[Highfrequency-commits] r70 - pkg/highfrequency/man

noreply at r-forge.r-project.org noreply at r-forge.r-project.org
Wed Aug 27 16:29:42 CEST 2014 

Author: kboudt
Date: 2014-08-27 16:29:42 +0200 (Wed, 27 Aug 2014)
New Revision: 70

Modified:
   pkg/highfrequency/man/spotVol.rd
Log:
gsoc maarten schermer 

Modified: pkg/highfrequency/man/spotVol.rd
===================================================================
--- pkg/highfrequency/man/spotVol.rd	2013-12-24 11:02:39 UTC (rev 69)
+++ pkg/highfrequency/man/spotVol.rd	2014-08-27 14:29:42 UTC (rev 70)
@@ -1,84 +1,361 @@
-\name{spotVol}
-\Rdversion{1.1}
-\alias{spotVol}
-\title{
-Spot volatility estimation}
+% Generated by roxygen2 (4.0.1): do not edit by hand
+\name{spotvol}
+\alias{spotvol}
+\title{Spot volatility estimation}
+\usage{
+spotvol(data, method = "detper", ..., on = "minutes", k = 5,
+  marketopen = "09:30:00", marketclose = "16:00:00", tz = "GMT")
+}
+\arguments{
+\item{data}{Either an \code{\link{xts}} object, containing price data, or a
+\code{matrix} containing returns. For price data, irregularly spaced
+observations are allowed. They will be aggregated to the level specified by
+parameters \code{on} and \code{k}. For return data, the observations are
+assumed to be equispaced, with the time between them specified by \code{on}
+and \code{k}. Return data should be in matrix form, where each row
+corresponds to a day, and each column to an intraday period. The output
+will be in the same form as the input (\code{xts} or
+\code{matrix}/\code{numeric}).}
 
-\description{
-Function returns an estimate of the standard deviation \eqn{\sigma_{t,i}} of equispaced high-frequency returns \eqn{r_{t,i}} (read: the \eqn{i}th return
-on day \eqn{t}). The underlying assumption is that, in the absence of price jumps, high-frequency returns
-are normally distributed with mean zero and standard deviation \eqn{\sigma_{t,i}}, where 
-the standard deviation is the product between a deterministic periodic factor \eqn{f_{i}} (identical for every day in the sample)
-and a daily factor \eqn{s_{t}} (identical for all observations within a day). 
+\item{method}{specifies which method will be used to estimate the spot
+volatility. Options include \code{"detper"} and \code{"stochper"}.
+See 'Details'.}
 
-For the estimation of \eqn{s_{t}} one can choose between the realized volatility, the bipower variation of Barndorff-Nielsen and Shephard (2004)
-or the MedRV of Andersen et al. (2009). The latter two have the advantage of being robust to price jumps. 
+\item{on}{string indicating the time scale in which \code{k} is expressed.
+Possible values are: \code{"secs", "seconds", "mins", "minutes", "hours"}.}
 
-The function takes as input the tick-by-tick price series. From these prices, equispaced returns are computed as the change in the log price of previous
-tick interpolated prices sampled every k minutes.
+\item{k}{positive integer, indicating the number of periods to aggregate
+over. E.g. to aggregate an \code{xts} object to the 5 minute frequency, set
+\code{k = 5} and \code{on = "minutes"}.}
 
-The estimation of \eqn{f_{i}} is either based on scale or regression estimators. The scale estimator can be the standard deviation or its jump robust version
-called the weighted standard deviation. For regression, choose OLS for the classical estimation and TML (truncated maximum likelihood) for jump 
-robust regression. The regression specification consists either of one dummy for each intraday period (dummies=TRUE) or the flexible fourrier
-form with P1 cosinus and P2 sinus terms. For more details on the classical methods, see Taylor and Xu (1997) and Andersen et al. (1997). 
-For the jump robust versions, see Boudt et al. (2010).  
+\item{marketopen}{the market opening time. This should be in the time zone
+specified by \code{tz}. By default, \code{marketopen = "09:30:00"}.}
+
+\item{marketclose}{the market closing time. This should be in the time zone
+specified by \code{tz}. By default, \code{marketclose = "16:00:00"}.}
+
+\item{tz}{string specifying the time zone to which the times in \code{data}
+and/or \code{marketopen}/ \code{marketclose} belong. Default = \code{"GMT"}.}
+
+\item{...}{method-specific parameters (see 'Details').}
 }
+\value{
+A \code{spotvol} object, which is a list containing one or more of the
+following outputs, depending on the method used:
 
