push_covar: Update the trailing covariance matrix of streaming asset...

In algoquant/HighFreq: High Frequency Time Series Management

Update the trailing covariance matrix of streaming asset returns, with a row of new returns using an online recursive formula.

Description

Update the trailing covariance matrix of streaming asset returns, with a row of new returns using an online recursive formula.

Usage

push_covar(retsn, covmat, meanv, lambdacov)

Arguments

retsn	A vector of new asset returns.
covmat	A trailing covariance matrix of asset returns.
meanv	A vector of trailing means of asset returns.
lambdacov	A decay factor which multiplies the past covariance.

Details

The function push_covar() updates the trailing covariance matrix of streaming asset returns, with a row of new returns. It updates the covariance matrix in place, without copying the data in memory.

The streaming asset returns r_t contain multiple columns and the parameter retsn represents a single row of r_t - the asset returns at time t. The elements of the vectors retsn and meanv represent single rows of data with multiple columns.

The function push_covar() accepts pointers to the arguments covmat and meanv, and it overwrites the old values with the new values. It performs the calculation in place, without copying the data in memory, which can significantly increase the computation speed for large matrices.

First, the function push_covar() updates the trailing means \bar{r}_t of the streaming asset returns r_t by recursively weighting present and past values using the decay factor \lambda:

\bar{r}_t = \lambda \bar{r}_{t-1} + (1-\lambda) r_t

This recursive formula is equivalent to the exponentially weighted moving average of the streaming asset returns r_t.

It then calculates the demeaned returns:

\hat{r}_t = r_t - \bar{r}_t

Finally, it updates the trailing covariance matrix of the returns:

{cov}_t = \lambda {cov}_{t-1} + (1-\lambda) \hat{r}^T_t \hat{r}_t

The decay factor \lambda determines the strength of the updates, with smaller \lambda values giving more weight to the new data. If the asset returns are not stationary, then applying more weight to the new returns reduces the bias of the trailing covariance matrix, but it also increases its variance. Simulation can be used to find the value of the \lambda parameter to achieve the best bias-variance tradeoff.

The function push_covar() is written in RcppArmadillo C++ so it's much faster than R code.

Value

Void (no return value - modifies the trailing covariance matrix and the return means in place).

Examples

## Not run: 
# Calculate a time series of returns
retp <- na.omit(rutils::etfenv$returns[, c("IEF", "VTI", "DBC")])
# Calculate the returns without last row
nrows <- NROW(retp)
retss <- retp[-nrows]
# Calculate the covariance of returns
meanv <- colMeans(retss)
covmat <- cov(retss)
# Update the covariance of returns
HighFreq::push_covar(retsn=retp[nrows], covmat=covmat, meanv=meanv, lambdacov=0.9)

## End(Not run)

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