## Saturday, 2 February 2019

### Analysis of the return series calculated from the daily closing prices of Amazon

Analysis of the return series calculated from the daily closing prices of Amazon
library("quantmod", lib.loc="~/R/win-library/3.5")
> library("ggplot2", lib.loc="~/R/win-library/3.5")
Warning message:
package ‘ggplot2’ was built under R version 3.5.1
> getSymbols(c("AMZN")).
[1] "AMZN"
AMZN.Open AMZN.High AMZN.Low AMZN.Close
2007-01-03     38.68     39.06    38.05      38.70
2007-01-04     38.59     39.14    38.26      38.90
2007-01-05     38.72     38.79    37.60      38.37
2007-01-08     38.22     38.31    37.17      37.50
2007-01-09     37.60     38.06    37.34      37.78
2007-01-10     37.49     37.70    37.07      37.15
2007-01-03    12405100         38.70
2007-01-04     6318400         38.90
2007-01-05     6619700         38.37
2007-01-08     6783000         37.50
2007-01-09     5703000         37.78
2007-01-10     6527500         37.15
> barChart(AMZN,theme = "white.mono",bar.type = 'hlc')
> barChart(AMZN)

> addBBands(n=2,sd=2,ma='SMA',draw = "bands",on=-1)
> z = y - gamma*AMZN
> N <- 10
> x <- cumsum(rnorm(N))
> gamma <- 0.7
> y <- gamma * x + rnorm(N)
> z = y - gamma*AMZN
> library('vars')
> ret <- dailyReturn(Cl(AMZN), type='log')
> par(mfrow=c(2,2))
> acf(ret, main="Return ACF");
> pacf(ret, main="Return PACF");
> acf(ret^2, main="Squared return ACF");
> pacf(ret^2, main="Squared return PACF")

> m=mean(ret)
> s=sd(ret);
> par(mfrow=c(1,2))
> hist(ret, nclass=40, freq=FALSE, main='Return histogram');curve(dnorm(x,
+                                                                       mean=m,sd=s), from = -0.3, to = 0.2, add=TRUE, col="red")
> plot(density(ret), main='Return empirical distribution');curve(dnorm(x,
+                                                                      mean=m,sd=s), from = -0.3, to = 0.2, add=TRUE, col="red")

> kurtosis(ret)
Error in kurtosis(ret) : could not find function "kurtosis"
> plot(density(ret), main='Return EDF - upper tail', xlim = c(0.1, 0.2),
+      ylim=c(0,2));
> curve(dnorm(x, mean=m,sd=s), from = -0.3, to = 0.2, add=TRUE, col="red")

> plot(density(ret), xlim=c(-5*s,5*s),log='y', main='Density on log-scale')
> qqnorm(ret);qqline(ret);