Exploración de Datos
Oikos Venezuela
22/2/2020
##Carga de Datos
BTCSP <- read.csv("C:/Users/Personal/Desktop/BTCSP.csv", sep=";")
apple<-BTCSP
head(apple)## Date BTC.Close SP.Close
## 1 01.01.2014 740.3 1842.95
## 2 02.01.2014 775.0 1826.50
## 3 03.01.2014 812.1 1825.50
## 4 06.01.2014 934.5 1820.75
## 5 07.01.2014 791.0 1830.75
## 6 08.01.2014 828.5 1832.50tail(apple)## Date BTC.Close SP.Close
## 1599 24.01.2020 8447.1 3293.50
## 1600 26.01.2020 8621.6 3259.12
## 1601 27.01.2020 8912.0 3239.50
## 1602 28.01.2020 9393.7 3278.25
## 1603 29.01.2020 9304.2 3272.50
## 1604 30.01.2020 9512.7 3289.38##Activación Paquete Zoo
library(zoo)##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericapple.zoo=zoo(apple[,-1], order.by=as.Date(strptime(as.character(apple[,1]), "%d.%m.%Y")))
plot(apple.zoo, main="Precios de Cierre BTC y S&P 500 (2014-2020)")
##Función Rollapply ##Gráfica para visualizar Tendencias
library(chron)
plot(rollapply(apple.zoo, width=120, mean, na.rm=T), main="Mean of Rolling 120 Obs.")
plot(rollapply(apple.zoo, width=120, mean, by=120, na.rm=T),main="Mean of Each 120 Obs.")
##Análisis de Retornos
library(PerformanceAnalytics)## Loading required package: xts##
## Attaching package: 'PerformanceAnalytics'## The following object is masked from 'package:graphics':
##
## legendtmp <- merge(apple.zoo[,"BTC.Close"], apple.zoo[,"SP.Close"])
tmp.ret <- CalculateReturns(tmp)
colnames(tmp) <- colnames(tmp.ret) <- c("BTC.Close","SP.Close")
plot(tmp.ret, main="Retornos Precios Cierre BTC y S&P 500 (2014-2020)", xlab="Date")
##Función coredata
plot(coredata(na.omit(tmp.ret)), pch=".", main="Retornos Precios Cierre BTC y S&P 500 (2014-2020)")
##Coeficientes de regresión
rr <- rollapply(na.approx(na.trim(tmp, side="both")), width = 120,
FUN = function(z) coef(lm(BTC.Close ~ SP.Close, data = as.data.frame(z))),
by.column = FALSE, align = "right")
rr.var <- rollapply(na.approx(na.trim(tmp, side="both")), width = 120,
FUN = function(z) sd(residuals(lm(BTC.Close ~ SP.Close, data = as.data.frame(z)))),
by.column = FALSE, align = "right")
res <- merge(rr,rr.var)
colnames(res)[3] <- "Desv Estandar Res."
plot(res, main="Coeficiente de Regresion.", xlab="Date")
##Resumen e Histograma
summary(res)## Index (Intercept) SP.Close
## Min. :2014-06-18 Min. :-120844.4 Min. :-10.3194
## 1st Qu.:2015-11-13 1st Qu.: -14978.2 1st Qu.: -0.1529
## Median :2017-04-11 Median : -903.8 Median : 0.8113
## Mean :2017-04-11 Mean : -10054.0 Mean : 5.2066
## 3rd Qu.:2018-09-06 3rd Qu.: 702.8 3rd Qu.: 7.5255
## Max. :2020-01-30 Max. : 40337.8 Max. : 50.1830
## Desv Estandar Res.
## Min. : 17.97
## 1st Qu.: 65.97
## Median : 108.01
## Mean : 673.01
## 3rd Qu.: 997.44
## Max. :3048.28hist(res[,"SP.Close"], breaks=100, main="Histograma de los coeficientes estimados", xlab="Value")
##Coeficientes de regresión residuos
rr <- rollapply(na.approx(na.trim(tmp.ret, side="both")), width = 120,
FUN = function(z) coef(lm(BTC.Close~ SP.Close, data = as.data.frame(z))),
by.column = FALSE, align = "right")
rr.var <- rollapply(na.approx(na.trim(tmp.ret, side="both")), width = 120,
FUN = function(z) sd(residuals(lm (BTC.Close~ SP.Close, data = as.data.frame(z)))),
by.column = FALSE, align = "right")
res.ret <- merge(rr,rr.var)
colnames(res.ret)[3] <- "St. Dev. Resid."
plot(res.ret, main="Coeficiente de regression de los retornos de las series.", xlab="Date")
##Resumen e Histograma
summary(res.ret)## Index (Intercept) SP.Close St. Dev. Resid.
