# [Eventstudies-commits] r344 - pkg/vignettes

Thu May 15 19:24:26 CEST 2014

Author: chiraganand
Date: 2014-05-15 19:24:26 +0200 (Thu, 15 May 2014)
New Revision: 344

Removed:
pkg/vignettes/AMM.Rnw
pkg/vignettes/AMM.bib
pkg/vignettes/ees.Rnw
pkg/vignettes/ees.bib
pkg/vignettes/new.Rnw
Log:
Removed old vignettes.

Deleted: pkg/vignettes/AMM.Rnw
===================================================================
--- pkg/vignettes/AMM.Rnw	2014-05-15 17:08:18 UTC (rev 343)
+++ pkg/vignettes/AMM.Rnw	2014-05-15 17:24:26 UTC (rev 344)
@@ -1,176 +0,0 @@
-\documentclass[a4paper,11pt]{article}
-\usepackage{graphicx}
-\usepackage{a4wide}
-\usepackage{natbib}
-\usepackage{float}
-\usepackage{tikz}
-\usepackage{parskip}
-\usepackage{amsmath}
-\title{Augmented Market Models}
-\author{Ajay Shah \and Vikram Bahure \and Chirag Anand}
-\begin{document}
-%\VignetteIndexEntry{eventstudies: Extreme events functionality}
-% \VignetteDepends{}
-% \VignetteKeywords{extreme event analysis}
-% \VignettePackage{eventstudies}
-\maketitle
-
-\begin{abstract}
-The document demonstrates the application of Augmented market model
-(AMM) from the paper \citet{patnaik2010amm} to extract currency
-exposure and AMM residuals from the model.
-\end{abstract}
-
-\SweaveOpts{engine=R,pdf=TRUE}
-\section{Introduction}
-
-Augmented market models (AMM) extends the classical market model \citep{sharpe1964capm, lintner1965capm} to introduce additional right hand side variables like currency returns or interest rates to understand the effect of macro variations in addition to market movements on stock returns. The package provides functionality to estimate augmented market models as well as produce augmented market model residuals (AMM abnormal returns) stripped of market and macro variations to run event studies. The function set was originally written and applied in \citet{patnaik2010amm}. \citet{adler1984exposure} and \citet{jorion1990exchange} are the first papers to use augmented market models to study currency exposure. The standard currency exposure AMM is as follows
-
-$$- r_j = \alpha_j + \beta_{1j} r_{M1} + \beta_{2j} r_{M2} + \epsilon -$$
-
-In the original usage of augmented market models, Currency exposure is
-expressed as the regression coefficient on currency returns (M2). The
-model uses firm stock price as the information set of firm positions
-and it relates firm returns $r_j$ to market index movements $r_{M1}$
-and currency fluctuations $r_{M2}$. The coefficient $\beta_{2j}$
-measures the sensitivity of the valuation of firm $j$ to changes in
-the exchange rate. This is a  widely used technique with multiple
-variations including asymmetric exposures.
-
-The AMM implementation in the package has some key innovations as compared to the original implementation of currency exposure AMM's by \citet{adler1984exposure} and \citet{jorion1990exchange}.
-$$- r_{jt} = \alpha + \beta_1 r_{M1,t} - + \sum_{i=0}^{k} a_i e_{t-i} + \epsilon_t -$$
-
-\begin{enumerate}
-\item Exchange rate series is re-expressed as a series of innovations with an AIC selected AR process. Under this specification, an innovation $e_t$ on the currency market has an impact on the stock price at time $t$ and the following $k$ time periods.  Under the above model, currency exposure is embedded in the vector of $a_i$ coefficients; it is no longer a simple scalar $\beta_2$ as was the case under the standard model
-\item Heteroscedasticity in $r_{M1}$ \& $r_{M2}$ : This is resolved by
-  using a HAC estimator
-\item Decomposition of market exposure from firm exposure: Market exposure issue solved by orthogonalising the market index  time-series by first estimating a regression model explaining $r_{M1}$  as a function of past and present currency innovations, and extracting the residual from this regression. These residuals represent uncontaminated market returns
-\end{enumerate}
-
-In the section below, we explain the estimation of currency exposure,
-AMM residuals and performing event study analysis. In section \ref{sec:ce}, we
-replicate the methodology used in \citet{patnaik2010amm} using the
-package. In section \ref{sec:es}, we take the AMM methodology a step ahead to
-extract residuals from AMM methodology which we use the to
-% Need to talk more about generalisation used for variables other than currency
-
-
-\section{Software approach}\label{sec:ce}
-The package has functions which enable the user to compute linear
-model AMM output, along with currency exposure, using the AMM
-methodology employed in \citet{patnaik2010amm}. In the subsections
-below we describe construction of data-set to input in \texttt{lmAMM}
-function and further computing AMM output and currency exposure.
