ExponentialMovingAverage

ExponentialMovingAverage[list,α]

gives the exponential moving average of list with smoothing constant α.

Details

Examples

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Basic Examples  (2)

Exponential moving average in symbolic form:

Exponential moving average for numeric values:

Scope  (4)

Compute exponential moving averages at machine precision:

Exponential moving averages of matrices are matrices:

Obtain results for lists of any precision:

Obtain results for smoothing coefficients of any precision:

Generalizations & Extensions  (2)

Compute results for a SparseArray:

Compute results for a TemporalData object:

Applications  (3)

Smooth noisy data:

Compute an exponential moving average using an initial starting value:

Compute the exponential moving average of a financial time series:

Properties & Relations  (3)

Terms of an exponential moving average satisfy a recurrence relation:

Exponential moving average with a smoothing coefficient of 0 is a constant:

Exponential moving average with a smoothing coefficient of 1 is the original list:

Wolfram Research (2007), ExponentialMovingAverage, Wolfram Language function, https://reference.wolfram.com/language/ref/ExponentialMovingAverage.html.

Text

Wolfram Research (2007), ExponentialMovingAverage, Wolfram Language function, https://reference.wolfram.com/language/ref/ExponentialMovingAverage.html.

CMS

Wolfram Language. 2007. "ExponentialMovingAverage." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ExponentialMovingAverage.html.

APA

Wolfram Language. (2007). ExponentialMovingAverage. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ExponentialMovingAverage.html

BibTeX

@misc{reference.wolfram_2025_exponentialmovingaverage, author="Wolfram Research", title="{ExponentialMovingAverage}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ExponentialMovingAverage.html}", note=[Accessed: 21-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_exponentialmovingaverage, organization={Wolfram Research}, title={ExponentialMovingAverage}, year={2007}, url={https://reference.wolfram.com/language/ref/ExponentialMovingAverage.html}, note=[Accessed: 21-February-2025 ]}