-\usage{
-spotVol(pdata, dailyvol = "bipower", periodicvol = "TML", 
-    on = "minutes", k = 5, dummies = FALSE, P1 = 4, P2 = 2,  
-    marketopen = "09:30:00", marketclose = "16:00:00")}
+\code{spot}
 
-\arguments{
-  \item{pdata}{xts object, containing the price series.}
-  \item{dailyvol}{determines the estimation method for the component of intraday volatility that is constant over the day, but changes 
-  from day to day. Possible values are "bipower","rv", "medrv".}
-   \item{periodicvol}{determines the estimation method for the component of intraday volatility that depends in a deterministic way on the intraday time
-   at which the return is observed. Possible values are "TML","SD", "WSD", "OLS".}
-   \item{on}{ character, indicating the time scale in which "k" is expressed. Possible values are: "secs", "seconds", "mins", "minutes","hours".}
-   \item{k}{ positive integer, indicating the number of periods to aggregate over. E.g. to aggregate a 
-   xts object to the 5 minute frequency set k=5 and on="minutes".}
-   \item{dummies}{ boolean, in case it is TRUE, the parametric estimator of periodic standard deviation  specifies the periodicity function as the sum of dummy variables corresponding to each intraday period. 
-   If it false, the parametric estimator uses the Flexible Fourrier specification. FALSE by default.}
-   \item{P1}{ is a positive integer valued parameter that corresponds to the number of cosinus terms used in the flexible fourrier specification for the periodicity function, see Andersen et al. (1997) for details.}
-   \item{P2}{ is a positive integer valued parameter that corresponds to the number of sinus terms used in the flexible fourrier specification for the periodicity function, see Andersen et al. (1997) for details.}
-   \item{marketopen}{the market opening time, by default: marketopen = "09:30:00".}
-   \item{marketclose}{the market closing time, by default: marketclose = "16:00:00".} 
+An \code{xts} or \code{matrix} object (depending on the input) containing
+spot volatility estimates \eqn{\sigma_{t,i}}, reported for each interval
+\eqn{i} between \code{marketopen} and \code{marketclose} for every day
+\eqn{t} in \code{data}. The length of the intervals is specifiedby \code{k}
+and \code{on}. Methods that provide this output: All.
+
+\code{daily}
+
+An \code{xts} or \code{numeric} object (depending on the input) containing
+estimates of the daily volatility levels for each day \eqn{t} in \code{data},
+if the used method decomposed spot volatility into a daily and an intraday
+component. Methods that provide this output: \code{"detper"}.
+
+\code{periodic}
+
+An \code{xts} or \code{numeric} object (depending on the input) containing
+estimates of the intraday periodicity factor for each day interval \eqn{i}
+between \code{marketopen} and \code{marketclose}, if the spot volatility was
+decomposed into a daily and an intraday component. If the output is in
+\code{xts} format, this periodicity factor will be dated to the first day of
+the input data, but it is identical for each day in the sample. Methods that
+provide this output: \code{"detper"}.
+
+\code{par}
+
+A named list containing parameter estimates, for methods that estimate one
+or more parameters. Methods that provide this output:
+\code{"stochper", "kernel"}.
+
+\code{cp}
+
+A vector containing the change points in the volatility, i.e. the observation
+indices after which the volatility level changed, according to the applied
+tests. The vector starts with a 0. Methods that provide this output:
+\code{"piecewise"}.
+
+\code{ugarchfit}
+
+A \code{\link{ugarchfit}} object, as used by the \code{\link{rugarch}}
+package, containing all output from fitting the GARCH model to the data.
+Methods that provide this output: \code{"garch"}.
 }
+\description{
+The \code{spotvol} function offers several methods to estimate spot
+volatility and its intraday seasonality, using high-frequency data. It
+returns an object of class \code{spotvol}, which can contain various outputs,
+depending on the method used. See 'Details' for a description of each method.
+In any case, the output will contain the spot volatility estimates.
 
