R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for a HTML browser interface to help.
Type 'q()' to quit R.

> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("fMultivar-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('fMultivar')
Loading required package: mgcv
This is mgcv 1.3-1 
Loading required package: nnet
Loading required package: fBasics

Rmetrics, (C) 1999-2005, Diethelm Wuertz, GPL
fBasics: Markets, Basic Statistics, Date and Time
Loading required package: fCalendar

Rmetrics, (C) 1999-2005, Diethelm Wuertz, GPL
fCalendar: Markets, Basic Statistics, Date and Time
Loading required package: fSeries

Rmetrics, (C) 1999-2005, Diethelm Wuertz, GPL
fSeries: The Dynamical Process Behind Financial Markets

Rmetrics, (C) 1999-2005, Diethelm Wuertz, GPL
fSeries 2: Multivariate Financial Markets Analysis
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "A1-RegressionModelling"
> 
> ### * A1-RegressionModelling
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: RegressionModelling
> ### Title: Univariate Regression Modelling
> ### Aliases: RegressionModelling fREG fREG-class regFit predict.fREG
> ###   print.fREG plot.fREG summary.fREG fitted.values.fREG residuals.fREG
> ###   OLS print.OLS plot.OLS summary.OLS
> ### Keywords: models
> 
> ### ** Examples
> 
> ## SOURCE("fBasics.A0-SPlusCompatibility")
> ## SOURCE("fMultivar.A1-RegressionModelling")
> 
> ## regFit -
>    xmpMultivar("\nStart: Load US Recession Modelling Data Set > ")
>    data(recession) 
>    
> ## myPlot -
>    xmpMultivar("\nNext: Write Internal Plot Function > ")
>    myPlot = function(recession, in.sample) {
+      Date = recession[, "date"]
+      Date = trunc(Date/100) + (Date-100*trunc(Date/100))/12
+      Recession = recession[, "recession"]
+      inSample = as.vector(in.sample)
+      plot(Date, Recession, type = "n", main = "US Recession")
+      grid()
+      lines(Date, Recession, type = "h", col = "steelblue3")
+      lines(Date, inSample) }
>    
> ## Generalized Additive Modelling:
>    xmpMultivar("\nNext: Generalized Additive Modelling > ")
>    require(mgcv)
[1] TRUE
>    par(mfrow = c(2, 2))
>    fit = regFit(formula = recession ~ s(tbills3m) + s(tbonds10y),
+          family = gaussian(), data = recession, method = "GAM")
>    # In Sample Prediction:
>    in.sample = predict(fit, newdata = recession)$fit  
>    myPlot(recession, in.sample)
>    # Summary:
>    summary(fit)

Title:
Generalized Additive Modelling 

Formula:
~ recession s(tbills3m) + s(tbonds10y) 

Family:
gaussian identity 

Model Parameters:
   (Intercept)   s(tbills3m).1   s(tbills3m).2   s(tbills3m).3   s(tbills3m).4  
      0.143187        0.166458       -0.013294        0.222052        0.380716  
 s(tbills3m).5   s(tbills3m).6   s(tbills3m).7   s(tbills3m).8   s(tbills3m).9  
      0.128114       -0.034126        0.062578        0.657062       -0.154918  
s(tbonds10y).1  s(tbonds10y).2  s(tbonds10y).3  s(tbonds10y).4  s(tbonds10y).5  
     -0.455603       -0.400592        0.091034       -0.529471        0.036311  
s(tbonds10y).6  s(tbonds10y).7  s(tbonds10y).8  s(tbonds10y).9  
     -0.096968        0.001936       -1.372433        0.469935  

Residual Variance:
 0.07675891

Parametric coefficients:
              Estimate  std. err.    t ratio    Pr(>|t|)
(Intercept)    0.14319    0.01355      10.56    < 2.22e-16

Approximate significance of smooth terms:
                    edf       chi.sq     p-value
 s(tbills3m)       7.55       104.58     2.4655e-16
s(tbonds10y)      7.567        84.11     5.6757e-13

R-sq.(adj) = 0.353   Deviance explained = 37.6%
GCV score = 0.082618   Scale est. = 0.079542  n = 433
Parametric coefficients:
              Estimate  std. err.    t ratio    Pr(>|t|)
(Intercept)    0.14319    0.01355      10.56    < 2.22e-16

Approximate significance of smooth terms:
                    edf       chi.sq     p-value
 s(tbills3m)       7.55       104.58     2.4655e-16
s(tbonds10y)      7.567        84.11     5.6757e-13

R-sq.(adj) = 0.353   Deviance explained = 37.6%
GCV score = 0.082618   Scale est. = 0.079542  n = 433
>    # Add plots from the original plot method:
>    gam.fit = fit@fit
>    class(gam.fit) = "gam"
>    plot(gam.fit)
>     
> ## POLYMARS Modelling:
>    xmpMultivar("\nNext: Polymars Modelling - Mode Parameters> ")
>    par(mfrow = c(3, 2), ask = FALSE)
>    fit = regFit(formula = recession ~ tbills3m + tbonds10y,
+          family = gaussian(), data = recession, method = "POLYMARS")
>    fit

Title:
Polytochomous MARS Modeling 

Formula:
~ recession tbills3m + tbonds10y 

Model Parameters:
   pred1 knot1 pred2 knot2       coefs     SE
1      0    NA     0    NA  2.32863760 0.4916
2      1    NA     0    NA -0.54932042 0.1028
3      1 12.47     0    NA -0.40928942 0.0986
4      1  7.96     0    NA -0.30320408 0.0718
5      1 10.12     0    NA  0.54966250 0.0954
6      2    NA     0    NA -0.41989700 0.0750
7      2 11.86     0    NA  0.42038000 0.1096
8      2  9.17     0    NA  0.40340104 0.0762
9      1    NA     2    NA  0.09842815 0.0152
10     2  7.59     0    NA  0.36797423 0.1601
11     1    NA     2  7.59 -0.13632768 0.0264

> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "A2-RegressionTests"
> 
> ### * A2-RegressionTests
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: RegressionTests
> ### Title: Regression Tests
> ### Aliases: RegressionTests lmTest bgTest bpTest dwTest gqTest harvTest
> ###   hmcTest rainTest resetTest
> ### Keywords: htest
> 
> ### ** Examples
> 
> ## SOURCE("fBasics.A0-SPlusCompatibility")
> ## SOURCE("fMultivar.A2-RegressionTests")
> 
> ## bg -
>    xmpMultivar("\nStart: Breusch-Godfrey Test > ")
>    # Generate a Stationary and an AR(1) Series:
>    x = rep(c(1, -1), 50)
>    y1 = 1 + x + rnorm(100)
>    # Perform Breusch-Godfrey Test for 1st order serial correlation:
>    lmTest(y1 ~ x, "bg")

	Breusch-Godfrey test for serial correlation of order 1

data:  formula 
LM test = 0.0037, df = 1, p-value = 0.9516

>    # ... or for fourth order serial correlation:
>    lmTest(y1 ~ x, "bg", order = 4)    

	Breusch-Godfrey test for serial correlation of order 4

data:  formula 
LM test = 3.0822, df = 4, p-value = 0.5442

>    # Compare with Durbin-Watson Test Results:
>    lmTest(y1 ~ x, "dw")

	Durbin-Watson test

data:  formula 
DW = 1.9762, p-value = 0.4924
alternative hypothesis: true autocorrelation is greater than 0 

>    y2 = filter(y1, 0.5, method = "recursive")
>    lmTest(y2 ~ x, "bg") 

	Breusch-Godfrey test for serial correlation of order 1

data:  formula 
LM test = 19.9075, df = 1, p-value = 8.128e-06

>    
> ## bp -
>    xmpMultivar("\nStart: Breusch-Pagan Test > ")
>    # Generate a Regressor:
>    x = rep(c(-1, 1), 50)
>    # Generate heteroskedastic and homoskedastic Disturbances
>    err1 = rnorm(100, sd = rep(c(1, 2), 50))
>    err2 = rnorm(100)
>    # Generate a Linear Relationship:
>    y1 = 1 + x + err1
>    y2 = 1 + x + err2
>    # Perform Breusch-Pagan Test
>    bp = lmTest(y1 ~ x, "bp")
>    bp

	studentized Breusch-Pagan test

data:  formula 
BP = 14.7875, df = 1, p-value = 0.0001203

>    # Calculate Critical Value for 0.05 Level
>    qchisq(0.95, bp$parameter)
[1] 3.841459
>    lmTest(y2 ~ x, "bp")

	studentized Breusch-Pagan test

data:  formula 
BP = 0.8683, df = 1, p-value = 0.3514

>    
> ## dw -
>    xmpMultivar("\nNext: Durban-Watson Test > ")
>    # Generate two AR(1) Error Terms 
>    # with parameter rho = 0 (white noise) 
>    # and rho = 0.9 respectively
>    err1 = rnorm(100)
>    # Generate Regressor and Dependent Variable
>    x = rep(c(-1,1), 50)
>    y1 = 1 + x + err1
>    # Perform Durbin-Watson Test:
>    lmTest(y1 ~ x, "dw")

	Durbin-Watson test

data:  formula 
DW = 1.9072, p-value = 0.3565
alternative hypothesis: true autocorrelation is greater than 0 

>    err2 = filter(err1, 0.9, method = "recursive")
>    y2 = 1 + x + err2
>    lmTest(y2 ~ x, "dw")

	Durbin-Watson test

data:  formula 
DW = 0.3091, p-value < 2.2e-16
alternative hypothesis: true autocorrelation is greater than 0 

>    
> ## gq -
>    xmpMultivar("\nNext: Goldfeld-Quandt Test > ")
>    # Generate a Regressor:
>    x = rep(c(-1, 1), 50)
>    # Generate Heteroskedastic and Homoskedastic Disturbances:
>    err1 = c(rnorm(50, sd = 1), rnorm(50, sd = 2))
>    err2 = rnorm(100)
>    # Generate a Linear Relationship:
>    y1 = 1 + x + err1
>    y2 = 1 + x + err2
>    # Perform Goldfeld-Quandt Test:
>    lmTest(y1 ~ x, "gq")

	Goldfeld-Quandt test

data:  formula 
GQ = 5.1153, df1 = 48, df2 = 48, p-value = 4.309e-08

>    lmTest(y2 ~ x, "gq")

	Goldfeld-Quandt test

data:  formula 
GQ = 1.1985, df1 = 48, df2 = 48, p-value = 0.2664

>    
> ## harv -
>    xmpMultivar("\nNext: Harvey-Collier Test > ")
>    # Generate a Regressor and Dependent Variable:
>    x = 1:50
>    y1 = 1 + x + rnorm(50)
>    y2 = y1 + 0.3*x^2
>    # Perform Harvey-Collier Test:
>    harv = lmTest(y1 ~ x, "harv")
>    harv

	Harvey-Collier test

data:  formula 
HC = 0.1187, df = 47, p-value = 0.906

>    # Calculate Critical Value vor 0.05 level:
>    qt(0.95, harv$parameter)
[1] 1.677927
>    lmTest(y2 ~ x, "harv")

	Harvey-Collier test

data:  formula 
HC = 8.0213, df = 47, p-value = 2.368e-10

>    
> ## hmc -
>    xmpMultivar("\nNext: Harrison-McCabe Test > ")
>    # Generate a Regressor:
>    x = rep(c(-1, 1), 50)
>    # Generate Heteroskedastic and Homoskedastic Disturbances:
>    err1 = c(rnorm(50, sd = 1), rnorm(50, sd = 2))
>    err2 = rnorm(100)
>    # Generate a Linear Relationship:
>    y1 = 1 + x + err1
>    y2 = 1 + x + err2
>    # Perform Harrison-McCabe Test:
>    lmTest(y1 ~ x, "hmc")

	Harrison-McCabe test

data:  formula 
HMC = 0.1855, p-value < 2.2e-16

>    lmTest(y2 ~ x, "hmc")

	Harrison-McCabe test

data:  formula 
HMC = 0.4213, p-value = 0.147

>    
> ## rain -
>    xmpMultivar("\nNext: Rainbow Test > ")
>    # Generate Series:
>    x = c(1:30)
>    y = x^2 + rnorm(30, 0, 2)
>    # Perform rainbow Test
>    rain = lmTest(y ~ x, "rain")
>    rain

