncertainty: there is no single universally enforced TII formula across all platforms and articles. So the only way to have a reliable worked example is to define a specific formula for the example and then stick to it.
A worked numerical example (with explicit assumptions)
Below is one transparent example using a simplified, reproducible TII-style computation.
Assumptions (state all choices)
- Data: Use a 5-bar window with closing prices.
- Direction: Compute direction using net change over the window: last close minus first close.
- Intensity: Normalize the absolute net change by the sum of absolute step changes inside the window.
- Formula for this example:
- Let prices be P0, P1, P2, P3, P4.
- Net change = (P4 − P0).
- Sum of absolute steps = |P1−P0| + |P2−P1| + |P3−P2| + |P4−P3|.
- TII (example definition) = |Net change| / (Sum of absolute steps).
- This produces a value between 0 and 1 by construction (given non-zero steps).
- No market fees, spreads, or execution are included because TII is computed from prices only.
Input prices (assumed)
Assume the last 5 closes are:
- P0 = 100.0
- P1 = 101.0
- P2 = 102.0
- P3 = 103.0
- P4 = 104.0
Step-by-step calculation
- Net change = P4 − P0 = 104.0 − 100.0 = 4.0.
- Absolute steps:
- |P1−P0| = |101.0−100.0| = 1.0
- |P2−P1| = |102.0−101.0| = 1.0
- |P3−P2| = |103.0−102.0| = 1.0
- |P4−P3| = |104.0−103.0| = 1.0
- Sum of absolute steps = 1.0 + 1.0 + 1.0 + 1.0 = 4.0.
- TII (example) = |4.0| / 4.0 = 1.0.
Interpretation under these exact assumptions: TII = 1.0 because every step moved in the same direction with no cancellation. That is “high trend intensity” for this example definition.
Contrast scenario (shows sensitivity)
Keep the same window length but assume zig-zag prices:
- P0 = 100.0
- P1 = 101.0
- P2 = 100.5
- P3 = 101.5
- P4 = 101.0
Compute:
- Net change = 101.0 − 100.0 = 1.0.
- Absolute steps:
- |101.0−100.0| = 1.0
- |100.5−101.0| = 0.5
- |101.5−100.5| = 1.0
- |101.0−101.5| = 0.5
- Sum of absolute steps = 1.0 + 0.5 + 1.0 + 0.5 = 3.0.
- TII (example) = |1.0| / 3.0 = 0.333…
Interpretation: the net change is positive, but the path alternates direction, so the intensity is lower.
How this “worked example” relates to real TII implementations
To verify any TII value you see on a platform, you need to confirm at least:
- The exact formula (some use directional components differently, sometimes include additional smoothing, and sometimes compute trend vs. a baseline).
- The lookback length and whether it counts bars the same way.
- The price input (close vs. other series).
Because different implementations can output different numbers even on the same prices, a worked example only helps when it matches the method behind your chart.
Limitations and failure modes
- Formula mismatch risk: if your provider’s TII uses a different definition, the reproduced number will not match. 2. Parameter sensitivity: changing the window length or smoothing can significantly change the intensity level. 3. Noise and microstructure: short windows can react to small reversals, producing unstable intensity readings. 4. **Correlation vs.