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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?

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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
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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.

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