-
-\subsection{Constructing data set}
-We need to construct usable data set, before performing AMM analysis
-on firm returns using this package. There are two steps to be
-followed constructing \texttt{X} (regressors) and firm returns
-(regressands), to perform OLS as shown in the \citet{patnaik2010amm}.
-\subsubsection{Regressors \& Regressands}
-Regressors in the AMM equation are market returns and currency
-returns, while regressands is firm returns. All the variables should
-have balanced panel if not then merge the time series variable to get
-one. \textit{AMMData} is an time series object with market returns as
-\textit{Nifty} and currency returns as \textit{INR/USD}. If
-currency exposure is to be estimated for different periods separately
-then argument \textit{dates} will be helpful or else \textit{NULL}
-will be provided to perform for full period.
-
-The function \textit{makeX} considers that
-there is impact of currency on market returns and with the argument
-\textit{market.returns.purge}, we orthogonalise the market returns to currency
-returns before using AMM model.
-
-<<>>=
-# Create RHS before running subperiod.lmAMM()
-library(eventstudies)
-data("AMMData")
-nifty <- AMMData$index.nifty -inrusd <- AMMData$currency.inrusd
-regressand <- AMMData[,c("Infosys","TCS")]
-regressors <- makeX(nifty, others=inrusd,
-                    switch.to.innov=TRUE, market.returns.purge=TRUE, nlags=1,
-                    dates=as.Date(c("2012-02-01","2013-01-01","2014-01-20")), verbose=FALSE)
-@
-
-\subsection{Augmented market model}
-Augmented market model output with a class of \textit{amm} is
-generated using the function \texttt{lmAMM}. This function takes firm
-returns (regressand) and regressor as input. Output of \texttt{lmAMM}
-function is a list object with linear model output of AMM,
-currency exposure, standard deviation and significance of the
-exposure.
-<<>>=
-## AMM residual to time series
-timeseries.lmAMM <- function(firm.returns,X,verbose=FALSE,nlags=1){
-  tmp <- resid(lmAMM(firm.returns,X,nlags))
-  tmp.res <- zoo(tmp,as.Date(names(tmp)))
-}
-## One firm
-amm.output.one <- lmAMM(regressand[,1],X=regressors,nlags=1)
-amm.resid.one <- timeseries.lmAMM(firm.returns=regressand[,1],
-                                  X=regressors, verbose=FALSE, nlags=1)
-summary(amm.output.one)
-
-## More than one firm
-                                        # Extracting and merging
-tmp.resid <- sapply(colnames(regressand)[1:2],function(y)
-                    timeseries.lmAMM(firm.returns=regressand[,y],
-                                  X=regressors,
-                                  verbose=FALSE,
-                                  nlags=1))
-amm.resid <- zoo(tmp.resid,as.Date(rownames(tmp.resid)))
-@
-
-All the basic functionality are available for object with class
-\textit{amm}. \texttt{print},\texttt{summary} and \texttt{plot}
-commands can be used to do preliminary analysis. The plot
-\ref{fig:amm} compares the AMM residuals with abnormal firm returns.
-\begin{figure}[t]
-  \begin{center}
-    \label{fig:amm}
-    \caption{Augment market model}
-    \setkeys{Gin}{width=0.8\linewidth}
-    \setkeys{Gin}{height=0.8\linewidth}
-<<fig=TRUE,echo=FALSE>>=
-plot(amm.output.one)
-@
-  \end{center}
-  \label{fig:one}
-\end{figure}
-
-\subsection{Getting currency exposure}
-The output of \texttt{makeX} function is used in \textit{subperiod.lmAMM} and
-\textit{lmAMM} function to get currency exposure of the firms and AMM
-residuals respectively. In the example below, we demonstrate the use
-of \textit{subperiod.lmAMM} function to estimate currency exposure for
-firms.
