[Highfrequency-commits] r55 - pkg/highfrequency/man

[noreply at r-forge.r-project.org]

Author: kboudt
Date: 2013-10-14 14:01:06 +0200 (Mon, 14 Oct 2013)
New Revision: 55

Added:
   pkg/highfrequency/man/heavyModelC.Rd
Log:
doc heavymodelC

Added: pkg/highfrequency/man/heavyModelC.Rd
===================================================================
--- pkg/highfrequency/man/heavyModelC.Rd	                        (rev 0)
+++ pkg/highfrequency/man/heavyModelC.Rd	2013-10-14 12:01:06 UTC (rev 55)
@@ -0,0 +1,115 @@
+\name{heavyModelC}  
+\Rdversion{1.1}
+\alias{heavyModelC}
+\title{HEAVY Model estimation using C code}
+
+\description{
+This function is the same as heavyModel function, except for using C code to speed up the calculation process. 
+
+This function calculatest the High frEquency bAsed VolatilitY (HEAVY) model proposed in Shephard and Sheppard (2010). This function is used as a predictive volatility model built to exploit highfrequency data.  
+
+
+}
+
+\usage{
+heavyModelC(data, p=matrix( c(0,0,1,1),ncol=2 ), q=matrix( c(1,0,0,1),ncol=2 ), 
+          startingvalues = NULL, LB = NULL, UB = NULL, 
+            backcast = NULL, compconst = FALSE);
+}
+
+\arguments{ 
+   \item{data}{ a (T x K) matrix containing the data, with T the number of days. For the traditional HEAVY model: K = 2, the first column contains the squared daily demeaned returns, the second column contains the realized measures.
+   }
+   \item{p}{ a (K x K) matrix containing the lag length for the model innovations. Position (i, j) in the matrix indicates the number of lags in equation i of the model for the innovations in data column j. For the traditional heavy model p is given by matrix( c(0,0,1,1),ncol=2 ) (default). 
+   }
+   \item{q}{ 
+   a (K x K) matrix containing the lag length for the conditional variances. Position (i, j) in the matrix indicates the number of lags in equation i of the model for conditional variances corresponding to series j. For the traditionalheavy model introduced above q is given by matrix( c(1,0,0,1),ncol=2 ) (default).
+   }
+   \item{startingvalues}{ a vector containing the starting values to be used in the optimization to find the optimal parameters estimates.
+   }
+   \item{LB}{ a vector of length K indicating the lower bounds to be used in the estimation. If NULL it is set to a vector of zeros by default.
+   }
+   \item{UB}{ a vector of length K indicating the upper bounds to be used in the estimation. If NULL it is set to a vector of Inf by default.}
+   \item{backcast}{ a vector of length K used to initialize the estimation. If NULL the unconditional estimates are taken.
+   }
+   \item{compconst}{ a boolean variable. In case TRUE, the omega values are estimated in the optimization. In case FALSE, volatility targeting is done and omega is just 1 minus the sum of all relevant alpha's and beta's multiplied by the unconditional variance.
+   }
+}
+
+\details{ 
+Assume there are \eqn{T} daily returns and realized measures in the period \eqn{t}. Let \eqn{r_i} and \eqn{RM_i} be the \eqn{i^{th}} daily return and daily realized measure respectively (with \eqn{i=1, \ldots,T}).
+
+The most basic heavy model is the one with lag matrices p of \eqn{\left( \begin{array}{ccc} 0 & 1 \\ 0 & 1 \end{array} \right)} and q of \eqn{\left( \begin{array}{ccc} 1 & 0 \\ 0 & 1 \end{array} \right)}. This can be reprensented by the following equations: 
+\deqn{
+\mbox{var}{\left(r_t \right)} = h_t = w + \alpha RM_{t-1} + \beta h_{t-1}; w,\alpha \geq 0, \beta \in [0,1]
+}
+\deqn{
+\mbox{E}{\left(RM_t \right)} = \mu_t = w_R + \alpha_R RM_{t-1} + \beta_R \mu_{t-1}; w_R,\alpha_R, \beta_R \geq 0, \alpha_R+\beta_R \in [0,1]
+}
+
+Equivalently, they can be presented in terms of matrix notation as below:
+
+\deqn{
