ohlc_variance: Calculate a time series of point estimates of variance for an...

In algoquant/HighFreq: High Frequency Time Series Management

Calculate a time series of point estimates of variance for an OHLC time series, using different range estimators for variance.

Description

Calculates the point variance estimates from individual rows of OHLC prices (rows of data), using the squared differences of OHLC prices at each point in time, without averaging them over time.

Usage

ohlc_variance(ohlc, method = "yang_zhang", scalit = TRUE)

Arguments

ohlc	An OHLC time series of prices in xts format.
method	A character string representing the method for estimating variance. The methods include: "close" close to close, "garman_klass" Garman-Klass, "garman_klass_yz" Garman-Klass with account for close-to-open price jumps, "rogers_satchell" Rogers-Satchell, "yang_zhang" Yang-Zhang, (default is "yang_zhang")
scalit	Boolean argument: should the returns be divided by the number of seconds in each period? (default is TRUE)

Details

The function ohlc_variance() calculates a time series of point variance estimates of percentage returns, from OHLC prices, without averaging them over time. For example, the method "close" simply calculates the squares of the differences of the log Close prices.

The other methods calculate the squares of other possible differences of the log OHLC prices. This way the point variance estimates only depend on the price differences within individual rows of data (and possibly from the neighboring rows.) All the methods are implemented assuming zero drift, since the calculations are performed only for a single row of data, at a single point in time.

The user can choose from several different variance estimation methods. The methods "close", "garman_klass_yz", and "yang_zhang" do account for close-to-open price jumps, while the methods "garman_klass" and "rogers_satchell" do not account for close-to-open price jumps. The default method is "yang_zhang", which theoretically has the lowest standard error among unbiased estimators.

The point variance estimates can be passed into function roll_vwap() to perform averaging, to calculate rolling variance estimates. This is appropriate only for the methods "garman_klass" and "rogers_satchell", since they don't require subtracting the rolling mean from the point variance estimates.

The point variance estimates can also be considered to be technical indicators, and can be used as inputs into trading models.

If scalit is TRUE (the default), then the variance is divided by the squared differences of the time index (which scales the variance to units of variance per second squared.) This is useful for example, when calculating intra-day variance from minutely bar data, because dividing returns by the number of seconds decreases the effect of overnight price jumps.

If scalit is TRUE (the default), then the variance is expressed in the scale of the time index of the OHLC time series. For example, if the time index is in seconds, then the variance is given in units of variance per second squared. If the time index is in days, then the variance is equal to the variance per day squared.

The time index of the ohlc time series is assumed to be in POSIXct format, so that its internal value is equal to the number of seconds that have elapsed since the epoch.

The function ohlc_variance() performs similar calculations to the function volatility() from package TTR, but it assumes zero drift, and doesn't calculate a running sum using runSum(). It's also a little faster because it performs less data validation.

Value

An xts time series with a single column and the same number of rows as the argument ohlc.

Examples

# Create minutely OHLC time series of random prices
ohlc <- HighFreq::random_ohlc()
# Calculate variance estimates for ohlc
var_running <- HighFreq::ohlc_variance(ohlc)
# Calculate variance estimates for SPY
var_running <- HighFreq::ohlc_variance(HighFreq::SPY, method="yang_zhang")
# Calculate SPY variance without overnight jumps
var_running <- HighFreq::ohlc_variance(HighFreq::SPY, method="rogers_satchell")

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