[Returnanalytics-commits] r2840 - pkg/FactorAnalytics/vignettes

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

Author: chenyian
Date: 2013-08-20 21:32:30 +0200 (Tue, 20 Aug 2013)
New Revision: 2840

Modified:
   pkg/FactorAnalytics/vignettes/fundamentalFM.Rnw
Log:
add section time series factor model for vignette

Modified: pkg/FactorAnalytics/vignettes/fundamentalFM.Rnw
===================================================================
--- pkg/FactorAnalytics/vignettes/fundamentalFM.Rnw	2013-08-20 18:44:57 UTC (rev 2839)
+++ pkg/FactorAnalytics/vignettes/fundamentalFM.Rnw	2013-08-20 19:32:30 UTC (rev 2840)
@@ -171,12 +171,12 @@
 \section{Standardizing Factor Exposure}
 It is common to standardize factor exposure to have weight mean 0 and standard deviation equal to 1. The weight are often taken as proportional to square root of market capitalization, although other weighting schemes are possible. 
 
-We will try example 1 but with stardarized factor exposure with square root of market capitalization. First we create a weighting variable.
+We will try example 1 but with standardized factor exposure with square root of market capitalization. First we create a weighting variable.
 
 <<standardized.fund>>=
 equity$weight <- sqrt(exp(equity$MV)) # we take log for MV before.
 @
-We can choose \verb at standardized.factor.exposure@ to be \verb at TRUE@ and \verb at weight.var@ equal to weighting variabel. 
+We can choose \verb at standardized.factor.exposure@ to be \verb at TRUE@ and \verb at weight.var@ equal to weighting variable. 
 <<s.fit>>=
 fit.fund2 <- fitFundamentalFactorModel(exposure.names=c("BM","MV"),
                                      datevar="yearqtr",returnsvar ="RET",
@@ -187,7 +187,7 @@
 
 \section{Statistical Factor Model}
 
-In statistical factor model, neighter factor exposure b (normally called factor loadings in statistical factor model) nor factor returns $f_t$ are observed in equation \ref{fm2}:
+In statistical factor model, neither factor exposure b (normally called factor loadings in statistical factor model) nor factor returns $f_t$ are observed in equation \ref{fm2}:
 \begin{equation} 
  r_t = bf_t + \epsilon_t\;,t=1 \cdots T \label{fm2} 
 \end{equation}
@@ -199,7 +199,7 @@
 
 In some cases, when number of assets N is larger than number of time period T. Connor and Korajczyk (1986) develop an alternative method called asymptotic principal components, building on the approximate factor model theory of Chamberlain and Rothschild (1983). Connor and Korajczyk analyze the eigenvector of the T X T cross product of  matrix returns rather then N X N covariance matrix of returns. They show the first k eigenvectors of this cross product matrix provide consistent estimates of the k X T matrix of factor returns. 
 
-We can use function \verb at fitStatisticalFactorModel@ to fit statistical factor model. First, we need asset returns in time series or xts format. We choose xts to work with because time index is easy to handle but this is not restircted to the model fit. 
+We can use function \verb at fitStatisticalFactorModel@ to fit statistical factor model. First, we need asset returns in time series or xts format. We choose xts to work with because time index is easy to handle but this is not restricted to the model fit. 
 
 <<create.xts>>=
 library(xts)
@@ -222,7 +222,7 @@
 names(fit.stat)
 @
 
-5 factors is choosen by Bai and Ng (2002). Factor retunrs can be found using \verb@$factors at .    
+5 factors is chosen by Bai and Ng (2002). Factor returns can be found using \verb@$factors at .    
 <<stat.factor.returns>>=
 fit.stat$k
 @
@@ -258,6 +258,45 @@
 
 Similar to \verb at fitFundamentalFactorModel@, generic functions like \verb at summary@, \verb at print@, \verb at plot@ and \verb at predict@ can be used for statistical factor model. 
 
+\section{Time Series Factor Model}
+In Time Series facto model, factor returns $f_t$ is observed and takens as macroeconomic time series like GDP or other time series like market returns or credit spread. In our package, we have provided some common used times series in data set \verb at CommonFactors@. \verb at factors@ is monthly time series and \verb at factors.Q@ is quarterly time series.
 
+<<common.factors>>=
+data(CommonFactors)
+names(factors.Q)
+@
 
+We can combine with our data \verb at ret@ and get rid of NA values.
+
+<<merge>>=
+ts.factors <- xts(factors.Q,as.yearqtr(index(factors.Q),format="%Y-%m-%d")) 
+ts.data <- na.omit(merge(ret,ts.factors))
+@
+
+We will use SP500, 10 years and 3 months term spread and difference of VIX as our factors. 
+
+<<fit.ts>>=
+fit.time <- fitTimeSeriesFactorModel(assets.names=tic,factors.names=c("SP500","Term.Spread","dVIX"),data=ts.data,fit.method="OLS")
+names(fit.time)
+@
+
+\veb at asset.fit@ can show model fit of each assets, for example for asset \verb at AA@. 
+<<single.asset.fit>>=
+summary(fit.time$asset.fit$AA)
+@
+shows only beta of SP500 is significant.  
+
+\verb at fitTimeSeriesFactorModel@ also have various variable selection algorithm to choose. One can include all the factor and let the function to decide which one is the best model. For example, we inlcude all common factors and use method \verb at stepwise@ which utilizes \verb at step@ function in \verb at stat@ package 
+
+<<fit.ts>>=
+fit.time2 <- fitTimeSeriesFactorModel(assets.names=tic,factors.names=names(ts.factors),data=ts.data,fit.method="OLS",variable.selection = "stepwise")
+@
+There are 5 factors chosen for asset AA for example. 
+<<AA.fit>>=
+fit.time2$asset.fit$AA
+@
+
+Generic functions like \verb at summary@, \verb at print@, \verb at plot@ and \verb at predict@ can be used for Time Series factor model as well like previous section.
+
+
 \end{document}
\ No newline at end of file