+\left( \begin{array}{ccc} h_t \\ \mu_t \end{array} \right) = \left( \begin{array}{ccc} w \\ w_R \end{array} \right)  + \left( \begin{array}{ccc} 0 & \alpha \\ 0 & \alpha_R \end{array} \right) \left( \begin{array}{ccc} r^2_{t-1} \\ RM_{t-1} \end{array} \right) + \left( \begin{array}{ccc} \beta & 0 \\ 0 & \beta_R \end{array} \right) \left( \begin{array}{ccc} h_{t-1} \\ \mu_{t-1} \end{array} \right)
+}
+
+In this version, the parameters vector to be estimated is \eqn{\left( w, w_R,\alpha, \alpha_R, \beta, \beta_R \right) }.
+
+In terms of startingvalues, Shephard and Sheppard recommend for this version of the Heavy model to set  \eqn{\beta} be around 0.6 and sum of \eqn{\alpha}+\eqn{\beta} to be close to but slightly less than one. 
+
+In general, the lag length for the model innovation and the conditional covariance can be greater than 1. Consider, for example, matrix p is  \eqn{\left( \begin{array}{ccc} 0 & 2 \\ 0 & 1 \end{array} \right)} and matrix q is the same as above. Matrix notation will be as below: 
+\deqn{
+\left( \begin{array}{ccc} h_t \\ \mu_t \end{array} \right) = \left( \begin{array}{ccc} w \\ w_R \end{array} \right)  + \left( \begin{array}{ccc} 0 & \alpha_1 \\ 0 & \alpha_R \end{array} \right) \left( \begin{array}{ccc} r^2_{t-1} \\ RM_{t-1} \end{array} \right) +\left( \begin{array}{ccc} 0 & \alpha_2 \\ 0 & 0 \end{array} \right) \left( \begin{array}{ccc} r^2_{t-2} \\ RM_{t-2} \end{array} \right) + \left( \begin{array}{ccc} \beta & 0 \\ 0 & \beta_R \end{array} \right) \left( \begin{array}{ccc} h_{t-1} \\ \mu_{t-1} \end{array} \right)
+}
+
+In this version, the parameters vector to be estimated is \eqn{\left( w, w_R,\alpha_1, \alpha_R, \alpha_2, \beta, \beta_R \right) }.
+
+
+}
+
+
+\value{ 
+A list with the following values:
+(i) loglikelihood: The log likelihood evaluated at the parameter estimates.
+(ii) likelihoods: an xts object of length T containing the log likelihoods per day.
+(iii) condvar: a (T x K) xts object containing the conditional variances
+(iv) estparams: a vector with the parameter estimates. The order in which the
+parameters are reported is as follows: First the estimates for omega then the
+estimates for the non-zero alpha's with the most recent lags first in case max(p) > 1,
+then the estimates for the non-zero beta's with the most recent lag first in case
+max(q) > 1.
+(v) convergence: an integer code indicating the successfulness of the optimization. See \verb{optim} for more information.
+}
+
+\references{
+Shephard, N. and K. Sheppard (2010). Realising the future: forecasting with high
+frequency based volatility (heavy) models. Journal of Applied Econometrics 25,
+197-231. 
+}
+
+\examples{ 
+ # Implementation of the heavy model on DJI:
+ data("realized_library");
+ returns =  realized_library$Dow.Jones.Industrials.Returns; 
+ rk      =  realized_library$Dow.Jones.Industrials.Realized.Kernel; 
+ returns = returns[!is.na(rk)];  rk = rk[!is.na(rk)]; # Remove NA's 
+ data = cbind( returns^2, rk ); # Make data matrix with returns and realized measures
+ backcast = matrix( c(var(returns),mean(rk)) ,ncol=1);
+ 
+ #For traditional (default) version:
+ startvalues = c(0.004,0.02,0.44,0.41,0.74,0.56); # Initial values;
+ output = heavyModelC( data = as.matrix(data,ncol=2), compconst=FALSE, 
+                    startingvalues = startvalues, backcast=backcast); 
+                    
+ #For general version: 
+ startvalues = c(0.004,0.02,0.44,0.4,0.41,0.74,0.56); # Initial values;
+ p = matrix(c(2, 0,0 , 1), ncol = 2);
+ q = matrix(c(1,0, 0, 1), ncol = 2);
+ 
+ output = heavyModelC( data = as.matrix(data,ncol=2), p=p, q=q, compconst=FALSE, 
+                    startingvalues = startvalues, backcast=backcast); 
+
+}
+
+\author{Giang Nguyen, Jonathan Cornelissen and Kris Boudt}
+\keyword{forecasting}
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