-% MakeX and subperiod.lmAMM
-<<>>=
-# Run AMM for one firm across different periods
-  deprintize<-function(f){
-    return(function(...) {capture.output(w<-f(...));return(w);});
-  }
-firm.exposure <- deprintize(subperiod.lmAMM)(firm.returns=regressand[,1],
-                                             X=regressors,
-                                             nlags=1,
-                                             verbose=TRUE,
-                                             dates= as.Date(c("2012-02-01",
-                                               "2013-01-01","2014-01-31")))
-str(firm.exposure)
-@
-
- We can also perform event study analysis, directly on AMM residuals
- using \textit{eventstudy} function. which is presented in
- \textit{eventstudies} vignette.
-
-\bibliographystyle{jss} \bibliography{AMM}
-\end{document}

Deleted: pkg/vignettes/AMM.bib
===================================================================
--- pkg/vignettes/AMM.bib	2014-05-15 17:08:18 UTC (rev 343)
+++ pkg/vignettes/AMM.bib	2014-05-15 17:24:26 UTC (rev 344)
@@ -1,53 +0,0 @@
-
- at article{patnaik2010amm,
-  title={Does the currency regime shape unhedged currency exposure?},
-  author={Patnaik, Ila and Shah, Ajay},
-  journal={Journal of International Money and Finance},
-  volume={29},
-  number={5},
-  pages={760-769},
-  year={2010},
-  publisher={Elsevier}
-}
-
- at article{sharpe1964capm,
-  title={Capital asset Prices: A Theory of market equilibrium under conditions of risk},
-  author={Sharpe, William F},
-  journal={The Journal of Finance},
-  volume={19},
-  number={3},
-  pages={425-442},
-  year={1964},
-  publisher={Wiley Online Library}
-}
-
- at article{lintner1965capm,
-  title={The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets},
-  author={Lintner, John},
-  journal={The Review of Economics and Statistics},
-  volume={47},
-  number={1},
-  pages={13-37},
-  year={1965},
-  publisher={JSTOR}
-}
-
-  title={Exposure to currency risk: definition and measurement},
-  author={Adler, Michael and Dumas, Bernard},
-  journal={Financial management},
-  pages={41-50},
-  year={1984},
-  publisher={JSTOR}
-}
-
- at article{jorion1990exchange,
-  title={The exchange-rate exposure of US multinationals},
-  author={Jorion, Philippe},
-  pages={331-345},
-  year={1990},
-  publisher={JSTOR}
-}
-
-

Deleted: pkg/vignettes/ees.Rnw
===================================================================
--- pkg/vignettes/ees.Rnw	2014-05-15 17:08:18 UTC (rev 343)
+++ pkg/vignettes/ees.Rnw	2014-05-15 17:24:26 UTC (rev 344)
@@ -1,245 +0,0 @@
-\documentclass[a4paper,11pt]{article}
-\usepackage{graphicx}
-\usepackage{a4wide}
-\usepackage{natbib}
-\usepackage{float}
-\usepackage{tikz}
-\usepackage{parskip}
-\usepackage{amsmath}
-\title{Introduction to the \textbf{extreme events} functionality}
-\author{Vikram Bahure \and Vimal Balasubramaniam \and Ajay Shah}
-\begin{document}
-% \VignetteIndexEntry{eventstudies: Extreme events functionality}
-% \VignetteDepends{}
-% \VignetteKeywords{extreme event analysis}
-% \VignettePackage{eventstudies}
-\maketitle
-
-\begin{abstract}
-  One specific application of the eventstudies package is
-  \citet{PatnaikShahSingh2013}.  This vignette reproduces results from
-  the paper and explains a specific functionality of the pacakge: to
-  perform analysis of tail events. \texttt{ees} is a wrapper available
-  in the package for users to undertake similar extreme-events''
-  analysis.
-\end{abstract}
-
-\SweaveOpts{engine=R,pdf=TRUE}
-
-\section{Introduction}
-
-Extreme events functionality is the analysis of an outcome variable
-and its behaviour around tail events of another variable, the event
-variable. This package includes an extreme events functionality as a
-wrapper in \texttt{ees}.
-
-Non-parametric studies of events on tails poses several research
-challenges:
-
-\begin{enumerate}
-\item What constitutes tail events, i.e., the cut-off points on the
-  distribution of the event variable?
-\item What is the event window, i.e., the window of observation before
-  and after the event?
