Vamos carregar as séries de preços de fechamento ajustados de ambas as séries em uma única estrutura de dados de séries temporais chamada act1Prices.z.
Note que utilizamos o pacote zoo, logo é necessário tê-lo carregado previamente.
# SP500
sp500.df <- read.csv('data/GSPC-1962-1994.daily.csv', header=TRUE, stringsAsFactors=FALSE)
sp500.df$Date <- as.Date(sp500.df$Date)
sp500.df <- sp500.df[order(sp500.df$Date),]
sp500Prices.df <- sp500.df[, "Adj.Close", drop=FALSE]
rownames(sp500Prices.df) <- sp500.df[, "Date"]
colnames(sp500Prices.df) <- c("SP500")
sp500.prices <- as.zoo(sp500Prices.df)
index(sp500.prices) <- sp500.df[, "Date"]
head(sp500.prices)
## SP500
## 1962-01-03 71.13
## 1962-01-04 70.64
## 1962-01-05 69.66
## 1962-01-08 69.12
## 1962-01-09 69.15
## 1962-01-10 68.96
# IBM
ibm.df <- read.csv('data/IBM-1962-1994.daily.csv', header=TRUE, stringsAsFactors=FALSE)
ibm.df$Date <- as.Date(ibm.df$Date)
ibm.df <- ibm.df[order(ibm.df$Date),]
ibmPrices.df <- ibm.df[, "Adj.Close", drop=FALSE]
rownames(ibmPrices.df) <- ibm.df[, "Date"]
colnames(ibmPrices.df) <- c("IBM")
ibm.prices <- as.zoo(ibmPrices.df)
index(ibm.prices) <- ibm.df[, "Date"]
head(ibm.prices)
## IBM
## 1962-01-03 2.56
## 1962-01-04 2.54
## 1962-01-05 2.49
## 1962-01-08 2.44
## 1962-01-09 2.47
## 1962-01-10 2.47
# Merging series
act1Prices.z <- merge(sp500.prices, ibm.prices)
head(act1Prices.z)
## SP500 IBM
## 1962-01-03 71.13 2.56
## 1962-01-04 70.64 2.54
## 1962-01-05 69.66 2.49
## 1962-01-08 69.12 2.44
## 1962-01-09 69.15 2.47
## 1962-01-10 68.96 2.47
# Calculando retornos
act1Returns.z <- diff(log(act1Prices.z))
plot(act1Returns.z, col="red", lwd=2, main="Daily cc returns")
Bem, calculados os retornos, vamos dividir as séries em 4 partes iguais.
# Quantidade de linhas
n = nrow(sp500.prices)
# SP500
dim(sp500.prices) <- c(n/4, 4)
## Warning in `dim<-.zoo`(`*tmp*`, value = c(2074, 4)): setting this dimension
## may lead to an invalid zoo object
colnames(sp500.prices) <- paste("SP500", 1:4)
head(sp500.prices)
## SP500 1 SP500 2 SP500 3 SP500 4
## 1962-01-03 71.13 79.44 98.44 234.41
## 1962-01-04 70.64 78.60 99.08 236.68
## 1962-01-05 69.66 77.85 99.54 235.85
## 1962-01-08 69.12 76.53 100.00 235.48
## 1962-01-09 69.15 75.44 100.68 235.91
## 1962-01-10 68.96 76.90 100.66 235.37
# IBM
dim(ibm.prices) <- c(n/4, 4)
## Warning in `dim<-.zoo`(`*tmp*`, value = c(2074, 4)): setting this dimension
## may lead to an invalid zoo object
colnames(ibm.prices) <- paste("IBM", 1:4)
head(ibm.prices)
## IBM 1 IBM 2 IBM 3 IBM 4
## 1962-01-03 2.56 4.98 7.16 19.21
## 1962-01-04 2.54 4.90 7.17 19.11
## 1962-01-05 2.49 4.84 7.24 18.29
## 1962-01-08 2.44 4.72 7.31 18.53
## 1962-01-09 2.47 4.60 7.37 18.29
## 1962-01-10 2.47 4.64 7.32 18.12
# Merging series
act1partsPrices.z <- merge(sp500.prices[,1:4], ibm.prices[,1:4])
head(act1partsPrices.z)
## SP500 1 SP500 2 SP500 3 SP500 4 IBM 1 IBM 2 IBM 3 IBM 4
## 1962-01-03 71.13 79.44 98.44 234.41 2.56 4.98 7.16 19.21
## 1962-01-04 70.64 78.60 99.08 236.68 2.54 4.90 7.17 19.11
## 1962-01-05 69.66 77.85 99.54 235.85 2.49 4.84 7.24 18.29
## 1962-01-08 69.12 76.53 100.00 235.48 2.44 4.72 7.31 18.53
## 1962-01-09 69.15 75.44 100.68 235.91 2.47 4.60 7.37 18.29
## 1962-01-10 68.96 76.90 100.66 235.37 2.47 4.64 7.32 18.12
act1partsReturns.z <- diff(log(act1partsPrices.z))
plot(act1partsReturns.z, col="red", lwd=1, main="Daily cc returns")
Infelizmente uma coisa tricky, as funções do core do R não funcionam adequadamente com objetos zoo de séries temporais, logo, devemos fazer uma cópia do objeto em forma de matriz.
