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Wilder ATR Initialization and the Recommended 14-Period Average

Article Quant Q&A · Author: user11980328
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Summary

The discussion clarifies how to initialize Average True Range when using Wilder’s volatility formula. It answers that the initial simple moving average of true range should use the same period, N, as the subsequent Wilder smoothing. The source cited in the discussion recommends averaging daily true range over 14 days for the Volatility Index Indicator, making the initial ATR a 14-period SMA in that setting.

After initialization, Wilder’s recursive update combines the previous ATR, weighted by N minus one, with the latest true range, then divides by N. The cited 14-period update uses the previous indicator weighted by 13 and today’s true range. This connects the initial SMA with the smoothing recurrence, but the recommendation is specific to Wilder’s cited indicator and does not establish that 14 periods suit every instrument, timeframe, or trading objective.

Key ideas

  • Initialize ATR with an N-period simple moving average of true range.
  • Wilder’s cited Volatility Index Indicator uses a 14-day period.
  • After initialization, the recursive Wilder update weights the previous ATR by N minus one and adds the latest true range.
  • The 14-period recommendation is specific to the cited indicator and need not suit every market or timeframe.

Tags

Technical indicatorsVolatilityFuturesStatistics
Full text
# Definition of wilder's moving average


# Definition of wilder's moving average












https://www.marketvolume.com/technicalanalysis/wildersvolatility.asp

I see this page describes wilder's moving average. But the first step `ATR = SMA(TR)` is not clear. How many periods should be used to compute this simple moving average? Should it be N?

```
...
Step #2: Apply the moving average to the defined TR.

ATR = SMA(TR)

Wilder uses simplified formula to calculate Average of True Range:

ATR = Wilder's Volatility = ((N-1) x Previous ATR + TR) / N
...
```
```

## Answer by Pleb (score 1)

https://quant.stackexchange.com/a/70310

#### Yes, the SMA should be computed with $N$ periods in your situation:

In the original book of Wilder, J. W. (1978). New concepts in technical trading systems. the author writes the following about the Volatility Index Indicator (see p. 21 (bottom)):

> In order for the range to be a meaningful tool as a measure of volatility, more than one day's range must be considered. The answer is to consider an average of the true range made per day over a number of days. A volatility indicator will be fast or slow, depending on the number of days used to obtain the average daily true range. How many days should be used to obtain the average daily true range? After extensive testing, I have found that about 14 days gives the best indicator of volatility to use for the Volatility Index Indicator.

In conclusion, he recommends the average true range (ATR) to be computed with a period of 14 days (ie. a 14-day SMA) which is equivalent to $N$ in your situation.

This can be further seen, since he defines the Volatility Index Indicator on p. 22 as:

$$ VI_{today} = \frac{13 \cdot VI_{previous} + TR_1}{14}, $$ where $TR_1$ is today's true range. This is equivalent to $N=14$ in your specified formula.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.