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Summary table of data cleaning Podolskij method.R
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Summary table of data cleaning Podolskij method.R
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#will contain the summary statistics following Hautsch & Podolskij (2013).
library(xts)
library(highfrequency)
library(matlib)
library(tidyverse)
dataTLT <- readRDS("dataTLT.rds")
dataSPY <- readRDS("dataSPY.rds")
#-------------------------------Calculating average time in seconds between each trade:
timeobjectsTLT <- list()
timeobjectsSPY <- list()
for(i in 1:length(dataTLT)){
timeobjectsTLT[[i]] <- c(index(dataTLT[[i]]))
timeobjectsSPY[[i]] <- c(index(dataSPY[[i]]))
}
for(i in 1:length(dataTLT)){
timeobjectsTLT[[i]] <- unlist(lapply((str_split(timeobjectsTLT[[i]], " ")), function(x) x[2]))
timeobjectsSPY[[i]] <- unlist(lapply((str_split(timeobjectsSPY[[i]], " ")), function(x) x[2]))
}
for(i in 1:length(dataTLT)){
timeobjectsTLT[[i]] <- as.numeric(gsub(":", "",timeobjectsTLT[[i]]))
timeobjectsSPY[[i]] <- as.numeric(gsub(":", "",timeobjectsSPY[[i]]))
}
seconddiffTLT <- list()
seconddiffSPY <- list()
for(i in 1:length(dataTLT)){
seconddiffTLT[[i]] <- c(
diff(timeobjectsTLT[[i]][timeobjectsTLT[[i]]<100000]),
diff(timeobjectsTLT[[i]][100000<timeobjectsTLT[[i]] & timeobjectsTLT[[i]]<110000]),
diff(timeobjectsTLT[[i]][110000<timeobjectsTLT[[i]] & timeobjectsTLT[[i]]<120000]),
diff(timeobjectsTLT[[i]][120000<timeobjectsTLT[[i]] & timeobjectsTLT[[i]]<130000]),
diff(timeobjectsTLT[[i]][130000<timeobjectsTLT[[i]] & timeobjectsTLT[[i]]<140000]),
diff(timeobjectsTLT[[i]][140000<timeobjectsTLT[[i]] & timeobjectsTLT[[i]]<150000]),
diff(timeobjectsTLT[[i]][150000<timeobjectsTLT[[i]] & timeobjectsTLT[[i]]<160000]))
seconddiffSPY[[i]] <- c(
diff(timeobjectsSPY[[i]][timeobjectsSPY[[i]]<100000]),
diff(timeobjectsSPY[[i]][100000<timeobjectsSPY[[i]] & timeobjectsSPY[[i]]<110000]),
diff(timeobjectsSPY[[i]][110000<timeobjectsSPY[[i]] & timeobjectsSPY[[i]]<120000]),
diff(timeobjectsSPY[[i]][120000<timeobjectsSPY[[i]] & timeobjectsSPY[[i]]<130000]),
diff(timeobjectsSPY[[i]][130000<timeobjectsSPY[[i]] & timeobjectsSPY[[i]]<140000]),
diff(timeobjectsSPY[[i]][140000<timeobjectsSPY[[i]] & timeobjectsSPY[[i]]<150000]),
diff(timeobjectsSPY[[i]][150000<timeobjectsSPY[[i]] & timeobjectsSPY[[i]]<160000]))
}
#Years are changing at, 252, 504, 754, 1006, 1258, 1510, 1762, 2013, 2264, 2516(end)
meantimeTLT <- unlist(lapply(seconddiffTLT, mean))
meantimeSPY <- unlist(lapply(seconddiffSPY, mean))
meantime20102012TLT <- mean(meantimeTLT[1:504])
meantime20122014TLT <- mean(meantimeTLT[505:1006])
meantime20142016TLT <- mean(meantimeTLT[1007:1510])
meantime20162018TLT <- mean(meantimeTLT[1511:2013])
meantime20182020TLT <- mean(meantimeTLT[2014:2516])
meantime20102012TLT
meantime20122014TLT
meantime20142016TLT
meantime20162018TLT
meantime20182020TLT
meantime20102012SPY <- mean(meantimeSPY[1:504])
meantime20122014SPY <- mean(meantimeSPY[505:1006])
meantime20142016SPY <- mean(meantimeSPY[1007:1510])
meantime20162018SPY <- mean(meantimeSPY[1511:2013])
meantime20182020SPY <- mean(meantimeSPY[2014:2516])
meantime20102012SPY
meantime20122014SPY
meantime20142016SPY
meantime20162018SPY
meantime20182020SPY
#average daily transaction time in seconds:
meantimeTLTTOTAL <- mean(meantimeTLT)
meantimeSPYTOTAL <- mean(meantimeSPY)
meantimeTLTTOTAL
meantimeSPYTOTAL
#---------------------------------------Average number of trades-------------------
rawtradesTLT <- numeric()
rawtradesSPY <- numeric()
for(i in 1:length(dataTLT)){
rawtradesTLT[i] <- length(dataTLT[[i]])
rawtradesSPY[i] <- length(dataSPY[[i]])
}
rawtradesTLT20102012 <- mean(rawtradesTLT[1:504])