-\item What happens when multiple tail events (Clustered events'')
-  occur within the event window?
-\end{enumerate}
-
-We facilitate these important technical questions with summary
-statistics on the distribution and run length of events, quantile
-values to determine the cut-off points on the distribution of the
-event variable, and depending on the frequency of analysis,
-period-wise distribution of extreme events. An analysis of all these
-summary statistics for clustered and unclustered events exist as
-well. This wrapper provides results for both cases: only unclustered
-events and both types of events.
-
-In the next few sections, we replicate a sub-section of results from
-\citet{PatnaikShahSingh2013} that studies whether extreme events on
-the S\&P 500 affects returns on the Indian stock index, the
-Nifty. Detailed mathematical overview of the methodology is available
-in the paper.
-
-
-\section{Extreme event analysis}
-
-Since the object of interest is the impact on returns of the outcome
-variable, nifty, with tail events on the S\&P 500, we first obtain a
-zoo object of returns data (EESData''). Next, we define tail events
-for a given probability value; if \textit{prob.value} is 5, then
-returns that fall under $0-5\%$ and $95-100\%$ of the probability
-distribution form our set of events.
-
-<<>>==
-library(eventstudies)
-data(EESData)
-
-input <- EESData$sp500 - -deprintize<-function(f){ - return(function(...){ - capture.output(w<-f(...));return(w);}) -} -output <- deprintize(ees)(input, prob.value=5) -@ - -As mentioned earlier, one of the most important aspect of a -non-parametric approach to an event study is if the -parameters for such an exercise is validated by the general summary -statistics of the data set being used. The object \texttt{output} is a -list of various relevant summary statistics for the data set, and with -an extreme event analysis for lower and upper tails. For each of the -tails, the following statistics are available: - -\begin{enumerate} -\item Extreme events data set (The input for event study analysis) -\item Distribution of clustered and unclustered tail events -\item Distribution of the run length -\item Quantile values of tail events -\item Yearly distribution of tail events -\end{enumerate} - -\subsection{Summary statistics} - -In \texttt{output\$data.summary}, we present the minimum, maximum,
-inter-quartile range (IQR), standard deviation (sd), and the
-distribution at 5\%, 25\%, Median, Mean, 75\%, and 95\%. This analysis
-for the S\&P 500 is identical to the results presented in Table 1 of
-Patnaik, Shah and Singh (2013).
-
-<<>>==
-output$data.summary -@ - -\subsection{Extreme events dataset} - -The output for upper tail and lower tail are in the same format as -mentioned above. The data set is a time series object with 2 columns; -the first column \textit{event.series} contains returns for extreme -events and the second column \textit{cluster.pattern} records the -number of consecutive days in the cluster. Here we show results for -the lower tail of S\&P 500. - -The overall dataset looks as follows: - -<<>>== -head(output$lower.tail$data) -str(output$lower.tail$data) -@ - -\subsection{Distribution of clustered and unclustered events} - -There are several types of clusters in an analysis of extreme -events. Clusters that are purely on either of the tails, or are -mixed. Events that have mixed clusters typically witness sharp -positive returns in the outcome variable, and soon after observing -large negative returns. This contamination'' might cause serious -downward bias in the magnitude and direction of impact due to an -extreme event. Therefore, it will be useful to ensure that such -occurrences are not included in the analysis.\footnote{While this is - interesting to study such mixed events by themselves, it is not the - subject for the specific question posed in this vignette.} - -Results from Table 2 of Patnaik, Shah and Singh (2013) show that there -are several mixed clusters in the data set. In other words, there are -many events on the S\&P 500 that provide large positive (negative) -returns followed by large negative (positive) returns in the data -set. As we look closely at the lower tail events in this vignette, the -output for the lower tail events looks like this: - -<<>>= -output$lower.tail$extreme.event.distribution -@ - -\texttt{unclstr}'' refers to unclustered events, -\texttt{used.clstr}'' refers to the clusters that are pure and -uncontaminated by mixed tail events, \texttt{removed.clstr}'' refers -to the mixed clusters. For the analysis in Patnaik, Shah and Singh -(2013) only 62 out of 102 events are used. These results are identical -to those documented in Table 2 of the paper. - -\subsection{Run length distribution of clusters} - -The next concern is the run length distribution of clusters used in -the analysis. Run length shows the total number of clusters with -\textit{n} consecutive days of its occurence. In the example used -here, we have 3 clusteres with \textit{two} consecutive events and 0 -clusters with \textit{three} consecutive events. This is also -identical the one presented in the paper by Patnaik, Shah and Singh -(2013). - -<<>>= -output$lower.tail$runlength -@ - -\subsection{Extreme event quantile values} -Quantile values show 0\%, 25\%, median, 75\%,100\% and mean values for -the extreme events data. The results shown below match the second row -of Table 4 in the paper. - -<<>>= -output$lower.tail$quantile.values -@ - -\subsection{Yearly distribution of extreme events} -This table shows the yearly distribution and the median value for -extreme events data. The results shown below are in line with the -third and forth column for S\&P 500 in the Table 5 of the paper. - -<<>>= -output$lower.tail$yearly.extreme.event -@ - -The yearly distribution for extreme events include unclustered event -and clustered events which are fused. While in extreme event -distribution of clustered and unclustered event, the clustered events -are defined as total events in a cluster. For example, if there is a -clustered event with three consecutive extreme events then we treat -that as a single event for analysis. - -\section{Extreme event study plot} - -The significance of an event study can be summarised well by visual -representations. With the steps outlined in the \texttt{eventstudies} -vignette, the wrapper \texttt{eesPlot} in the package provides a -convenient user interface to replicate Figure 7 from Patnaik, Shah and -Singh (2013). The plot presents events on the upper tail as Very -good'' and lower tail as Very bad'' on the event variable S\&P -500. The outcome variable studied here is the Nifty, and the y-axis -presents the cumulative returns in Nifty. This is an event graph, -where data is centered on event date (0'') and the graph shows 4 -days before and after the event. - -<<>>= -eesPlot(z=EESData, response.series.name="nifty", event.series.name="sp500", titlestring="S&P500", ylab="(Cum.) change in NIFTY", prob.value=5, width=5) -@ - -\begin{figure}[t] - \begin{center} - \caption{Extreme event on S\&P500 and response of NIFTY} - \setkeys{Gin}{width=1\linewidth} - \setkeys{Gin}{height=0.8\linewidth} -<<fig=TRUE,echo=FALSE>>= -res <- deprintize(eesPlot)(z=EESData, response.series.name="nifty", - event.series.name="sp500", - titlestring="S&P500", - ylab="(Cum.) change in NIFTY", - prob.value=5, width=5) -@ - \end{center} - \label{fig:one} -\end{figure} - -\section{Computational details} -The package code is written in R. It has dependencies to zoo -(\href{http://cran.r-project.org/web/packages/zoo/index.html}{Zeileis - 2012}) and boot -(\href{http://cran.r-project.org/web/packages/boot/index.html}{Ripley - 2013}). R itself as well as these packages can be obtained from -\href{http://CRAN.R-project.org/}{CRAN}. - -% \section{Acknowledgments} -\bibliographystyle{jss} \bibliography{ees} - -\end{document} Deleted: pkg/vignettes/ees.bib =================================================================== --- pkg/vignettes/ees.bib 2014-05-15 17:08:18 UTC (rev 343) +++ pkg/vignettes/ees.bib 2014-05-15 17:24:26 UTC (rev 344) @@ -1,10 +0,0 @@ - at Article{PatnaikShahSingh2013, - author = {Patnaik, Ila and Shah, Ajay and Singh, Nirvikar}, - title = {Foreign Investors Under Stress: Evidence from India }, - journal = {International Finance}, - year = 2013, -volume = 16, -number= 2, -pages = {213-244} -} - Deleted: pkg/vignettes/new.Rnw =================================================================== --- pkg/vignettes/new.Rnw 2014-05-15 17:08:18 UTC (rev 343) +++ pkg/vignettes/new.Rnw 2014-05-15 17:24:26 UTC (rev 344) @@ -1,260 +0,0 @@ -\documentclass[a4paper,11pt]{article} -\usepackage{graphicx} -\usepackage{a4wide} -\usepackage[colorlinks,linkcolor=blue,citecolor=red]{hyperref} -\usepackage{natbib} -\usepackage{float} -\usepackage{tikz} -\usepackage{parskip} -\usepackage{amsmath} -\title{Introduction to the \textbf{eventstudies} package in R} -\author{Ajay Shah} -\begin{document} -\maketitle - -\begin{abstract} -\end{abstract} -\SweaveOpts{engine=R,pdf=TRUE} - -\section{The standard event study in finance} - -In this section, we look at using the eventstudies package for the -purpose of doing the