Copyright © 2023 - Azat's Blog Azat's Blog
Objectives:
- The price of a financial instrument over time constitutes a time series
- Likewise, the return process of that instrument also constitute a time series
- We will be looking at descriptive and inferential statistics of those time series
- Both for getting familiar with the methods and for
- a better understanding of computational tools ( that is R for this course )
Getting the Data
# load the library
library("quantmod")
# get amazon.com price data frm the beginning of the year until september 9. 2020
data.AMZN <- getSymbols("AMZN",from="2020-01-02",to="2020-09-08",auto.assign=FALSE)
Code language: R (r)head(data.AMZN)
Code language: R (r)AMZN.Open AMZN.High AMZN.Low AMZN.Close AMZN.Volume AMZN.Adjusted 2020-01-02 93.7500 94.9005 93.2075 94.9005 80580000 94.9005 2020-01-03 93.2250 94.3100 93.2250 93.7485 75288000 93.7485 2020-01-06 93.0000 95.1845 93.0000 95.1440 81236000 95.1440 2020-01-07 95.2250 95.6945 94.6020 95.3430 80898000 95.3430 2020-01-08 94.9020 95.5500 94.3220 94.5985 70160000 94.5985 2020-01-09 95.4945 95.8910 94.7900 95.0525 63346000 95.0525
tail(data.AMZN)
Code language: R (r)AMZN.Open AMZN.High AMZN.Low AMZN.Close AMZN.Volume AMZN.Adjusted 2020-08-28 171.1500 171.6685 169.3250 170.0900 57940000 170.0900 2020-08-31 170.4495 174.7500 170.2500 172.5480 83718000 172.5480 2020-09-01 174.4790 175.6935 173.3500 174.9560 68644000 174.9560 2020-09-02 177.3500 177.6125 174.3345 176.5725 78630000 176.5725 2020-09-03 174.2500 174.4205 165.1500 168.4000 163222000 168.4000 2020-09-04 165.9000 169.0750 155.5565 164.7310 175636000 164.7310
Descriptive Statistics
Plotting the data
plot(data.AMZN$AMZN.Close)
Code language: R (r)
Some Commonly Used Indicators
Get longer time series
data.AMZN <- getSymbols("AMZN",from="2018-01-01",to="2020-09-08",auto.assign = FALSE)
Code language: R (r)Get only closing price of data
AMZN.sma <- data.AMZN[,4]
Code language: R (r)Display a few rows and the last row
AMZN.sma[c(1:3,nrow(AMZN.sma)),]
Code language: R (r)AMZN.Close 2018-01-02 59.4505 2018-01-03 60.2100 2018-01-04 60.4795 2020-09-04 164.7310
Moving average over 50 and 200 days
AMZN.sma$sma50 <- rollmeanr(AMZN.sma$AMZN.Close,k=50)
AMZN.sma$sma200 <- rollmeanr(AMZN.sma$AMZN.Close,k=200)
AMZN.sma[c(1:3,nrow(AMZN.sma)),]Code language: R (r)AMZN.Close sma50 sma200 2018-01-02 59.4505 NA NA 2018-01-03 60.2100 NA NA 2018-01-04 60.4795 NA NA 2020-09-04 164.7310 157.2444 117.8078
data.AMZN$AMZN.CloseCode language: R (r) AMZN.Close
2018-01-02 59.4505
2018-01-03 60.2100
2018-01-04 60.4795
2018-01-05 61.4570
2018-01-08 62.3435
2018-01-09 62.6350
2018-01-10 62.7165
2018-01-11 63.8340
2018-01-12 65.2600
2018-01-16 65.2430
...
2020-08-24 165.3730
2020-08-25 167.3245
2020-08-26 172.0925
2020-08-27 170.0000
2020-08-28 170.0900
2020-08-31 172.5480
2020-09-01 174.9560
2020-09-02 176.5725
2020-09-03 168.4000
2020-09-04 164.7310
plot(data.AMZN$AMZN.Close)
Code language: R (r)
plot(AMZN.sma$sma50)Code language: R (r)
plot(AMZN.sma$sma200)Code language: R (r)
Obtaining Rolling standard deviations
AMZN.sd<-data.AMZN[,4]
AMZN.sd$avg<-rollmeanr(AMZN.sd$AMZN.Close,k=20)
AMZN.sd$sd<-rollapply(AMZN.sd$AMZN.Close,width=20,FUN=sd,fill=NA)
AMZN.sdCode language: PHP (php) AMZN.Close avg sd
2018-01-02 59.4505 NA NA
2018-01-03 60.2100 NA NA
2018-01-04 60.4795 NA NA
2018-01-05 61.4570 NA NA
2018-01-08 62.3435 NA NA
2018-01-09 62.6350 NA NA
2018-01-10 62.7165 NA NA
2018-01-11 63.8340 NA NA
2018-01-12 65.2600 NA NA
2018-01-16 65.2430 NA NA
...