+The input can consist of price data or return data, either tick by tick or
+sampled at set intervals. The data will be converted to equispaced
+high-frequency returns \eqn{r_{t,i}} (read: the \eqn{i}th return on day
+\eqn{t}).
+}
 \details{
-Returns an xts object with first column equal to the high-frequency return series, second column is the estimated standard deviation, third column is the daily standard deviation factor and, finally, the fourth column is the periodic component. 
+The following estimation methods can be specified in \code{method}:
+
+\strong{Deterministic periodicity method (\code{"detper"})}
+
+Parameters:
+\tabular{ll}{
+\code{dailyvol} \tab A string specifying the estimation method for the daily
+component \eqn{s_t}. Possible values are \code{"bipower", "rv", "medrv"}.
+Default = \code{"bipower"}. \cr
+\code{periodicvol} \tab A string specifying the estimation method for the
+component of intraday volatility, that depends in a deterministic way on the
+intraday time at which the return is observed. Possible values are
+\code{"TML", "SD", "WSD", "OLS"}. See Boudt et al. (2011) for details.
+Default = \code{"TML"}.\cr
+\code{P1} \tab A positive integer corresponding to the number of cosinus
+terms used in the flexible Fourier specification of the periodicity function,
+see Andersen et al. (1997) for details. Default = 5. \cr
+\code{P2} \tab Same as \code{P1}, but for the sinus terms. Default = 5.\cr
+\code{dummies} \tab Boolean: in case it is \code{TRUE}, the parametric
+estimator of periodic standard deviation specifies the periodicity function
+as the sum of dummy variables corresponding to each intraday period. If it
+is \code{FALSE}, the parametric estimator uses the flexible Fourier
+specification. Default = \code{FALSE}.
 }
+Outputs (see 'Value' for a full description of each component):
+\itemize{
+\item{\code{spot}}
+\item{\code{daily}}
+\item{\code{periodic}}
+}
+The spot volatility is decomposed into a deterministic periodic factor
+\eqn{f_{i}} (identical for every day in the sample) and a daily factor
+\eqn{s_{t}} (identical for all observations within a day). Both components
+are then estimated separately. For more details, see Taylor and Xu (1997)
+and Andersen and Bollerslev (1997). The jump robust versions by Boudt et al.
+(2011) have also been implemented.
 
-\references{
-Andersen, T. G. and T. Bollerslev (1997). Intraday periodicity and volatility persistence in financial markets. 
-Journal of Empirical Finance 4, 115-158.
+\strong{Stochastic periodicity method (\code{"stochper"})}
 