standard event study using daily returns data in -financial economics. This is a workhorse application of event -studies. The treatment here assumes knowledge of event studies -\citep{Corrado2011}. - -To conduct an event study, you must have a list of firms with -associated dates, and you must have returns data for these -firms. These dates must be stored as a simple data frame. To -illustrate this, we use the object SplitDates' in the package which -is used for doing examples. - -<<show-the-events,results=verbatim>>= -library(eventstudies) -data(SplitDates) # The sample -str(SplitDates) # Just a data frame -head(SplitDates) -@ - -The representation of dates is a data frame with two columns. The -first column is the name of the unit of observation which experienced -the event. The second column is the event date. - -The second thing that is required for doing an event study is data for -stock price returns for all the firms. The sample dataset supplied in -the package is named StockPriceReturns': - -<<show-the-events,results=verbatim>>= -data(StockPriceReturns) # The sample -str(StockPriceReturns) # A zoo object -head(StockPriceReturns,3) # Time series of dates and returns. -@ - -The StockPriceReturns object is thus a zoo object which is a time -series of daily returns. These are measured in per cent, i.e. a value -of +4 is returns of +4\%. The zoo object has many columns of returns -data, one for each unit of observation which, in this case, is a -firm. The column name of the zoo object must match the firm name -(i.e. the name of the unit of observation) in the list of events. - -The package gracefully handles the three kinds of problems encountered -with real world data: (a) a firm where returns is observed but there -is no event, (b) a firm with an event where returns data is lacking -and (c) a stream of missing data in the returns data surrounding the -event date. - -With this in hand, we are ready to run our first event study, using -raw returns: - -<<no-adjustment>>= -es <- eventstudy(firm.returns = StockPriceReturns, - eventList = SplitDates, - width = 10, - type = "None", - to.remap = TRUE, - remap = "cumsum", - inference = TRUE, - inference.strategy = "bootstrap") -@ - -This runs an event study using events listed in SplitDates, and using -returns data for the firms in StockPriceReturns. An event window of 10 -days is analysed. - -Event studies with returns data typically do some kind of adjustment -of the returns data in order to reduce variance. In order to keep -things simple, in this first event study, we are doing no adjustment, -which is done by setting type' to None''. - -While daily returns data has been supplied, the standard event study -deals with cumulated returns. In order to achieve this, we set -to.remap to TRUE and we ask that this remapping be done using cumsum. - -Finally, we come to inference strategy. We instruct eventstudy to do -inference and ask for bootstrap inference. - -Let us peek and poke at the object es' that is returned. - -<<the-es-object,results=verbatim>>= -class(es) -str(es) -@ - -The object returned by eventstudy is of class es'. It is a list with -five components. Three of these are just a record of the way -eventstudy() was run: the inference procedure adopted (bootstrap -inference in this case), the window width (10 in this case) and the -method used for mapping the data (cumsum). The two new things are -outcomes' and eventstudy.output'. - -The vector outcomes' shows the disposition of each event in the -events table. There are 22 rows in SplitDates, hence there will be 22 -elements in the vector outcomes'. In this vector, success' denotes a -successful use of the event. When an event cannot be used properly, -various error codes are supplied. E.g. unitmissing' is reported when -the events table shows an event for a unit of observation where -returns data is not observed. - -\begin{figure} -\begin{center} -<<plot-es,fig=TRUE,width=4,height=2.5>>= -par(mai=c(.8,.8,.2,.2)) -plot(es, cex.axis=.7, cex.lab=.7) -@ -\end{center} -\caption{Plot method applied to es object}\label{f:esplot1} -\end{figure} - -% TODO: The x label should be "Event time (days)" and should -% automatically handle other situations like weeks or months or microseconds. -% The y label is much too long. - -Plot and print methods for the class es' are supplied. The standard -plot is illustrated in Figure \ref{f:esplot1}. In this case, we see -the 95\% confidence interval is above 0 and below 0 and in no case can -the null of no-effect, compared with the starting date (10 days before -the stock split date), be rejected. - -In this first example, raw stock market returns was utilised in the -event study. It is important to emphasise that the event study is a -statistically valid tool even under these circumstances. Averaging -across multiple events isolates the event-related -fluctuations. However, there is a loss of statistical efficiency that -comes from fluctuations of stock prices that can have nothing to do -with firm level news. In order to increase efficiency, we resort to -adjustment of the returns data. - -The standard methodology in the literature is to use a market -model. This estimates a time-series regression$r_{jt} = \alpha_j +