	Rainbow test

data:  formula 
Rain = 28.9885, df1 = 15, df2 = 13, p-value = 1.537e-07

>    # Compute Critical Value:
>    qf(0.95, rain$parameter[1], rain$parameter[2]) 
[1] 2.53311
>    
> ## reset -
>    xmpMultivar("\nNext: Reset Test > ")
>    # Generate Series:
>    x = c(1:30)
>    y1 = 1 + x + x^2 + rnorm(30)
>    y2 = 1 + x + rnorm(30)
>    # Perform RESET Test:
>    lmTest(y1 ~ x , "reset", power = 2, type = "regressor")

	RESET test

data:  formula 
RESET = 123136.6, df1 = 1, df2 = 27, p-value < 2.2e-16

>    lmTest(y2 ~ x , "reset", power = 2, type = "regressor")          

	RESET test

data:  formula 
RESET = 1.7037, df1 = 1, df2 = 27, p-value = 0.2028

>     
> 
> 
> 
> cleanEx(); ..nameEx <- "A3-EquationsModelling"
> 
> ### * A3-EquationsModelling
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: EquationsModelling
> ### Title: Regression Tests
> ### Aliases: EquationsModelling fEQNS fEQNS-class eqnsFit SUR predict.fEQNS
> ###   print.fEQNS plot.fEQNS summary.fEQNS coef.fEQNS fitted.fEQNS
> ###   residuals.fEQNS vcov.fEQNS
> ### Keywords: models
> 
> ### ** Examples
> 
> ## SOURCE("fBasics.A0-SPlusCompatibility")
> ## SOURCE("fMultivar.A3-EquationsModelling")
> 
> ## Note, "systemfit" is required:
>    SYSTEMFIT = require(systemfit)
Loading required package: systemfit
>    if (SYSTEMFIT) {
+    
+ ## Examples from the 'systemfit' Package:
+    data(kmenta)
+    
+ ## OLS Estimations:   
+    formulas = list(demand = q ~ p + d, supply = q ~ p + f + a )
+    FITOLS = eqnsFit(formulas, data = kmenta)
+    FITOLS
+    
+ ## OLS Estimation with 2 Restrictions:
+    Rrestr <- matrix(0, 2, 7)
+    qrestr <- matrix(0, 2, 1)
+    Rrestr[1,3] =  1
+    Rrestr[1,7] = -1
+    Rrestr[2,2] = -1
+    Rrestr[2,5] =  1
+    qrestr[2,1] =  0.5
+    FITOLS2 = eqnsFit(formulas, data = kmenta, R.restr = Rrestr, 
+      q.restr = qrestr)
+    FITOLS2
+    
+ ## Iterated SUR Estimation:
+    FITSUR = eqnsFit(formulas, data = kmenta, method = "SUR", maxit = 100)
+    FITSUR
+    # Coefficients, Fitted Values, Residuals and Variance-Covariance Matrix:
+    # Call by Method:
+    coef(FITSUR)
+    fitted(FITSUR)
+    residuals(FITSUR)
+    vcov(FITSUR)
+ 
+ ## 2SLS Estimation:
+    inst = ~ d + f + a
+    FIT2SLS = eqnsFit(formulas, data = kmenta, method = "2SLS", inst = inst)
+    FIT2SLS
+    # Coefficients, Fitted Values, Residuals and Variance-Covariance Matrix:
+    # Call by Slot:
+    FIT2SLS@fit$coef
+    FIT2SLS@fit$fitted
+    FIT2SLS@fit$residuals
+    FIT2SLS@fit$vcov
+ 
+ ## 2SLS Estimation with Different Instruments in Each Equation:
+    insts = list( ~ d + f, ~ d + f + a)
+    FIT2SLS2 = eqnsFit(formulas, data = kmenta, method = "2SLS", inst = insts)
+    FIT2SLS2
+ 
+ ## 3SLS Estimation with GMM-3SLS Formula:
+    instruments = ~ d + f + a
+    FIT3SLS = eqnsFit(formulas, data = kmenta, method = "3SLS", 
+          inst = instruments, formula3sls = "GMM")
+    FIT3SLS
+    
+    } # if (SYSTEMFIT)

Title:
3SLS Equations Fit

Formulas:
q ~ p + d
q ~ p + f + a

Fit Results:
  
     N DF      SSR     MSE    RMSE       R2   Adj R2
  1 20 17  65.7291 3.86642 1.96632 0.754847 0.726005
  2 20 16 107.9138 6.74461 2.59704 0.597508 0.522041
  
  The covariance matrix of the residuals used for estimation
          1       2
  1 3.86642 4.35744
  2 4.35744 6.03958
  
  The covariance matrix of the residuals
          1       2
  1 3.86642 5.00443
  2 5.00443 6.74461
  
  The correlations of the residuals
          1       2
  1 1.00000 0.97999
  2 0.97999 1.00000
  
  The determinant of the residual covariance matrix: 1.03320
  OLS R-squared value of the system: 0.676177
  McElroy's R-squared value for the system: 0.786468
  
  3SLS estimates for 1  (equation 1 )
  Model Formula: q ~ p + d
  Instruments: ~d + f + a
  
               Estimate Std. Error   t value Pr(>|t|)    
  (Intercept) 94.633304   7.920838 11.947385        0 ***
  p           -0.243557   0.096484 -2.524313 0.021832   *
  d            0.313992   0.046944  6.688695    4e-06 ***
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
  
  Residual standard error: 1.966321 on 17 degrees of freedom
  Number of observations: 20 Degrees of Freedom: 17 
  SSR: 65.729088 MSE: 3.866417 Root MSE: 1.966321 
  Multiple R-Squared: 0.754847 Adjusted R-Squared: 0.726005 
  
  
  3SLS estimates for 2  (equation 2 )
  Model Formula: q ~ p + f + a
  Instruments: ~d + f + a
  
               Estimate Std. Error  t value Pr(>|t|)    
  (Intercept) 52.197204  11.893372 4.388764 0.000458 ***
  p            0.228589   0.099673 2.293388 0.035706   *
  f            0.228158   0.043994 5.186139    9e-05 ***
  a            0.361138   0.072889 4.954608 0.000143 ***
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
  