2020-08-24 165.3730 158.6092 4.529263
2020-08-25 167.3245 159.4746 4.453943
2020-08-26 172.0925 160.4954 4.890786
2020-08-27 170.0000 161.3657 4.958957
2020-08-28 170.0900 161.9585 5.264138
2020-08-31 172.5480 162.8061 5.543032
2020-09-01 174.9560 163.7069 5.985849
2020-09-02 176.5725 164.5229 6.573644
2020-09-03 168.4000 164.8804 6.580700
2020-09-04 164.7310 165.1983 6.400910
Fitting a curve to price data
getSymbols("DJIA",src="FRED")
serie=DJIA["2015/2019"]
price=as.numeric(serie)
time = index(serie)
x=1:length(price)
model=lm(log(price)~x)
expo=exp(model$coef[1]+model$coef[2]*x)
plot(x=time,y=price, main="Dow Jones",type="l")
lines(time,expo,col=2,lwd=2)Code language: R (r)
lm(formula = log(price) ~ x)
Code language: R (r)Call:
lm(formula = log(price) ~ x)
Coefficients:
(Intercept) x
9.6876626 0.0004355
Percent and Logarithmic Returns
Daily price returns
data.IBM <- getSymbols("IBM", from="2010-12-31",to="2013-12-31", auto.assign = FALSE)
IBM.price <- data.IBM[,4]
str(data.IBM)Code language: R (r)An xts object on 2010-12-31 / 2013-12-30 containing:
Data: double [754, 6]
Columns: IBM.Open, IBM.High, IBM.Low, IBM.Close, IBM.Volume … with 1 more column
Index: Date [754] (TZ: “UTC”)
xts Attributes:
$ src : chr “yahoo”
$ updated: POSIXct[1:1], format: “2023-10-13 16:27:12”
Data: double [754, 6]
Columns: IBM.Open, IBM.High, IBM.Low, IBM.Close, IBM.Volume … with 1 more column
Index: Date [754] (TZ: “UTC”)
xts Attributes:
$ src : chr “yahoo”
$ updated: POSIXct[1:1], format: “2023-10-13 16:27:12”
IBM.price[c(1:3,nrow(IBM.price)),]
Code language: R (r)IBM.Close 2010-12-31 140.3059 2011-01-03 140.9943 2011-01-04 141.1472 2013-12-30 178.2122
the function ‘Delt’ obtains percent differences in data set.
IBM.price$IBM.ret<-Delt(IBM.price$IBM.Close)
IBM.price[c(1:3,nrow(IBM.price)),]
Code language: R (r)IBM.Close IBM.ret 2010-12-31 140.3059 NA 2011-01-03 140.9943 0.004905988 2011-01-04 141.1472 0.001084933 2013-12-30 178.2122 0.007186107
IBM.price$IBM.log.ret<-diff(log(IBM.price$IBM.Close))
IBM.price[c(1:3,nrow(IBM.price)),]Code language: R (r)IBM.Close IBM.ret IBM.log.ret 2010-12-31 140.3059 NA NA 2011-01-03 140.9943 0.004905988 0.004893993 2011-01-04 141.1472 0.001084933 0.001084345 2013-12-30 178.2122 0.007186107 0.007160410
plot(IBM.price$IBM.ret)
Code language: R (r)
plot(IBM.price$IBM.log.ret)
Code language: R (r)
More Examples
Getting basic statistics and displaying data
library("quantmod")
##retrieve historical price data for General Electric Co. from Yahoo Finance
getSymbols('GE',src='yahoo', from="2000-01-01", to="2009-12-30")
##to see headers of file
## extract Adjusted Close
geAdj = GE$GE.Adjusted["2000-01-01/2000-01-20"]
##compute max, min and mean
max(geAdj); min(geAdj); mean(geAdj)
Code language: R (r)168.641677856445 157.673141479492 163.422424316406Code language: CSS (css)## draw a chart
chartSeries(GE)
Code language: R (r)
Getting 4 data sets simultaneously
symbols <- c('GE','KO','AAPL','MCD')
getSymbols(symbols,src='yahoo',from="2012-02-01",to="2013-02-01")
# 'GE''KO''AAPL''MCD'
#obtain adjusted closed
GEad= GE$GE.Adjusted; KOad=KO$KO.Adjusted;
AAPLad=AAPL$AAPL.Adjusted; MCDad = MCD$MCD.Adjusted
#compute cumulative sum (cumsum) of daily returns (Delt)
#Remove first term of the series, with [-1,], since cumsum is not defined for it.
ge = cumsum((Delt(GEad)*100)[-1,])
ko = cumsum((Delt(KOad)*100)[-1,])
ap = cumsum((Delt(AAPLad)*100)[-1,])
md = cumsum((Delt(MCDad)*100)[-1,])
###range of values for the plot
lim = c(min(ge,ko,ap,md),max(ge,ko,ap,md))
###the plot
plot(ge,main="",ylim=lim,xlab="dates",ylab="% benefits")
lines(ko,col="red");
lines(ap,col="violet"); lines(md,col="yellow")
legend(x="topleft",cex=0.4,c("GE","KO","AAPL","MCD"),
lty=1, col=c("black","red","violet","yellow"))
Code language: R (r)