-\beta_j r_{Mt} + \epsilon_{jt}$where$r_{jt}$is returns for firm$j$-on date$t$, and$r_{Mt}$is returns on the market index on date -$t$. The market index captures market-wide fluctuations, which have -nothing to do with firm-specific factors. The event study is then -conducted with the cumulated$\epsilon_{jt}$time series. This yields -improved statistical efficiency as$\textrm{Var}(\epsilon_j) <
-\textrm{Var}(r_j)$. - -This is invoked by setting type' to marketResidual': - -<<mm-adjustment>>= -data(OtherReturns) -es.mm <- eventstudy(firm.returns = StockPriceReturns, - eventList = SplitDates, - width = 10, - type = "marketResidual", - to.remap = TRUE, - remap = "cumsum", - inference = TRUE, - inference.strategy = "bootstrap", - market.returns=OtherReturns$NiftyIndex
-                    )
-@
-
-In addition to setting type' to marketResidual', we are now required
-to supply data for the market index, $r_{Mt}$. In the above example,
-this is the data object NiftyIndex supplied from the OtherReturns data
-object in the package. This is just a zoo vector with daily returns of
-the stock market index.
-
-\begin{figure}
-\begin{center}
-<<plot-es-mm,fig=TRUE,width=4,height=2.5>>=
-par(mai=c(.8,.8,.2,.2))
-plot(es.mm, cex.axis=.7, cex.lab=.7)
-@
-\end{center}
-\end{figure}
-
-A comparison of the range of the $y$ axis in Figure \ref{f:esplot1}
-versus that seen in Figure \ref{f:esplotmm} shows the substantial
-improvement in statistical efficiency that was obtained by market
-
-We close our treatment of the standard finance event study with one
-step forward on further reducing $\textrm{Var}(\epsilon)$ : by doing
-an augmented market model' regression with more than one explanatory
-variable. The augmented market model uses regressions like:
-
-$-r_{jt} = \alpha_j + \beta_1,j r_{M1,t} + \beta_2,j r_{M2,t} - \epsilon_{jt} -$
-
-where in addition to the market index $r_{M1,t}$, there is an
-additional explanatory variable $r_{M2,t}$. One natural candidate is
-the returns on the exchange rate, but there are many other candidates.
-
-An extensive literature has worked out the unique problems of
-econometrics that need to be addressed in doing augmented market
-models. The package uses the synthesis of this literature as presented
-in \citet{patnaik2010amm}.\footnote{The source code for augmented
-  market models in the package is derived from the source code written
-  for \citet{patnaik2010amm}.}
-
-To repeat the stock splits event study using augmented market models,
-we use the incantation:
-
-% Check some error
-es.amm <- eventstudy(firm.returns = StockPriceReturns,
-                    eventList = SplitDates,
-                    width = 10,
-                    type = "lmAMM",
-                    to.remap = TRUE,
-                    remap = "cumsum",
-                    inference = TRUE,
-                    inference.strategy = "bootstrap",
-                    market.returns=OtherReturns$NiftyIndex, - others=OtherReturns$USDINR,
-                    market.returns.purge=TRUE
-                    )
-@
-
-Here the additional regressor on the augmented market model is the
-returns on the exchange rate, which is the slot USDINR in
-OtherReturns. The full capabilities for doing augmented market models
-from \citet{patnaik2010amm} are available. These are documented
-elsewhere. For the present moment, we will use the feature
-market.returns.purge without explaining it.
-
-Let us look at the gains in statistical efficiency across the three
-variants of the event study. We will use the width of the confidence
-interval at date 0 as a measure of efficiency.
-
-<<efficiency-comparison,results=verbatim>>=
-tmp <- rbind(es$eventstudy.output[10,], es.mm$eventstudy.output[10,])[,c(1,3)]
-rownames(tmp) <- c("None","MM")
-tmp[,2]-tmp[,1]
-@
-
-This shows a sharp reduction in the width of the bootstrap 95\%
-confidence interval from None to MM adjustment. Over and above this, a
-small gain is obtained when going from MM adjustment to AMM
`