  Residual standard error: 2.597039 on 16 degrees of freedom
  Number of observations: 20 Degrees of Freedom: 16 
  SSR: 107.913821 MSE: 6.744614 Root MSE: 2.597039 
  Multiple R-Squared: 0.597508 Adjusted R-Squared: 0.522041 
  
Description:
Wed Jul 13 14:08:22 2005 

>    
> ## SEE ALSO:
>    # Demo File: xmpEqnsGrunfeld.R
>    # Estimation of Grunfeld's Model Data with OLS and SUR
> 
> 
> 
> cleanEx(); ..nameEx <- "B1-MatrixAddon"
> 
> ### * B1-MatrixAddon
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: MatrixAddon
> ### Title: Matrix Arithmetics and Linear Algebra
> ### Aliases: MatrixAddon triang Triang pascal colVec rowVec colIds rowIds
> ###   colIds<- rowIds<- inv norm rk tr kron mexp vec vech tslag pdl
> ### Keywords: math
> 
> ### ** Examples
> 
> ## SOURCE("fBasics.A0-SPlusCompatibility")
> ## SOURCE("fMultivar.B1-MatrixAddon")
> 
> ## Create Pascal Matrix:
>    xmpMultivar("\nStart: Pascal Matrix > ")
>    P = pascal(3)
>    P
     [,1] [,2] [,3]
[1,]    1    1    1
[2,]    1    2    3
[3,]    1    3    6
>    # Create lower triangle matrix
>    L = triang(P)
>    L
     [,1] [,2] [,3]
[1,]    1    0    0
[2,]    1    2    0
[3,]    1    3    6
>    # Extract diagonal part
>    diag(P)
[1] 1 2 6
>    
> ## Add/Subtract/Multiply/Divide:  
>    xmpMultivar("\nNext: Math Operations > ")
>    X = P
>    # Multiply matrix with a constant
>    3 * X
     [,1] [,2] [,3]
[1,]    3    3    3
[2,]    3    6    9
[3,]    3    9   18
>    # Multiply two matrices elementwise
>    X * P                     
     [,1] [,2] [,3]
[1,]    1    1    1
[2,]    1    4    9
[3,]    1    9   36
>    # Multiplies rows/columns of a matrix by a vector
>    X %*% diag(P)            
     [,1]
[1,]    9
[2,]   23
[3,]   43
>    diag(P) %*% X           
     [,1] [,2] [,3]
[1,]    9   23   43
>        
> ## Operate on Subsets of a Matrix:
>    xmpMultivar("\nNext: Matrix Subsets > ")
>    n = 3; i = 2; j = 3
>    D = diag(1:3)
>    # Return the dimension of a matrix
>    dim(P)                         
[1] 3 3
>    # Get the last colum of a matrix
>    P[, ncol(P)]                   
[1] 1 3 6
>    # Delete a column of a matrix
>    P[, -i]                      
     [,1] [,2]
[1,]    1    1
[2,]    1    3
[3,]    1    6
>    # Permute the columns of a matrix
>    P[c(3, 1, 2), ]              
     [,1] [,2] [,3]
[1,]    1    3    6
[2,]    1    1    1
[3,]    1    2    3
>    # Augments matrix horizontally 
>    cbind(P, D)                           
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    1    1    1    1    0    0
[2,]    1    2    3    0    2    0
[3,]    1    3    6    0    0    3
>       
> ## Apply a function to all Elements of a Matrix: 
>    xmpMultivar("\nNext: Operate Element by Element > ")
>    # Return square root for each element
>    sqrt(P)
     [,1]     [,2]     [,3]
[1,]    1 1.000000 1.000000
[2,]    1 1.414214 1.732051
[3,]    1 1.732051 2.449490
>    # Exponentiate the matrix elementwise
>    exp(P)
         [,1]      [,2]       [,3]
[1,] 2.718282  2.718282   2.718282
[2,] 2.718282  7.389056  20.085537
[3,] 2.718282 20.085537 403.428793
>    # Compute the median of each column
>    apply(P, 2, "median") 
[1] 1 2 3
>    # Test on all elements of a matrix       
>    all( P > 2 )   
[1] FALSE
>    # test on any element in a matrix                
>    any( P > 2 )                  
[1] TRUE
>      
> ## More Matrix Operations:
>    xmpMultivar("\nNext: More Matrix Operations > ")
>    # Return the product of two matrices
>    P %*% D   
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    1    4    9
[3,]    1    6   18
>    # Return the Kronecker Product                     
>    P %x% D                        
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
 [1,]    1    0    0    1    0    0    1    0    0
 [2,]    0    2    0    0    2    0    0    2    0
 [3,]    0    0    3    0    0    3    0    0    3
 [4,]    1    0    0    2    0    0    3    0    0
 [5,]    0    2    0    0    4    0    0    6    0
 [6,]    0    0    3    0    0    6    0    0    9
 [7,]    1    0    0    3    0    0    6    0    0
 [8,]    0    2    0    0    6    0    0   12    0
 [9,]    0    0    3    0    0    9    0    0   18
>    # Return the transposed matrix
>    t(P)                           
     [,1] [,2] [,3]
[1,]    1    1    1
[2,]    1    2    3
[3,]    1    3    6
>    # Return the inverse of a matrix
>    inv(P)  
     [,1] [,2] [,3]
[1,]    3   -3    1
[2,]   -3    5   -2
[3,]    1   -2    1
>    # Return the norm of a matrix                      
>    norm(P)                        
[1] 7.872983
>    # Return the determinante of a matrix
>    det(P)                         
[1] 1
>    # Return the rank of a matrix
>    rk(P)                            
[1] 3
>    # Return trace of a matrix
>    tr(P)                          
[1] 9
>    # Return the variance matrix
>    var(P)     
     [,1] [,2]     [,3]
[1,]    0  0.0 0.000000
[2,]    0  1.0 2.500000
[3,]    0  2.5 6.333333
>    # Return the covariance matrix                   
>    cov(P) 
     [,1] [,2]     [,3]
[1,]    0  0.0 0.000000
[2,]    0  1.0 2.500000
[3,]    0  2.5 6.333333
>    # Stack a matrix
>    vec(P) 
      [,1]
 [1,]    1
 [2,]    1
 [3,]    1
 [4,]    1
 [5,]    2
 [6,]    3
 [7,]    1
 [8,]    3
 [9,]    6
>    # Stack the lower triangle
>    vech(P)
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    1    1    1    2    3    6
>       
> ## Matrix Exponential:
>    xmpMultivar("\nNext: Linear Algebra > ")   
>    # Test case 1 from Ward (1977)
>    test1 = t(matrix(c(
+      4, 2, 0,
+      1, 4, 1,
+      1, 1, 4), 3, 3))
>    mexp(test1)
         [,1]     [,2]      [,3]
[1,] 147.8666 183.7651  71.79703
[2,] 127.7811 183.7651  91.88257
[3,] 127.7811 163.6796 111.96811
attr(,"accuracy")
[1] 1.774935e-13
attr(,"method")
[1] "pade"
attr(,"order")
[1] 8
>    # Results on Power Mac G3 under Mac OS 10.2.8 
>    #                    [,1]               [,2]               [,3]
>    # [1,] 147.86662244637000 183.76513864636857  71.79703239999643
>    # [2,] 127.78108552318250 183.76513864636877  91.88256932318409
>    # [3,] 127.78108552318204 163.67960172318047 111.96810624637124
>    # -- these agree with ward (1977, p608)
> ## Not run: 
> ##D    # A naive alternative to mexp, using spectral decomposition:
> ##D    mexp2 = function(matrix){
> ##D      z = eigen(matrix, sym = FALSE)
> ##D      Re(z$vectors %*% diag(exp(z$values)) %*% solve(z$vectors)) }
> ##D    mexp2(test1)
> ##D    # -- hopelessly inaccurate in all but the first column.
> ##D    # Test case 4 from Ward (1977)
> ##D    test4 <- structure(c(
> ##D      0, 0, 0, 0, 0, 0, 0, 0, 0, 1e-10,
> ##D      1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
> ##D      0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
> ##D      0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
> ##D      0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
> ##D      0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
> ##D      0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
> ##D      0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
> ##D      0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
> ##D      0, 0, 0, 0, 0, 0, 0, 0, 1, 0), .Dim = c(10, 10))
> ##D    attributes(mexp(test4))
> ##D    max(abs(mexp(test4) - mexp2(test4)))
> ##D    #[1] 8.746826694186494e-08
> ##D    # -- mexp2 is accurate to 7 d.p., whereas mexp to at least 14 d.p.              
> ## End(Not run)
>    
> ## More Linear Algebra:
>    xmpMultivar("\nNext: Linear Algebra > ")
>    X = P; b = c(1, 2, 3)
>    # Return the Cholesky factor matrix
>    chol(X)                        
     [,1] [,2] [,3]
[1,]    1    1    1
[2,]    0    1    2
[3,]    0    0    1
>    # Return eigenvalues and eigenvectors
>    eigen(X)                       
$values
[1] 7.8729833 1.0000000 0.1270167