-Andersen, T. G., D. Dobrev, and E. Schaumburg (2009). Jump-robust volatility 
-estimation using nearest neighbor truncation. NBER Working Paper No.
-15533.
+Parameters:
+\tabular{ll}{
+\code{P1} \tab A positive integer corresponding to the number of cosinus
+terms used in the flexible Fourier specification of the periodicity function.
+Default = 5. \cr
+\code{P2} \tab Same as \code{P1}, but for the sinus terms. Default = 5.\cr
+\code{init} \tab A named list of initial values to be used in the
+optimization routine (\code{"BFGS"} in \code{\link{optim}}). Default =
+\code{list(sigma = 0.03, sigma_mu = 0.005, sigma_h = 0.005, sigma_k = 0.05,
+phi = 0.2, rho = 0.98, mu = c(2, -0.5), delta_c = rep(0, max(1,P1)),
+delta_s = rep(0, max(1,P2)))}. See Beltratti & Morana (2001) for a definition
+of each parameter. \code{init} can contain any number of these parameters.
+For parameters not specified in \code{init}, the default initial value will
+be used.\cr
+\code{control} \tab A list of options to be passed down to
+\code{\link{optim}}.
+}
+Outputs (see 'Value' for a full description of each component):
+\itemize{
+\item{\code{spot}}
+\item{\code{par}}
+}
+This method by Beltratti and Morana (2001) assumes the periodicity factor to
+be stochastic. The spot volatility estimation is split into four components:
+a random walk, an autoregressive process, a stochastic cyclical process and
+a deterministic cyclical process. The model is estimated using a
+quasi-maximum likelihood method based on the Kalman Filter. The package
+\code{\link[=fkf]{FKF}} is used to apply the Kalman filter. In addition to
+the spot volatility estimates, all parameter estimates are returned.
 
-Barndorff-Nielsen, O. and N. Shephard (2004). Power and bipower variation with 
-stochastic volatility and jumps. Journal of Financial Econometrics 2 (1), 1-37.
+\strong{Nonparametric filtering (\code{"kernel"})}
 
-Boudt K., Croux C. and Laurent S. (2011).  Robust estimation of intraweek periodicity 
-in volatility and jump detection. Journal of Empirical Finance 18, 353-367.
+Parameters:
+\tabular{ll}{
+\code{type} \tab String specifying the type of kernel to be used. Options
+include \code{"gaussian", "epanechnikov", "beta"}. Default =
+\code{"gaussian"}.\cr
+\code{h} \tab Scalar or vector specifying bandwidth(s) to be used in kernel.
+If \code{h} is a scalar, it will be assumed equal throughout the sample. If
+it is a vector, it should contain bandwidths for each day. If left empty,
+it will be estimated. Default = \code{NULL}. \cr
+\code{est} \tab String specifiying the bandwidth estimation method. Possible
+values include \code{"cv", "quarticity"}. Method \code{"cv"} equals
+cross-validation, which chooses the bandwidth that minimizes the Integrated
+Square Error. \code{"quarticity"} multiplies the simple plug-in estimator
+by a factor based on the daily quarticity of the returns. \code{est} is
+obsolete if \code{h} has already been specified by the user. Default =
+\code{"cv"}.\cr
+\code{lower} \tab Lower bound to be used in bandwidth optimization routine,
+when using cross-validation method. Default is \eqn{0.1n^{-0.2}}. \cr
+\code{upper} \tab Upper bound to be used in bandwidth optimization routine,
+when using cross-validation method. Default is \eqn{n^{-0.2}}. \cr
+}
+Outputs (see 'Value' for a full description of each component):
+\itemize{
+\item{\code{spot}}
+\item{\code{par}}
+}
+This method by Kristensen (2010) filters the spot volatility in a
+nonparametric way by applying kernel weights to the standard realized
+volatility estimator. Different kernels and bandwidths can
+be used to focus on specific characteristics of the volatility process.
 
