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# Momentum Indicator

## Rate of Change

Syntax: `roc(period)`
Arguments:
• `period` - the length of period to use in the calculation
Return: A time series of values representing the rate of change for the input time series.
Description: The rate of change (ROC) is a momentum indicator that measures the proportional change in the input time series. It is calculated as the difference between the current value and a prior value, divided by the prior value.
Example:
roc_values = SPY.close -> roc(15)

## Relative Strength Index

Definition: Normalizes a time series based on the recent values.
Syntax: `rsi(length)`
Arguments: `length` = the number of previous values to use in the calculation.
Return: A time series of values, normalized to a range of +/- 100.
Description: Harmonization, or normalization, transforms data to enable operations, such as adding or averaging, on disparate time series (eg, asset prices).
Example:
normalized = SPY.close -> rsi(30)

## True Strength Index

Definition: Calculates the True Strength Index, which is a momentum indicator that uses double smoothing to reduce lag.
Syntax: `tsi(shortLength, longLength, averageLength)`
Arguments:
• `longLength`: The number of previous values to use for the long trend line calculation.
• `shortLength`: The number of previous values to use for the short trend line calculation.
• `avgLength`: The number of previous values to use in the averaging calculation.
Return: Time series of true strength index values with a range of +/- 100.
Description: It is calculated by smoothing out the difference between two exponential moving averages of an asset's price and dividing it by the sum of the smoothed difference and a third exponential moving average.
Example:
tsiValues = SPY.close -> tsi(30, 90, 60)

## Market Momentum Indicator

Definition: Calculates the difference between the value of the current value of a time series and a previous value.
Syntax: `mom(length)`
Arguments: `length` = number of values back used in the calculation
Return: Time series of differences
Description: Market momentum can be used as a measure of market sentiment.
Example:
momValue = SPY.close -> mom(20)

## Directional Oscillator

Name: dx
Definition: Determines whether a current value is greater than, less than, or equal to a previous value. The resulting value is +1, -1, or 0, respectively, times a scale factor.
Syntax: `dx(length, scale)`
Arguments:
• `length`: number of values back used in the calculation
• `scale`: scale factor for values (default = 100)
Return: Time series of directional values
Description: Compares the current value to a previous value. The output value is +1, -1, or 0, if the current value is greater than, less than, or equal to the previous value, respectively, multiplied by a scale factor.
Example:
SPY.close -> dx(15)
SPY.close -> dx(50, scale=1.0)