leqwma: The logarithm of an Equally Weighted Moving Average (EqWMA) of the pth. exponentiated absolute values

Description

The default is that the logarithm of an Equally Weighted Moving Average (EqWMA) of the pth. exponentiated absolute values is returned. As a volatility model, this is also known as the 'historical' model or as an integrated ARCH model where the ARCH coefficients all have the same value with sum equal to one. In the log-volatility specification the lag of log(EqWMA) is thus a volatility proxy. It is an imperfect volatility proxy compared with high-frequency data (which can also be included as regressors anyway), but - in contrast to high-frequency data - is always available and easy to compute

Usage

leqwma(x, length = 5, lag = 1, start = 1, p = 2)

Arguments

numeric vector, time-series or zoo object. Note that missing values in the beginning or at the end of the series is allowed, as they are removed with the na.trim command from the zoo package

length

integer or vector of integers each equal to or greater than 1. The length or lengths of the moving window or windows of averages. Default: length=20

lag

integer equal to or greater than 0. If 0, then the moving averages are not lagged. Default: lag=1

start

integer equal to or greater than 1. Where to start the moving windows of averages. Default: start=1 (the first observation)

numeric greater than zero. The exponent or p in abs(x)^p. Default: p=2

Value

ewmanumeric vector, time series or zoo object (depending on the properties of x, the input) containing the values of the moving average

Details

The function's intended primary use is to construct volatility proxies in logarithms for inclusion in the log-volatility specification. The default is the lagged log of an equally weighted moving average of the squared residuals, where each average is made up of m observations. This is equivalent to an integrated ARCH(m) model where all the m ARCH-coefficients are equal. For further details on the use of log(EqWMA) as a volatility proxy, see Sucarrat and Escribano (2012)

Examples

Run this code

#Generate an iid normal series:
set.seed(123)
x <- rnorm(200)

#Compute lag of log(EqWMA(20)) for x^2:
leqwma(x, p=2)

#Compute lag of log(EqWMA(30)) for abs(x)^1:
eqwma(x, length=30, p=1)

#Compute lag of log(EqWMA(5)) and lag of log(EqWMA(20))
#for abs(x)^2:
eqwma(x, length=c(5,20))