$vectors
           [,1]       [,2]       [,3]
[1,] -0.1938227  0.8164966  0.5438438
[2,] -0.4722473  0.4082483 -0.7812271
[3,] -0.8598926 -0.4082483  0.3064605

>    # Return the singular value decomposition
>    svd(X)                         
$d
[1] 7.8729833 1.0000000 0.1270167

$u
           [,1]       [,2]       [,3]
[1,] -0.1938227  0.8164966  0.5438438
[2,] -0.4722473  0.4082483 -0.7812271
[3,] -0.8598926 -0.4082483  0.3064605

$v
           [,1]       [,2]       [,3]
[1,] -0.1938227  0.8164966  0.5438438
[2,] -0.4722473  0.4082483 -0.7812271
[3,] -0.8598926 -0.4082483  0.3064605

>    # Return the condition number of a matrix
>    kappa(X)                       
[1] 104.4232
>    # Return the QR decomposition of a matrix
>    qr(X)                          
$qr
           [,1]       [,2]       [,3]
[1,] -1.7320508 -3.4641016 -5.7735027
[2,]  0.5773503 -1.4142136 -3.5355339
[3,]  0.5773503  0.9659258  0.4082483

$rank
[1] 3

$qraux
[1] 1.5773503 1.2588190 0.4082483

$pivot
[1] 1 2 3

attr(,"class")
[1] "qr"
>    # Solve a system of linear equations
>    # ... use backsolve when the matrix is upper triangular
>    # ... use forwardsolve when the matrix is lower triangular
>    solve(X, b)  
[1] 0 1 0
>    backsolve(Triang(X), b)
[1] 0.25 0.25 0.50
>    solve(Triang(X), b)                 
[1] 0.25 0.25 0.50
>    forwardsolve(triang(X), b) 
[1] 1.00000000 0.50000000 0.08333333
>    solve(triang(X), b)                                        
[1] 1.00000000 0.50000000 0.08333333
> 
> 
> 
> cleanEx(); ..nameEx <- "B2-MissingValues"
> 
> ### * B2-MissingValues
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: MissingValues
> ### Title: Handling Missing Values
> ### Aliases: MissingValues removeNA substituteNA interpNA knnNA
> ### Keywords: math
> 
> ### ** Examples
> 
> ## SOURCE("fBasics.A0-SPlusCompatibility")
> ## SOURCE("fMultivar.B2-MissingValues")
> 
> ## Create a Matrix with NAs:
>    X = matrix(rnorm(100), ncol = 5)
>    # a single NA inside:
>    X[3, 5] = NA
>    # three in a row inside:
>    X[17, 2:4] = c(NA, NA, NA)
>    # three in a column inside:
>    X[13:15, 4] = c(NA, NA, NA)
>    # two at the right border:
>    X[11:12, 5] = c(NA, NA)
>    # one in the lower left corner:
>    X[20, 1] = NA
>    print(X)
             [,1]        [,2]       [,3]         [,4]       [,5]
 [1,] -0.62645381  0.91897737 -0.1645236  2.401617761 -0.5686687
 [2,]  0.18364332  0.78213630 -0.2533617 -0.039240003 -0.1351786
 [3,] -0.83562861  0.07456498  0.6969634  0.689739362         NA
 [4,]  1.59528080 -1.98935170  0.5566632  0.028002159 -1.5235668
 [5,]  0.32950777  0.61982575 -0.6887557 -0.743273209  0.5939462
 [6,] -0.82046838 -0.05612874 -0.7074952  0.188792300  0.3329504
 [7,]  0.48742905 -0.15579551  0.3645820 -1.804958629  1.0630998
 [8,]  0.73832471 -1.47075238  0.7685329  1.465554862 -0.3041839
 [9,]  0.57578135 -0.47815006 -0.1123462  0.153253338  0.3700188
[10,] -0.30538839  0.41794156  0.8811077  2.172611670  0.2670988
[11,]  1.51178117  1.35867955  0.3981059  0.475509529         NA
[12,]  0.38984324 -0.10278773 -0.6120264 -0.709946431         NA
[13,] -0.62124058  0.38767161  0.3411197           NA  1.1604026
[14,] -2.21469989 -0.05380504 -1.1293631           NA  0.7002136
[15,]  1.12493092 -1.37705956  1.4330237           NA  1.5868335
[16,] -0.04493361 -0.41499456  1.9803999  0.291446236  0.5584864
[17,] -0.01619026          NA         NA           NA -1.2765922
[18,]  0.94383621 -0.05931340 -1.0441346  0.001105352 -0.5732654
[19,]  0.82122120  1.10002537  0.5697196  0.074341324 -1.2246126
[20,]          NA  0.76317575 -0.1350546 -0.589520946 -0.4734006
>      
> ## Remove rows with NA's
>    removeNA(X)
             [,1]        [,2]       [,3]         [,4]       [,5]
 [1,] -0.62645381  0.91897737 -0.1645236  2.401617761 -0.5686687
 [2,]  0.18364332  0.78213630 -0.2533617 -0.039240003 -0.1351786
 [3,]  1.59528080 -1.98935170  0.5566632  0.028002159 -1.5235668
 [4,]  0.32950777  0.61982575 -0.6887557 -0.743273209  0.5939462
 [5,] -0.82046838 -0.05612874 -0.7074952  0.188792300  0.3329504
