Lecture 8 Note
2021-07-30
Chapter 1 Some update of goodness of fit
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## as.data.frame, units1.1 Plot the value
par(mfcol=c(1,1))
Y00=casestudy1.data0.00[,Y00.name0]
plot(Y00, ylab="Value",main=Y00.name0)
1.2 Plot the daily return
y00<-zoo( x=as.matrix(exp(diff(log(Y00)))-1),
order.by=time(Y00)[-1])
names(y00)<-"y00"
plot(y00, ylab="Daily Returns (pct)",main=Y00.name0)
1.3 Use base plot to plot Rolling Estimates of mu/median
# 4.1 Use base plot to plot Rolling Estimates of mu/median -----
y00both<-c(y00_df1$muNormal ,
y00_df1$thetaLaplace)
ylim0<-c(min(y00both,na.rm=TRUE), max(y00both,na.rm=TRUE))
plot(x=y00_df1$date,y=y00_df1$thetaLaplace,
ylim=ylim0,
col='red',type="l",
ylab="mu or theta",xlab="date")
lines(x=y00_df1$date,y=y00_df1$muNormal, col='blue',type="l")
title(main=paste(c(
"Center Distribution Estimates of ", Y00.name0,
"\nNormal(blue) and Laplace(red)",
"\nRolling Windows (ndays=",ndays0,")"),
collapse=""))
1.4 Use base plot to plot Rolling Estimates of st. devs
# 4.2 Use base plot to plot Rolling Estimates of st. devs -----
y00both<-c(y00_df1$sigmaNormal ,
y00_df1$scaleLaplace*sqrt(2))
ylim0<-c(min(y00both,na.rm=TRUE), max(y00both,na.rm=TRUE))
plot(x=y00_df1$date,y=y00_df1$scaleLaplace*sqrt(2),
ylim=ylim0,
col='red',type="l",
ylab="st dev ",xlab="date")
lines(x=y00_df1$date,y=y00_df1$sigmaNormal, col='blue',type="l")
title(main=paste(c(
"St Dev of Distribution Estimates of ", Y00.name0,
"\nNormal(blue) and Laplace(red)",
"\nRolling Windows (ndays=",ndays0,")"),
collapse=""))
1.5 Use base plot to plot Rolling Volatilities
# 4.3 Use base plot() to plot Rolling Volatilities ----
y00both<-c(y00_df1$volLaplace, y00_df1$volNormal)
ylim0<-c(min(y00both,na.rm=TRUE), max(y00both,na.rm=TRUE))
plot(x=y00_df1$date,y=y00_df1$volLaplace,
ylim=ylim0,
col='red',type="l",
ylab="volatility",xlab="date")
lines(x=y00_df1$date,y=y00_df1$volNormal, col='blue',type="l",
ylab="volatility")
title(main=paste(c(
"Volatility Estimates of ", Y00.name0,
"\nNormal(blue) and Laplace(red)",
"\nRolling Windows (ndays=",ndays0,")"),
collapse=""))
1.6 Use ggplot2 to plot Rolling Volatilities
# 4.4 Use ggplot2 to plot Rolling Volatilities ----
df2<-rbind(
data.frame(
date=y00_df1$date,
vol=y00_df1$volNormal,
model="NormalMLE",
ndays=ndays0),
data.frame(
date=y00_df1$date,
vol=y00_df1$volLaplace,
model="LaplaceMLE",
ndays=ndays0))
df2$model=as.factor(df2$model)
dim(df2)## [1] 4860 4gg0<-ggplot(df2, aes(x=date, y=vol, col=model)) + geom_line() +
theme(legend.position="bottom") +
ggtitle(paste(c("Volatilities \nRolling Windows(ndays=", as.character(ndays0),
")\n", Y00.name0),collapse="")
)
print(gg0)## Warning: Removed 238 row(s) containing missing values (geom_path).
#4.4 Use ggplot2 to plot pvalues of Rolling Fits1.7 Plot pvalues for entire period
# 4.5 Plot pvalues for entire period ----
gg3<-ggplot(df3, aes(x=date, y=pval, col=model))+geom_line()
print(gg3+ggtitle(label=paste(c(
Y00.name0,": ndays=",df3$ndays[1]),
collapse="")
)) ## Warning: Removed 357 row(s) containing missing values (geom_path).
1.8 Sample plot of pvalues since 2019
# 4.6 Sample plot of pvalues since 2019 ----
gg4<-df3 %>% filter(date>=as.Date("2019-01-01")) %>%
ggplot( aes(x=date, y=pval, col=model))+geom_line()
print(gg4 + ggtitle(label=paste(c(
Y00.name0,": ndays=",df3$ndays[1]),
collapse="")
))## Warning: Removed 180 row(s) containing missing values (geom_path).
1.9 Change \(y\) scale to \(log(p)/log(0.05)\)
# 4.5 Plot pvalues for entire period ----
gg3b<-ggplot(df3, aes(x=date, y=log(pval)/log(0.05), col=model))+geom_line()
print(gg3+ggtitle(label=paste(c(
Y00.name0,": ndays=",df3$ndays[1]),
collapse="")
)) ## Warning: Removed 357 row(s) containing missing values (geom_path).
1.10 Sample plot of log pvalues since 2019
# 4.6 Sample plot of pvalues since 2019 ----
df3$logpval=log(df3$pval)
gg4<-df3 %>% filter(date>=as.Date("2019-01-01")) %>%
ggplot( aes(x=date, y=logpval, col=model))+geom_line()+
geom_hline(yintercept=log(0.05), col='red')+
geom_hline(yintercept=log(0.01),col='red', lwd=2)
geom_hline(yintercept=log(0.01),col='red', lwd=2)## mapping: yintercept = ~yintercept
## geom_hline: na.rm = FALSE
## stat_identity: na.rm = FALSE
## position_identityprint(gg4 + ggtitle(label=paste(c(
Y00.name0,": ndays=",df3$ndays[1]),
collapse="")
))## Warning: Removed 180 row(s) containing missing values (geom_path).
# 4.6 Sample plot of pvalues since 2019 ----
df3$logpval=log(df3$pval)
gg4<-df3 %>% filter(date>=as.Date("2015-01-01")) %>%
ggplot( aes(x=date, y=logpval, col=model))+geom_line()+
geom_hline(yintercept=log(0.05), col='red')+
geom_hline(yintercept=log(0.01),col='red', lwd=2)
geom_hline(yintercept=log(0.01),col='red', lwd=2)## mapping: yintercept = ~yintercept
## geom_hline: na.rm = FALSE
## stat_identity: na.rm = FALSE
## position_identityprint(gg4 + ggtitle(label=paste(c(
Y00.name0,": ndays=",df3$ndays[1]),
collapse="")
))## Warning: Removed 180 row(s) containing missing values (geom_path).
df2_sub1<-df2_AAPL_120 %>% filter(model=="LaplaceMLE")
dim(df2_sub1)## [1] 2430 4pval_sub<-pvals_AAPL_120 %>% filter(model=="LaplaceMLE")
dim(pval_sub)## [1] 2430 4names(pval_sub)## [1] "date" "pval" "model" "ndays"df2_sub1$pval<-pval_sub$pval
df2_sub1$signif<-.05*(pval_sub$pval < .05) + .01*(pval_sub$pval<.01)
df2_sub1$signif<-factor(df2_sub1$signif)
ggplot(df2_sub1, aes(x=date, y=vol, col=signif)) + geom_point()## Warning: Removed 119 rows containing missing values (geom_point).