-Taylor, S. J. and X. Xu (1997). The incremental volatility information in one million foreign exchange quotations. 
-Journal of Empirical Finance 4, 317-340.
+Estimation results heavily depend on the bandwidth parameter \eqn{h}, so it
+is important that this parameter is well chosen. However, it is difficult to
+come up with a method that determines the optimal bandwidth for any kind of
+data or kernel that can be used. Although some estimation methods are
+provided, it is advised that you specify \eqn{h} yourself, or make sure that
+the estimation results are appropiate.
+
+One way to estimate \eqn{h}, is by using cross-validation. For each day in
+the sample, \eqn{h} is chosen as to minimize the Integrated Square Error,
+which is a function of \eqn{h}. However, this function often has multiple
+local minima, or no minima at all (\eqn{h -> \Inf}). To ensure a reasonable
+optimum is reached, strict boundaries have to be imposed on \eqn{h}. These
+can be specified by \code{lower} and \code{upper}, which by default are
+\eqn{0.1n^{-0.2}} and \eqn{n^{-0.2}} respectively, where \eqn{n} is the
+number of observations in a day.
+
+When using the method \code{"kernel"}, in addition to the spot volatility
+estimates, all used values of the bandwidth \eqn{h} are returned.
+
+\strong{Piecewise constant volatility (\code{"piecewise"})}
+
+Parameters:
+\tabular{ll}{
+\code{type} \tab String specifying the type of test to be used. Options
+include \code{"MDa", "MDb", "DM"}. See Fried (2012) for details. Default =
+\code{"MDa"}.\cr
+\code{m} \tab Number of observations to include in reference window.
+Default = \code{40}. \cr
+\code{n} \tab Number of observations to include in test window.
+Default = \code{20}. \cr
+\code{alpha} \tab Significance level to be used in tests. Note that the test
+will be executed many times (roughly equal to the total number of
+observations), so it is advised to use a small value for \code{alpha}, to
+avoid a lot of false positives. Default = \code{0.005}. \cr
+\code{volest} \tab String specifying the realized volatility estimator to be
+used in local windows. Possible values are \code{"bipower", "rv", "medrv"}.
+Default = \code{"bipower"}. \cr
+\code{online} \tab Boolean indicating whether estimations at a certain point
+\eqn{t} should be done online (using only information available at
+\eqn{t-1}), or ex post (using all observations between two change points).
+Default = \code{TRUE}.  \cr
 }
+Outputs (see 'Value' for a full description of each component):
+\itemize{
+\item{\code{spot}}
+\item{\code{cp}}
+}
 
+This nonparametric method by Fried (2012) assumes the volatility to be
+piecewise constant over local windows. Robust two-sample tests are applied to
+detect changes in variability between subsequent windows. The spot volatility
+can then be estimated by evaluating regular realized volatility estimators
+within each local window.
+
+Along with the spot volatility estimates, this method will return the
+detected change points in the volatility level. When plotting a
+\code{spotvol} object containing \code{cp}, these change points will be
+visualized.
+
+\strong{GARCH models with intraday seasonality  (\code{"garch"})}
+
+Parameters:
+\tabular{ll}{
+\code{model} \tab String specifying the type of test to be used. Options
+include \code{"sGARCH", "eGARCH"}. See \code{\link{ugarchspec}} in the
+\code{\link{rugarch}} package. Default = \code{"eGARCH"}. \cr
+\code{garchorder} \tab Numeric value of length 2, containing the order of
+the GARCH model to be estimated. Default = \code{c(1,1)}. \cr
+\code{dist} \tab String specifying the distribution to be assumed on the
+innovations. See \code{distribution.model} in \code{\link{ugarchspec}} for
+possible options. Default = \code{"norm"}. \cr
+\code{solver.control} \tab List containing solver options.
+See \code{\link{ugarchfit}} for possible values. Default = \code{list()}. \cr
+\code{P1} \tab A positive integer corresponding to the number of cosinus
+terms used in the flexible Fourier specification of the periodicity function.
+Default = 5. \cr
+\code{P2} \tab Same as \code{P1}, but for the sinus terms. Default = 5.\cr
+}
+Outputs (see 'Value' for a full description of each component):
+\itemize{
+\item{\code{spot}}
+\item{\code{ugarchfit}}
+}
+This method generates the external regressors needed to model the intraday
+seasonality with a Flexible Fourier form. The \code{\link{rugarch}} package
+is then employed to estimate the specified GARCH(1,1) model.
+
+Along with the spot volatility estimates, this method will return the
+\code{\link{ugarchfit}} object used by the \code{\link{rugarch}} package.
+}
 \examples{
-data("sample_real5minprices");
+data(sample_prices_5min)
 
