Maths::ExponentialMovingVariance< T > Struct Template Reference

A structure for calculating an exponential moving variance. More...

#include <exponential_moving_variance.hpp>

Public Member Functions
	ExponentialMovingVariance (T alpha_, T observation=0)
	Initialize an exponential moving variance with given \(\alpha\) and \(o_0\). More...
void	reset (T observation=0)
	Reset the average to initial state \({\mu}_0\) with observation \(o_0\). The initial variance \({\sigma^2}_0\) is 0. More...
void	set_alpha (T alpha_)
	Set the \(\alpha\) parameter to a new value. More...
T	get_alpha () const
	Return the \(\alpha\) parameter. More...
T	process (T observation)
	Calculate the next average \({\mu}_t\) and variance \({\sigma^2}_t\) based on observation \(o_t\). More...
T	get_average () const
	Return the current value of the exponential moving average \({\mu}_t\). More...
T	get_variance () const
	Return the current value of the exponential moving variance \({\sigma^2}_t\). More...
T	get_stddev () const
	Return the current value of the exponential moving standard deviation \({\sigma}_t\). More...

Static Public Attributes
static constexpr T	ALPHA_MIN = 0
	the minimal value for alpha to take
static constexpr T	ALPHA_MAX = 1
	the maximal value for alpha to take

Detailed Description

template<typename T = float>
struct Maths::ExponentialMovingVariance< T >

A structure for calculating an exponential moving variance.

Template Parameters

T	the type for the exponential moving average/variance

The change in value between the current average \({\mu}_{t-1}\) and next observation \(o_t\) for event \(t\) is defined as \(\delta_t\):

\[ \delta_t \gets o_t - {\mu}_{t-1} \]

The exponential moving average \({\mu}_t\) for event \(t\), corresponding change \(\delta_t\), initial observation \(o_0\), and rate of change parameter \(\alpha\) is defined as:

\[ {\mu}_t \gets {\mu}_{t - 1} + \alpha \cdot \delta_t | {\mu}_0 = o_0 \]

The exponential moving variance \({\sigma}^2_t\) for event \(t\), corresponding change \(\delta_t\), and rate of change parameter \(\alpha\) is defined as:

\[ {\sigma^2}_t \gets (1 - \alpha) \cdot ({\sigma^2}_{t-1} + \alpha \cdot \delta^2_t) | {\sigma^2_0} = 0 \]

where:

• \(\alpha \in [0, 1]\)
• \({\mu}_t \in (-\infty, \infty)\)
• \({\sigma^2}_t \in (-\infty, \infty)\)
• \(o_t \in (-\infty, \infty)\)

Constructor & Destructor Documentation

ExponentialMovingVariance()

template<typename T = float>

Maths::ExponentialMovingVariance< T >::ExponentialMovingVariance ( T  alpha_, T  observation = 0  )

inlineexplicit

Initialize an exponential moving variance with given \(\alpha\) and \(o_0\).

Parameters

alpha_	the \(\alpha\) parameter, i.e., rate of change
observation	the initial observation \(o_0\) for the average

Member Function Documentation

get_alpha()

template<typename T = float>

T Maths::ExponentialMovingVariance< T >::get_alpha ( ) const

inline

Return the \(\alpha\) parameter.

Returns

the \(\alpha\) parameter for calculating the average and variance

get_average()

template<typename T = float>

T Maths::ExponentialMovingVariance< T >::get_average ( ) const

inline

Return the current value of the exponential moving average \({\mu}_t\).

Returns

the current average \({\mu}_t\)

get_stddev()

template<typename T = float>

T Maths::ExponentialMovingVariance< T >::get_stddev ( ) const

inline

Return the current value of the exponential moving standard deviation \({\sigma}_t\).

Returns

the current standard deviation \({\sigma}_t\)

get_variance()

template<typename T = float>

T Maths::ExponentialMovingVariance< T >::get_variance ( ) const

inline

Return the current value of the exponential moving variance \({\sigma^2}_t\).

Returns

the current variance \({\sigma^2}_t\)

process()

template<typename T = float>

T Maths::ExponentialMovingVariance< T >::process ( T  observation )

inline

Calculate the next average \({\mu}_t\) and variance \({\sigma^2}_t\) based on observation \(o_t\).

Parameters

observation

the observation \(o_t\) to integrate into the average and variance

Returns

the change in value between the observation and current average

reset()

template<typename T = float>

void Maths::ExponentialMovingVariance< T >::reset ( T  observation = 0 )

inline

Reset the average to initial state \({\mu}_0\) with observation \(o_0\). The initial variance \({\sigma^2}_0\) is 0.

Parameters

observation

the initial observation \(o_0\) for the average

set_alpha()

template<typename T = float>

void Maths::ExponentialMovingVariance< T >::set_alpha ( T  alpha_ )

inline

Set the \(\alpha\) parameter to a new value.

Parameters

alpha_

the \(\alpha\) parameter, i.e., rate of change

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The documentation for this struct was generated from the following file:

• include/maths/exponential_moving_variance.hpp