calc_hurst_ohlc: Calculate the Hurst exponent from the volatility ratio of...

In algoquant/HighFreq: High Frequency Time Series Management

Calculate the Hurst exponent from the volatility ratio of aggregated OHLC prices.

Description

Calculate the Hurst exponent from the volatility ratio of aggregated OHLC prices.

Usage

calc_hurst_ohlc(
  ohlc,
  step,
  method = "yang_zhang",
  closel = 0L,
  scale = TRUE,
  index = 0L
)

Arguments

ohlc	A time series or a matrix of OHLC prices.
step	The number of time periods in each interval between neighboring end points.
method	A character string representing the price range estimator for calculating the variance. The estimators include: "close" close-to-close estimator, "rogers_satchell" Rogers-Satchell estimator, "garman_klass" Garman-Klass estimator, "garman_klass_yz" Garman-Klass with account for close-to-open price jumps, "yang_zhang" Yang-Zhang estimator, (The default is the method = "yang_zhang".)
closel	A vector with the lagged close prices of the OHLC time series. This is an optional argument. (The default is closel = 0).
scale	Boolean argument: Should the returns be divided by the time index, the number of seconds in each period? (The default is scale = TRUE).
index	A vector with the time index of the time series. This is an optional argument (the default is index = 0).

Details

The function calc_hurst_ohlc() calculates the Hurst exponent from the ratios of the variances of aggregated OHLC prices.

The aggregated volatility \sigma_t increases with the length of the aggregation interval \Delta t. The aggregated volatility increases as the length of the aggregation interval \Delta t raised to the power of the Hurst exponent H:

\sigma_t = \sigma {\Delta t}^H

Where \sigma is the daily return volatility.

The Hurst exponent H is equal to the logarithm of the ratio of the volatilities divided by the logarithm of the time interval \Delta t:

H = \frac{\log{\sigma_t} - \log{\sigma}}{\log{\Delta t}}

The function calc_hurst_ohlc() calls the function calc_var_ohlc_ag() to calculate the aggregated variance \sigma^2_t.

Value

The Hurst exponent calculated from the volatility ratio of aggregated OHLC prices.

Examples

## Not run: 
# Calculate the log ohlc prices
ohlc <- log(rutils::etfenv$VTI)
# Calculate the Hurst exponent from 21 day aggregations
calc_hurst_ohlc(ohlc, step=21)

## End(Not run)

algoquant/HighFreq documentation built on Feb. 9, 2024, 8:15 p.m.