-# Compute and plot intraday periodicity:
-out = spotVol(sample_real5minprices,P1=6,P2=4,periodicvol="TML",k=5, dummies=FALSE);
-head(out);
+# default method, deterministic periodicity
+vol1 <- spotvol(sample_prices_5min)
+par.def <- par(no.readonly = TRUE)
+plot(vol1)
+par(par.def)
+
+# compare to stochastic periodicity
+init = list(sigma = 0.03, sigma_mu = 0.005, sigma_h = 0.007,
+            sigma_k = 0.06, phi = 0.194, rho = 0.986, mu = c(1.87,-0.42),
+            delta_c = c(0.25, -0.05, -0.2, 0.13, 0.02), delta_s = c(-1.2,
+            0.11, 0.26, -0.03, 0.08))
+# next method will take around 110 iterations
+vol2 <- spotvol(sample_prices_5min, method = "stochper", init = init)
+plot(as.numeric(vol1$spot[1:780]), type="l")
+lines(as.numeric(vol2$spot[1:780]), col="red")
+legend("topright", c("detper", "stochper"), col = c("black", "red"), lty=1)
+
+# various kernel estimates
+h1 = bw.nrd0((1:nrow(sample_returns_5min))*(5*60))
+vol3 <- spotvol(sample_returns_5min, method = "kernel", h = h1)
+vol4 <- spotvol(sample_returns_5min, method = "kernel", est = "quarticity")
+vol5 <- spotvol(sample_returns_5min, method = "kernel", est = "cv")
+plot(vol3, length = 2880)
+lines(as.numeric(t(vol4$spot))[1:2880], col="red")
+lines(as.numeric(t(vol5$spot))[1:2880], col="blue")
+legend("topright", c("h = simple estimate", "h = quarticity corrected",
+       "h = crossvalidated"), col = c("black", "red", "blue"), lty=1)
+par(par.def)
+
+# piecewise constant volatility, using an example from Fried (2012)
+simdata <- matrix(sqrt(5/3)*rt(3000, df = 5), ncol = 500, byrow = TRUE)
+simdata <- c(1, 1, 1.5, 1.5, 2, 1)*simdata
+# the volatility of the simulated now changes at 1000, 2000 and 2500
+vol6 <- spotvol(simdata, method = "piecewise", m = 200, n  = 100,
+                online = FALSE)
+plot(vol6)
+
+# compare regular GARCH(1,1) model to eGARCH, both with external regressors
+vol7 <- spotvol(sample_returns_5min, method = "garch", model = "sGARCH")
+vol8 <- spotvol(sample_returns_5min, method = "garch", model = "eGARCH")
+plot(as.numeric(t(vol7$spot)), type = "l")
+lines(as.numeric(t(vol8$spot)), col = "red")
+legend("topleft", c("GARCH", "eGARCH"), col = c("black", "red"), lty=1)
 }
+\references{
+Andersen, T. G. and T. Bollerslev (1997). Intraday periodicity and volatility
+persistence in financial markets. Journal of Empirical Finance 4, 115-158.
 
-\keyword{volatility}
+Beltratti, A. and C. Morana (2001). Deterministic and stochastic methods for estimation
+of intraday seasonal components with high frequency data. Economic Notes 30, 205-234.
 
-\author{Jonathan Cornelissen and Kris Boudt}
+Boudt K., Croux C. and Laurent S. (2011). Robust estimation of intraweek periodicity
+in volatility and jump detection. Journal of Empirical Finance 18, 353-367.
 
-%cd C:\package\TradeAnalytics\pkg\RTAQ\man
-%R CMD Rdconv --type=html --output=sample_5minprices.htm sample_5minprices.Rd
+Fried, Roland (2012). On the online estimation of local constant volatilities.
+Computational Statistics and Data Analysis 56, 3080-3090.
+
+Kristensen, Dennis (2010). Nonparametric filtering of the realized spot volatility:
+A kernel-based approach. Econometric Theory 26, 60-93.
+
+Taylor, S. J. and X. Xu (1997). The incremental volatility information in one million
+foreign exchange quotations. Journal of Empirical Finance 4, 317-340.
+}
+

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