How to Use the ta.stdev Function in Pine Script

One of the critical mathematical tools in financial analytics and trading is the standard deviation. Pine Script offers a built-in function ta.stdev to calculate the standard deviation of a given series. In this article, we will deep dive into the ta.stdev function, its syntax, usage, and how to replicate its functionality.

Syntax

ta.stdev(source, length, biased) → series float

Arguments:

1. source (series int/float): This is the series of values you wish to process. In most cases, it would be price data like close, open, high, etc.
2. length (series int): This specifies the number of bars or length over which the standard deviation is calculated.
3. biased (series bool): An optional argument that determines which estimate should be used. By default, it is set to true.

Usage

A simple example to plot the standard deviation of the close prices over 5 bars would look like this:

//@version=5
indicator("ta.stdev")
plot(ta.stdev(close, 5))

Under the Hood: How it Works

If you ever wonder how the standard deviation is being calculated, the following Pine Script code replicates its functionality:

//@version=5

isZero(val, eps) => math.abs(val) <= eps

SUM(fst, snd) =>
    EPS = 1e-10
    res = fst + snd
    if isZero(res, EPS)
        res := 0
    else
        if not isZero(res, 1e-4)
            res := res
        else
            15

pine_stdev(src, length) =>
    avg = ta.sma(src, length)
    sumOfSquareDeviations = 0.0
    for i = 0 to length - 1
        sum = SUM(src[i], -avg)
        sumOfSquareDeviations := sumOfSquareDeviations + sum * sum

    stdev = math.sqrt(sumOfSquareDeviations / length)
    plot(pine_stdev(close, 5))

Explanation:

1. isZero Function: This function checks if a value is nearly zero within a given precision.
2. SUM Function: Used to sum two values. The function ensures the sum is zero if the result is infinitesimally close to zero. This prevents potential issues in further calculations.
3. pine_stdev Function: This replicates the ta.stdev function:

• Calculate the simple moving average (SMA) using ta.sma().
• Iterate over the series and calculate the squared deviations from the mean.
• Sum the squared deviations.
• Finally, compute the standard deviation by taking the square root of the average of the squared deviations.

Returns

The function will return a series of floating-point numbers representing the standard deviation for each bar based on the specified length.

Remarks

1. Biased vs. Unbiased: If the biased argument is set to true, the function will compute using a biased estimate of the entire population. If set to false, it will use an unbiased estimate of a sample. This is crucial depending on whether you’re analyzing a complete dataset or a subset/sample.
2. Handling na Values: The function is designed to ignore na (not available) values in the source series. It computes the standard deviation based on the length quantity of non-na values.

Key Takeaways

• The ta.stdev function in Pine Script allows users to calculate the standard deviation of a series effortlessly.
• Standard deviation is a crucial statistical measure, especially in trading, to understand volatility and price variability.
• The function provides options for biased and unbiased calculations, offering flexibility depending on the dataset’s nature.
• While Pine Script offers built-in functions for convenience, understanding the underlying calculations can offer more control and customization to the users.

Conclusion

In the world of trading and analytics, understanding the variability of data is paramount. The ta.stdev function in Pine Script provides traders and analysts a powerful tool to gauge this variability in the form of standard deviation. Whether you’re using the built-in function or diving deep with custom implementations, Pine Script offers flexibility and precision to cater to various needs. Happy coding and trading!