 [6,]  0.48742905 -0.15579551  0.3645820 -1.804958629  1.0630998
 [7,]  0.73832471 -1.47075238  0.7685329  1.465554862 -0.3041839
 [8,]  0.57578135 -0.47815006 -0.1123462  0.153253338  0.3700188
 [9,] -0.30538839  0.41794156  0.8811077  2.172611670  0.2670988
[10,] -0.04493361 -0.41499456  1.9803999  0.291446236  0.5584864
[11,]  0.94383621 -0.05931340 -1.0441346  0.001105352 -0.5732654
[12,]  0.82122120  1.10002537  0.5697196  0.074341324 -1.2246126
>    # Now we have only 12 lines!
>    
> ## Subsitute NA's by zeros or column mean
>    substituteNA(X, type = "zeros")
             [,1]        [,2]       [,3]         [,4]       [,5]
 [1,] -0.62645381  0.91897737 -0.1645236  2.401617761 -0.5686687
 [2,]  0.18364332  0.78213630 -0.2533617 -0.039240003 -0.1351786
 [3,] -0.83562861  0.07456498  0.6969634  0.689739362  0.0000000
 [4,]  1.59528080 -1.98935170  0.5566632  0.028002159 -1.5235668
 [5,]  0.32950777  0.61982575 -0.6887557 -0.743273209  0.5939462
 [6,] -0.82046838 -0.05612874 -0.7074952  0.188792300  0.3329504
 [7,]  0.48742905 -0.15579551  0.3645820 -1.804958629  1.0630998
 [8,]  0.73832471 -1.47075238  0.7685329  1.465554862 -0.3041839
 [9,]  0.57578135 -0.47815006 -0.1123462  0.153253338  0.3700188
[10,] -0.30538839  0.41794156  0.8811077  2.172611670  0.2670988
[11,]  1.51178117  1.35867955  0.3981059  0.475509529  0.0000000
[12,]  0.38984324 -0.10278773 -0.6120264 -0.709946431  0.0000000
[13,] -0.62124058  0.38767161  0.3411197  0.000000000  1.1604026
[14,] -2.21469989 -0.05380504 -1.1293631  0.000000000  0.7002136
[15,]  1.12493092 -1.37705956  1.4330237  0.000000000  1.5868335
[16,] -0.04493361 -0.41499456  1.9803999  0.291446236  0.5584864
[17,] -0.01619026  0.00000000  0.0000000  0.000000000 -1.2765922
[18,]  0.94383621 -0.05931340 -1.0441346  0.001105352 -0.5732654
[19,]  0.82122120  1.10002537  0.5697196  0.074341324 -1.2246126
[20,]  0.00000000  0.76317575 -0.1350546 -0.589520946 -0.4734006
>    substituteNA(X, type = "mean")
             [,1]        [,2]       [,3]         [,4]       [,5]
 [1,] -0.62645381  0.91897737 -0.1645236  2.401617761 -0.5686687
 [2,]  0.18364332  0.78213630 -0.2533617 -0.039240003 -0.1351786
 [3,] -0.83562861  0.07456498  0.6969634  0.689739362  0.0325636
 [4,]  1.59528080 -1.98935170  0.5566632  0.028002159 -1.5235668
 [5,]  0.32950777  0.61982575 -0.6887557 -0.743273209  0.5939462
 [6,] -0.82046838 -0.05612874 -0.7074952  0.188792300  0.3329504
 [7,]  0.48742905 -0.15579551  0.3645820 -1.804958629  1.0630998
 [8,]  0.73832471 -1.47075238  0.7685329  1.465554862 -0.3041839
 [9,]  0.57578135 -0.47815006 -0.1123462  0.153253338  0.3700188
[10,] -0.30538839  0.41794156  0.8811077  2.172611670  0.2670988
[11,]  1.51178117  1.35867955  0.3981059  0.475509529  0.0325636
[12,]  0.38984324 -0.10278773 -0.6120264 -0.709946431  0.0325636
[13,] -0.62124058  0.38767161  0.3411197  0.253439667  1.1604026
[14,] -2.21469989 -0.05380504 -1.1293631  0.253439667  0.7002136
[15,]  1.12493092 -1.37705956  1.4330237  0.253439667  1.5868335
[16,] -0.04493361 -0.41499456  1.9803999  0.291446236  0.5584864
[17,] -0.01619026  0.01393998  0.1654293  0.253439667 -1.2765922
[18,]  0.94383621 -0.05931340 -1.0441346  0.001105352 -0.5732654
[19,]  0.82122120  1.10002537  0.5697196  0.074341324 -1.2246126
[20,]  0.16929348  0.76317575 -0.1350546 -0.589520946 -0.4734006
>    
> ## Interpolate NA's liearily:
>    interpNA(X, method = "linear")
             [,1]        [,2]       [,3]         [,4]       [,5]
 [1,] -0.62645381  0.91897737 -0.1645236  2.401617761 -0.5686687
 [2,]  0.18364332  0.78213630 -0.2533617 -0.039240003 -0.1351786
 [3,] -0.83562861  0.07456498  0.6969634  0.689739362 -0.8293727
 [4,]  1.59528080 -1.98935170  0.5566632  0.028002159 -1.5235668
 [5,]  0.32950777  0.61982575 -0.6887557 -0.743273209  0.5939462
 [6,] -0.82046838 -0.05612874 -0.7074952  0.188792300  0.3329504
 [7,]  0.48742905 -0.15579551  0.3645820 -1.804958629  1.0630998
 [8,]  0.73832471 -1.47075238  0.7685329  1.465554862 -0.3041839