# Serie completa
ret.mat <- coredata(act1Returns.z)
class(ret.mat)
## [1] "matrix"
colnames(ret.mat)
## [1] "SP500" "IBM"
head(ret.mat)
## SP500 IBM
## [1,] -0.0069126324 -0.007843177
## [2,] -0.0139702914 -0.019881371
## [3,] -0.0077821404 -0.020284671
## [4,] 0.0004339336 0.012220111
## [5,] -0.0027514318 0.000000000
## [6,] 0.0059278710 0.012072581
# Para as partes
retparts.mat <- coredata(act1partsReturns.z)
Note que a estrutura de ordenação e colunas é mantida.
# Estatisticas para as series completas
apply(ret.mat, 2, mean)
## SP500 IBM
## 0.0002247264 0.0002085588
apply(ret.mat, 2, sd)
## SP500 IBM
## 0.008813746 0.014511225
myacf <- function(x) { acf(x, lag.max=1, type="correlation", plot=FALSE) }
apply(ret.mat, 2, myacf)
## $SP500
##
## Autocorrelations of series 'x', by lag
##
## 0 1
## 1.000 0.125
##
## $IBM
##
## Autocorrelations of series 'x', by lag
##
## 0 1
## 1.000 -0.005
# Para as partes
apply(retparts.mat, 2, mean)
## SP500 1 SP500 2 SP500 3 SP500 4 IBM 1
## 5.566338e-05 9.990556e-05 4.192965e-04 3.239473e-04 3.200254e-04
## IBM 2 IBM 3 IBM 4
## 1.717667e-04 4.957656e-04 -1.376888e-04
apply(retparts.mat, 2, sd)
## SP500 1 SP500 2 SP500 3 SP500 4 IBM 1 IBM 2
## 0.006486956 0.008745287 0.008827790 0.010692630 0.013117351 0.013967302
## IBM 3 IBM 4
## 0.013715575 0.016929063
apply(retparts.mat, 2, myacf)
## $`SP500 1`
##
## Autocorrelations of series 'x', by lag
##
## 0 1
## 1.000 0.183
##
## $`SP500 2`
##
## Autocorrelations of series 'x', by lag
##
## 0 1
## 1.000 0.268
##
## $`SP500 3`
##
## Autocorrelations of series 'x', by lag
##
## 0 1
## 1.000 0.097
##
## $`SP500 4`
##
## Autocorrelations of series 'x', by lag
##
## 0 1
## 1.000 0.027
##
## $`IBM 1`
##
## Autocorrelations of series 'x', by lag
##
## 0 1
## 1.000 0.034
##
## $`IBM 2`
##
## Autocorrelations of series 'x', by lag
##
## 0 1
## 1.000 0.067
##
## $`IBM 3`
##
## Autocorrelations of series 'x', by lag
##
## 0 1
## 1.000 -0.077
##
## $`IBM 4`
##
## Autocorrelations of series 'x', by lag
##
## 0 1
## 1.00 -0.03
IBM.hist = hist(ret.mat[,2], plot=FALSE, breaks=30)
par(mfrow=c(2,1))
hist(ret.mat[,1], main="SP500", col="slateblue1", xlab="returns", breaks=IBM.hist$breaks)
hist(ret.mat[,2], main="IBM", col="slateblue1", xlab="returns", breaks=IBM.hist$breaks)
par(mfrow=c(1,1))
densitySP500.density = density(ret.mat[,1])
hist(ret.mat[,1], main="Histogram and smoothed density", col="slateblue1", probability=TRUE, ylim=c(0,5), xlab="Returns")
points(SP500.density, type="l", col="orange", lwd=2)
boxplot(ret.mat[,1], ret.mat[,2], names=c("SP500","IBM"), outchar=TRUE, col="slateblue1", main="Comparison of return distributions", ylab="monthly cc return")
As funções skewness e kurtose pertencem ao pacote PerformanceAnalytics.
# Estatisticas para as series completas
apply(ret.mat, 2, skewness)
## SP500 IBM
## -2.1940742 -0.6043265
apply(ret.mat, 2, kurtosis)
## SP500 IBM
## 60.28919 18.34358
# Para as partes
apply(retparts.mat, 2, skewness)
## SP500 1 SP500 2 SP500 3 SP500 4 IBM 1 IBM 2
## -0.48180865 0.26893731 0.07840346 -5.02755742 -0.25419844 0.36540289
## IBM 3 IBM 4
## 0.42734872 -1.81069069
apply(retparts.mat, 2, kurtosis)
## SP500 1 SP500 2 SP500 3 SP500 4 IBM 1 IBM 2
## 10.142764 2.166363 1.865619 107.822154 4.436747 3.762453
## IBM 3 IBM 4
## 1.841794 35.061310