[Highfrequency-commits] r51 - pkg/highfrequency/man
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Tue Sep 24 14:16:59 CEST 2013
Author: kboudt
Date: 2013-09-24 14:16:58 +0200 (Tue, 24 Sep 2013)
New Revision: 51
Modified:
pkg/highfrequency/man/AJjumptest.Rd
pkg/highfrequency/man/BNSjumptest.Rd
pkg/highfrequency/man/JOjumptest.Rd
pkg/highfrequency/man/MRC.Rd
pkg/highfrequency/man/RKurt.Rd
pkg/highfrequency/man/RQPVar.Rd
pkg/highfrequency/man/RQuar.Rd
pkg/highfrequency/man/RSkew.Rd
pkg/highfrequency/man/RTPVar.Rd
pkg/highfrequency/man/RsV.Rd
pkg/highfrequency/man/ivInference.Rd
pkg/highfrequency/man/medRQ.Rd
pkg/highfrequency/man/minRQ.Rd
pkg/highfrequency/man/rMPV.Rd
Log:
Modified: pkg/highfrequency/man/AJjumptest.Rd
===================================================================
--- pkg/highfrequency/man/AJjumptest.Rd 2013-08-29 14:47:11 UTC (rev 50)
+++ pkg/highfrequency/man/AJjumptest.Rd 2013-09-24 12:16:58 UTC (rev 51)
@@ -1,106 +1,630 @@
-\name{AJjumptest}
-\alias{AJjumptest}
-\title{
-Ait- Sahalia and Jacod (2009) tests for the presence of jumps in the price series.
-}
-\description{
-
-This test examines the presence of jumps in highfrequency price series. It is based on the theory of Ait-Sahalia and Jacod (2009) (AJ). It consists in comparing the multipower variation of equispaced returns computed at a fast time scale (\eqn{h}), \eqn{r_{t,i}} (\eqn{i=1, \ldots,N}) and those computed at the slower time scale (\eqn{kh}), \eqn{y_{t,i}}(\eqn{i=1, \ldots ,\mbox{N/k}}).
-
-They found that the limit (for \eqn{N} \eqn{\to} \eqn{\infty} ) of the realized power variation is invariant for different sampling scales and that their ratio is \eqn{1} in case of jumps and \eqn{\mbox{k}^{p/2}-1} if no jumps.
-Therefore the AJ test detects the presence of jump using the ratio of realized power variation sampled from two scales. The null hypothesis is no jumps.
-
-Function returns three outcomes: 1.z-test value 2.critical value under confidence level of \eqn{95\%} and 3.p-value.
-
-Assume there is \eqn{N} equispaced returns in period \eqn{t}. Let \eqn{r_{t,i}} be a return (with \eqn{i=1, \ldots,N}) in period \eqn{t}.
-
-And there is \eqn{N/k} equispaced returns in period \eqn{t}. Let \eqn{y_{t,i}} be a return (with \eqn{i=1, \ldots ,\mbox{N/k}}) in period \eqn{t}.
-
-Then the AJjumptest is given by:
-\deqn{
-\mbox{AJjumptest}_{t,N}= \frac{S_t(p,k,h)-k^{p/2-1}}{\sqrt{V_{t,N}}}
-}
-
-in which,
-
-\deqn{
-\mbox{S}_t(p,k,h)= \frac{PV_{t,M}(p,kh)}{PV_{t,M}(p,h)}
-}
-
-\deqn{
-\mbox{PV}_{t,N}(p,kh)= \sum_{i=1}^{N/k}{|y_{t,i}|^p}
-}
-
-\deqn{
-\mbox{PV}_{t,N}(p,h)= \sum_{i=1}^{N}{|r_{t,i}|^p}
-}
-
-\deqn{
-\mbox{V}_{t,N}= \frac{N(p,k) A_{t,N(2p)}}{N A_{t,N(p)}}
-}
-
-\deqn{
-\mbox{N}(p,k)= \left(\frac{1}{\mu_p^2}\right)(k^{p-2}(1+k))\mu_{2p} + k^{p-2}(k-1) \mu_p^2 - 2k^{p/2-1}\mu_{k,p}
-}
-
-\deqn{
-\mbox{A}_{t,n(2p)}= \frac{(1/N)^{(1-p/2)}}{\mu_p} \sum_{i=1}^{N}{|r_{t,i}|^p} \ \ \mbox{for} \ \ |r_j|< \alpha(1/N)^w
-}
-
-\deqn{
-\mu_{k,p}= E(|U|^p |U+\sqrt{k-1}V|^p)
-}
-
-\eqn{U, V}: independent standard normal random variables; \eqn{h=1/N}; \eqn{p, k, \alpha, w}: parameters.
-
-}
-\usage{
-AJjumptest(pdata, p=4 , k=2, align.by= NULL, align.period = NULL, makeReturns= FALSE, ...)
-}
-
-\arguments{
- \item{pdata}{a zoo/xts object containing all prices in period t for one asset.}
- \item{p}{can be chosen among 2 or 3 or 4. The author suggests 4. 4 by default.}
- \item{k}{can be chosen among 2 or 3 or 4. The author suggests 2. 2 by default.}
- \item{align.by}{a string, align the tick data to "seconds"|"minutes"|"hours"}
- \item{align.period}{an integer, align the tick data to this many [seconds|minutes|hours].}
- \item{makeReturns}{boolean, should be TRUE when rdata contains prices instead of returns. FALSE by default.}
- \item{...}{additional arguments.}
-}
-
-\value{
-list
-}
-
-\details{
-The theoretical framework underlying jump test is that the logarithmic price process \eqn{X_t} belongs to the class of Brownian semimartingales, which can be written as:
-\deqn{
-\mbox{X}_{t}= \int_{0}^{t} a_udu + \int_{0}^{t}\sigma_{u}dW_{u} + Z_t
-}
-where \eqn{a} is the drift term, \eqn{\sigma} denotes the spot volatility process, \eqn{W} is a standard Brownian motion and \eqn{Z} is a jump process defined by:
-\deqn{
-\mbox{Z}_{t}= \sum_{j=1}^{N_t}k_j
-}
-where \eqn{k_j} are nonzero random variables. The counting process can be either finite or infinite for finite or infinite activity jumps.
-
-The Ait-Sahalia and Jacod test is that: Using the convergence properties of power variation and its dependence on the time scale on which it is measured, Ait-Sahalia and Jacod (2009) define a new variable which converges to 1 in the presence of jumps in the underlying return series, or to another deterministic and known number in the absence of jumps. (Theodosiou& Zikes(2009))
-}
-
-\references{
-Ait-Sahalia, Y. and Jacod, J. (2009). Testing for jumps in a discretely observed process. The Annals of Statistics, 37(1), 184- 222.
-
-Theodosiou, M., & Zikes, F. (2009). A comprehensive comparison of alternative tests for jumps in asset prices. Unpublished manuscript, Graduate School of Business, Imperial College London.
-}
-
-\author{
-Giang Nguyen, Jonathan Cornelissen and Kris Boudt
-}
-
-\examples{
-data(sample_tdata)
-AJjumptest(sample_tdata$PRICE, p= 2, k= 3, align.by= "seconds", align.period= 5, makeReturns= TRUE)
-}
-% Add one or more standard keywords, see file 'KEYWORDS' in the
-% R documentation directory.
-\keyword{ highfrequency }
-\keyword{ AJjumptest }
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+ <td class="blob-line-nums">
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+
+ </td>
+ <td class="blob-line-code">
[TRUNCATED]
To get the complete diff run:
svnlook diff /svnroot/highfrequency -r 51
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