 [9,]  0.57578135 -0.47815006 -0.1123462  0.153253338  0.3700188
[10,] -0.30538839  0.41794156  0.8811077  2.172611670  0.2670988
[11,]  1.51178117  1.35867955  0.3981059  0.475509529  0.5648667
[12,]  0.38984324 -0.10278773 -0.6120264 -0.709946431  0.8626347
[13,] -0.62124058  0.38767161  0.3411197 -0.459598264  1.1604026
[14,] -2.21469989 -0.05380504 -1.1293631 -0.209250098  0.7002136
[15,]  1.12493092 -1.37705956  1.4330237  0.041098069  1.5868335
[16,] -0.04493361 -0.41499456  1.9803999  0.291446236  0.5584864
[17,] -0.01619026 -0.23715398  0.4681326  0.146275794 -1.2765922
[18,]  0.94383621 -0.05931340 -1.0441346  0.001105352 -0.5732654
[19,]  0.82122120  1.10002537  0.5697196  0.074341324 -1.2246126
[20,]          NA  0.76317575 -0.1350546 -0.589520946 -0.4734006
>    # Note the corner missing value cannot be interpolated!
>    # Take previous values in a column:
>    interpNA(X, method = "before")
             [,1]        [,2]       [,3]         [,4]       [,5]
 [1,] -0.62645381  0.91897737 -0.1645236  2.401617761 -0.5686687
 [2,]  0.18364332  0.78213630 -0.2533617 -0.039240003 -0.1351786
 [3,] -0.83562861  0.07456498  0.6969634  0.689739362 -0.1351786
 [4,]  1.59528080 -1.98935170  0.5566632  0.028002159 -1.5235668
 [5,]  0.32950777  0.61982575 -0.6887557 -0.743273209  0.5939462
 [6,] -0.82046838 -0.05612874 -0.7074952  0.188792300  0.3329504
 [7,]  0.48742905 -0.15579551  0.3645820 -1.804958629  1.0630998
 [8,]  0.73832471 -1.47075238  0.7685329  1.465554862 -0.3041839
 [9,]  0.57578135 -0.47815006 -0.1123462  0.153253338  0.3700188
[10,] -0.30538839  0.41794156  0.8811077  2.172611670  0.2670988
[11,]  1.51178117  1.35867955  0.3981059  0.475509529  0.2670988
[12,]  0.38984324 -0.10278773 -0.6120264 -0.709946431  0.2670988
[13,] -0.62124058  0.38767161  0.3411197 -0.709946431  1.1604026
[14,] -2.21469989 -0.05380504 -1.1293631 -0.709946431  0.7002136
[15,]  1.12493092 -1.37705956  1.4330237 -0.709946431  1.5868335
[16,] -0.04493361 -0.41499456  1.9803999  0.291446236  0.5584864
[17,] -0.01619026 -0.41499456  1.9803999  0.291446236 -1.2765922
[18,]  0.94383621 -0.05931340 -1.0441346  0.001105352 -0.5732654
[19,]  0.82122120  1.10002537  0.5697196  0.074341324 -1.2246126
[20,]          NA  0.76317575 -0.1350546 -0.589520946 -0.4734006
>    # Also here, the corner value is excluded
>    
> ## Interpolate using the knn Algorithm:
>    knnNA(X)
             [,1]        [,2]       [,3]         [,4]        [,5]
 [1,] -0.62645381  0.91897737 -0.1645236  2.401617761 -0.56866873
 [2,]  0.18364332  0.78213630 -0.2533617 -0.039240003 -0.13517862
 [3,] -0.83562861  0.07456498  0.6969634  0.689739362  0.30002458
 [4,]  1.59528080 -1.98935170  0.5566632  0.028002159 -1.52356680
 [5,]  0.32950777  0.61982575 -0.6887557 -0.743273209  0.59394619
 [6,] -0.82046838 -0.05612874 -0.7074952  0.188792300  0.33295037
 [7,]  0.48742905 -0.15579551  0.3645820 -1.804958629  1.06309984
 [8,]  0.73832471 -1.47075238  0.7685329  1.465554862 -0.30418392
 [9,]  0.57578135 -0.47815006 -0.1123462  0.153253338  0.37001881
[10,] -0.30538839  0.41794156  0.8811077  2.172611670  0.26709879
[11,]  1.51178117  1.35867955  0.3981059  0.475509529 -0.67989562
[12,]  0.38984324 -0.10278773 -0.6120264 -0.709946431  0.01034039
[13,] -0.62124058  0.38767161  0.3411197  0.183826521  1.16040262
[14,] -2.21469989 -0.05380504 -1.1293631  1.295205030  0.70021365
[15,]  1.12493092 -1.37705956  1.4330237 -0.756756197  1.58683345
[16,] -0.04493361 -0.41499456  1.9803999  0.291446236  0.55848643
[17,] -0.01619026  1.00950137  0.2025980  1.237979542 -1.27659221
[18,]  0.94383621 -0.05931340 -1.0441346  0.001105352 -0.57326541
[19,]  0.82122120  1.10002537  0.5697196  0.074341324 -1.22461261
[20,]  0.25657555  0.76317575 -0.1350546 -0.589520946 -0.47340064
> 
> 
> 
> cleanEx(); ..nameEx <- "C1-TechnicalAnalysis"
> 
> ### * C1-TechnicalAnalysis
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: TechnicalAnalysis
> ### Title: Tools for the Technical Analysis
> ### Aliases: TechnicalAnalysis emaTA biasTA medpriceTA typicalpriceTA