## Min. :2014-06-19 Min. :-0.008115 Min. :-1.90007 Min. :0.01588
## 1st Qu.:2015-11-15 1st Qu.:-0.001573 1st Qu.:-0.50235 1st Qu.:0.03541
## Median :2017-04-11 Median : 0.002882 Median :-0.05253 Median :0.04189
## Mean :2017-04-11 Mean : 0.002795 Mean : 0.08352 Mean :0.04359
## 3rd Qu.:2018-09-06 3rd Qu.: 0.006041 3rd Qu.: 0.39382 3rd Qu.:0.04975
## Max. :2020-01-30 Max. : 0.017093 Max. : 3.41480 Max. :0.06856hist(res.ret[,"SP.Close"], breaks=100, main="Histograma coeficientes estimados de los retornos", xlab="Value")
##Análisis de desviación estándard
library(xts)
tail(to.yearly(apple.zoo))## apple.zoo.Open apple.zoo.High apple.zoo.Low apple.zoo.Close
## 2015-12-31 313.9 466.5 183.0 429.0
## 2016-12-30 432.9 981.7 358.9 959.3
## 2017-12-29 1019.3 18934.0 778.6 14317.0
## 2018-12-31 13354.0 16917.0 3282.8 3830.5
## 2019-12-31 3963.0 12876.0 3436.1 7208.3
## 2020-01-30 7212.7 9512.7 6989.4 9512.7start(apple.zoo)## [1] "2014-01-01"end(apple.zoo)## [1] "2020-01-30"plot(apply.monthly(window(apple.zoo [,"BTC.Close"], start="2014-01-01") ,function(x) sd(x, na.rm=TRUE)), main="D.E Mensual de los Precios de Cierre de BTC 2014-20", ylab="Desviacion Estandar", xlab="Año")
plot(apply.yearly(window(apple.zoo[,"BTC.Close"], start="2014-01-01",end="2019-12-30") ,function(x) sd(x, na.rm=TRUE)), main="D.E Anual de los Precios de Cierre de BTC 2014-19", ylab="Desviacion Estandar", xlab="Año")
plot(apply.monthly(window(apple.zoo [,"SP.Close"], start="2014-01-01") ,function(x) sd(x, na.rm=TRUE)), main="D.E Mensual de los Precios de Cierre del S&P500 2014-20", ylab="Desviacion Estandar", xlab="Año")
plot(apply.yearly(window(apple.zoo[,"SP.Close"], start="2014-01-01",end="2019-12-30") ,function(x) sd(x, na.rm=TRUE)), main="D.E Anual de los Precios de Cierre del S&P500 2014-19", ylab="Desviacion Estandar", xlab="Año")
#Modelización ARIMA
library(vars)## Loading required package: MASS## Loading required package: strucchange## Loading required package: sandwich## Loading required package: urca## Loading required package: lmtestlibrary(forecast)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## Registered S3 methods overwritten by 'forecast':
## method from
## fitted.fracdiff fracdiff
## residuals.fracdiff fracdifflibrary(TSA)## Registered S3 methods overwritten by 'TSA':
## method from
## fitted.Arima forecast
## plot.Arima forecast##
## Attaching package: 'TSA'## The following objects are masked from 'package:PerformanceAnalytics':
##
## kurtosis, skewness## The following objects are masked from 'package:stats':
##
## acf, arima## The following object is masked from 'package:utils':
##
## tarlibrary(ggplot2)
library(tseries)##
## Attaching package: 'tseries'## The following object is masked from 'package:chron':
##
## is.weekend##Graficamos y aplicamos un logaritmo para suavizar los datos
apple.mod <- na.approx(na.trim(apple.zoo[,"BTC.Close"], side="both"))
head(to.daily(apple.mod))## apple.mod.Open apple.mod.High apple.mod.Low apple.mod.Close
## 2014-01-01 740.3 740.3 740.3 740.3
## 2014-01-02 775.0 775.0 775.0 775.0
## 2014-01-03 812.1 812.1 812.1 812.1
## 2014-01-06 934.5 934.5 934.5 934.5
## 2014-01-07 791.0 791.0 791.0 791.0
## 2014-01-08 828.5 828.5 828.5 828.5apple.mod1 <- to.daily(apple.mod)[,"apple.mod.Close"]
start(apple.mod1)## [1] "2014-01-01"apple.ts <- ts(apple.mod1, start=c(2014,01,01), freq=270)
autoplot(log(apple.ts), main="Log de Los Precios de Cierre de BTC 2014-20")
#Aplicación de diferencias
ggtsdisplay(diff(log(apple.ts)))
##Pruebas de raÃz unitaria
adf.test(diff(log(apple.ts)))## Warning in adf.test(diff(log(apple.ts))): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: diff(log(apple.ts))
## Dickey-Fuller = -10.811, Lag order = 11, p-value = 0.01
## alternative hypothesis: stationarypp.test(diff(log(apple.ts), alternative="stationary"))## Warning in pp.test(diff(log(apple.ts), alternative = "stationary")): p-value
## smaller than printed p-value##
## Phillips-Perron Unit Root Test
##
## data: diff(log(apple.ts), alternative = "stationary")
## Dickey-Fuller Z(alpha) = -1696.1, Truncation lag parameter = 8, p-value
## = 0.01
## alternative hypothesis: stationary##Descomposición de retornos
plot(decompose(diff(log(apple.ts))))
##Arima
arima(log(apple.ts), order = c(0,1,0))##
## Call:
## arima(x = log(apple.ts), order = c(0, 1, 0))
##
##
## sigma^2 estimated as 0.002075: log likelihood = 2677.01, aic = -5354.03arima(log(apple.ts), order = c(1,1,1))##
## Call:
## arima(x = log(apple.ts), order = c(1, 1, 1))
##
## Coefficients:
## ar1 ma1
## 0.1991 -0.2177
## s.e. 0.8046 0.7909
##
## sigma^2 estimated as 0.002074: log likelihood = 2677.31, aic = -5350.62##Prueba Ljung box
tsdiag(arima(log(apple.ts), order = c(0,1,0)))
tsdiag(arima(log(apple.ts), order = c(1,1,1)))
checkresiduals(arima(log(apple.ts), order = c(0,1,0)))
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,0)
## Q* = 350.21, df = 321, p-value = 0.126
##
## Model df: 0. Total lags used: 321