> ###   wcloseTA rocTA oscTA momTA macdTA cdsTA cdoTA vohlTA vorTA fpkTA
> ###   fpdTA spdTA apdTA wprTA rsiTA SMA EWMA
> ### Keywords: math
> 
> ### ** Examples
> 
> ## SOURCE("fBasics.A0-SPlusCompatibility")
> ## SOURCE("fSeries.D1-TechnicalAnalysis")
> 
>         # Currently no examples ...
> 
> 
> 
> cleanEx(); ..nameEx <- "C2-BenchmarkAnalysis"
> 
> ### * C2-BenchmarkAnalysis
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: BenchmarkAnalysis
> ### Title: Utilities and Benchmark Analysis
> ### Aliases: BenchmarkAnalysis ohlcPlot sharpeRatio sterlingRatio
> ###   maxDrawDown getReturns
> ### Keywords: math
> 
> ### ** Examples
> 
> ## SOURCE("fBasics.A0-SPlusCompatibility")
> ## SOURCE("fMultivar.D2-BenchmarkAnalysis")
> ## Not run: 
> ##D ## ohlcPlot -
> ##D    # Plot OHLC for SP500
> ##D    # ohlcPlot(x, ylab = "price", main = instrument)
> ##D    
> ##D ## sharpeRatio -
> ##D    xmpMultivar("\nStart: Sharpe Ratio > ")
> ##D    # Sharpe Ratio for DAX and FTSE:
> ##D    data(EuStockMarkets)
> ##D    dax = log(EuStockMarkets[, "DAX"])
> ##D    ftse = log(EuStockMarkets[, "FTSE"])
> ##D    # Ratios:
> ##D    sharpeRatio(dax)
> ##D    sharpeRatio(ftse)
> ##D    
> ##D ## maxDrawDown -
> ##D    xmpMultivar("\nNext: Max-Draw-Downs for the DAX Index >")
> ##D    par(mfrow = c(1, 1), cex = 0.7)
> ##D    data(EuStockMarkets)
> ##D    dax = log(EuStockMarkets[, "DAX"])
> ##D    mdd = maxDrawDown(dax)
> ##D    mdd
> ##D    # Plot DAX:
> ##D    plot(dax)
> ##D    segments(time(dax)[mdd$from], dax[mdd$from],
> ##D      time(dax)[mdd$to], dax[mdd$from])
> ##D    segments(time(dax)[mdd$from], dax[mdd$to],
> ##D      time(dax)[mdd$to], dax[mdd$to])
> ##D    mid = time(dax)[(mdd$from + mdd$to)/2]
> ##D    arrows(mid, dax[mdd$from], mid, dax[mdd$to], col = 2)
> ##D    title(main = "DAX: Max Drawdown")
> ##D    
> ##D ## getReturns -
> ##D    xmpMultivar("\nNext: Returns for the DAX Index >")
> ##D    par(mfrow = c(1, 1), cex = 0.7)
> ##D    data(EuStockMarkets)
> ##D    dax = log(EuStockMarkets[, "DAX"])
> ##D    plot(getReturns(dax))
> ##D    title(main = "DAX: Returns")
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "C3-RollingAnalysis"
> 
> ### * C3-RollingAnalysis
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: RollingAnalysis
> ### Title: Rolling Analysis
> ### Aliases: RollingAnalysis rollFun rollMin rollMax rollMean rollVar
> ### Keywords: math
> 
> ### ** Examples
> 
> ## SOURCE("fBasics.A0-SPlusCompatibility")
> ## SOURCE("fMultivar.D3-RollingAnalysis")
> 
> ## Rolling Analysis:
> ## Not run: 
> ##D    xmpMultivar("\nNext: Rolling Analysis > ")
> ##D    x = (1:10)^2
> ##D    x
> ##D    trim =  c(TRUE, TRUE, FALSE, FALSE)
> ##D    na.rm = c(TRUE, FALSE, TRUE, FALSE)
> ##D    for (i in 1:4) 
> ##D      print(rollMin(x, 5, trim[i], na.rm[i]))
> ##D    for (i in 1:4) 
> ##D      print(rollMax(x, 5, trim[i], na.rm[i]))
> ##D    for (i in 1:4) 
> ##D      print(rollVar(x, 5, trim[i], unbiased = TRUE, na.rm[i]))
> ##D    for (i in 1:4) 
> ##D      print(rollVar(x, 5, trim[i], unbiased = FALSE, na.rm[i]))
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "X1-MultivarData"
> 
> ### * X1-MultivarData
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Series2Data
> ### Title: fSeries Data Sets
> ### Aliases: Series2Data CobbDouglas logCobbDouglas Greene4Table131 pr45
> ###   spc1970 spcindis
> ### Keywords: datasets
> 
> ### ** Examples
> 
> ## SOURCE("fBasics.A0-SPlusCompatibility")
> 
> ## none -
> 
> 
> 
> cleanEx(); ..nameEx <- "Z1-MultivarTools"
> 
> ### * Z1-MultivarTools
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: MultivarTools
> ### Title: fMultivar Tools
> ### Aliases: MultivarTools xmpMultivar xmpfMultivar
> ### Keywords: programming
> 
> ### ** Examples
> 
> ## SOURCE("fBasics.A0-SPlusCompatibility")
> 
> ## Not run: 
> ##D ## xmpfMultivar -
> ##D    # Popup the examples menu:
> ##D    xmpfMultivar()
> ## End(Not run)
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  3.07 0.15 3.27 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')