rawtradesTLT20122014 <- mean(rawtradesTLT[505:1006])
rawtradesTLT20142016 <- mean(rawtradesTLT[1007:1510])
rawtradesTLT20162018 <- mean(rawtradesTLT[1511:2013])
rawtradesTLT20182020 <- mean(rawtradesTLT[2014:2516])
rawtradesTLTtotal <- mean(rawtradesTLT)
rawtradesTLT20102012
rawtradesTLT20122014
rawtradesTLT20142016
rawtradesTLT20162018
rawtradesTLT20182020
rawtradesTLTtotal
rawtradesSPY20102012 <- mean(rawtradesSPY[1:504])
rawtradesSPY20122014 <- mean(rawtradesSPY[505:1006])
rawtradesSPY20142016 <- mean(rawtradesSPY[1007:1510])
rawtradesSPY20162018 <- mean(rawtradesSPY[1511:2013])
rawtradesSPY20182020 <- mean(rawtradesSPY[2014:2516])
rawtradesSPYtotal <- mean(rawtradesSPY)
rawtradesSPY20102012
rawtradesSPY20122014
rawtradesSPY20142016
rawtradesSPY20162018
rawtradesSPY20182020
rawtradesSPYtotal
#------------------------------Average number of cand.outliers (candidate outliers)----------------------
#the average number of daily candidate outliers as identified by the filtering procedure.
SummarystatsTLT <- read.csv("SummaryStatisticsforcleaning_TLT.csv", header = T)
SummarystatsSPY <- read.csv("SummaryStatisticsforcleaning_SPY.csv", header = T)
outliersSPY20102012 <- mean(SummarystatsSPY$T4[1:504])
outliersSPY20122014 <- mean(SummarystatsSPY$T4[505:1006])
outliersSPY20142016 <- mean(SummarystatsSPY$T4[1007:1510])
outliersSPY20162018 <- mean(SummarystatsSPY$T4[1511:2013])
outliersSPY20182020 <- mean(SummarystatsSPY$T4[2014:2513])
outliersSPYtotal <- mean(SummarystatsSPY$T4)
outliersSPY20102012
outliersSPY20122014
outliersSPY20142016
outliersSPY20162018
outliersSPY20182020
outliersSPYtotal
outliersTLT20102012 <- mean(SummarystatsTLT$T4[1:504])
outliersTLT20122014 <- mean(SummarystatsTLT$T4[505:1006])
outliersTLT20142016 <- mean(SummarystatsTLT$T4[1007:1510])
outliersTLT20162018 <- mean(SummarystatsTLT$T4[1511:2013])
outliersTLT20182020 <- mean(SummarystatsTLT$T4[2014:2515])
outliersTLTtotal <- mean(SummarystatsTLT$T4)
outliersTLT20102012
outliersTLT20122014
outliersTLT20142016
outliersTLT20162018
outliersTLT20182020
outliersTLTtotal
#----------------------------------------------------raw trades ---------------------------------------
#Raw trades/quotes is the total number of data available from these exchanges during the
#trading session, while #trades/quotes is the total sample remaining after filtering the data
allcleanedTLT <- rowSums(SummarystatsTLT[,c(1:4,8,10,12)])
allcleanedSPY <- rowSums(SummarystatsSPY[,c(1:4,8,10,12)])
datalengthTLT <- numeric()
datalengthSPY <- numeric()
for(i in 1:length(dataTLT)){
datalengthTLT[i] <- length(dataTLT[[i]])
datalengthSPY[i] <- length(dataSPY[[i]])
}
#missing the last days due to error in data.
rawtradesTLT <- allcleanedTLT + datalengthTLT[1:2515]
rawtradesSPY <- allcleanedSPY + datalengthSPY[1:2513]
#The average amount of raw trades for each day during the trading session.
mean(rawtradesTLT[1:504])
mean(rawtradesTLT[505:1006])
mean(rawtradesTLT[1007:1510])
mean(rawtradesTLT[1511:2013])
mean(rawtradesTLT[2014:2515])
mean(rawtradesTLT)
mean(rawtradesSPY[1:504]) +
mean(rawtradesSPY[505:1006]) +
mean(rawtradesSPY[1007:1510]) +
mean(rawtradesSPY[1511:2013]) +
mean(rawtradesSPY[2014:2513])
mean(rawtradesSPY)
#------------------------------------Average proportion of non-zero trade returns----------------------------
#Done by constructing return data from all of the transaction prices and can be based on TRTS employing
#all transactions.
#Intuitively, while the proportion might be close to the same proportion for a 1 second CTS scheme, we know that sparse
#sparse sampling further, will likely increase the proportion. Ie. the non-zero trades also indirectly describes the liquidity of our
#financial assets.
#YOU COULD DO CTS 1 SEC AND 5 SEC AND SHOW THE INCREASING PROPORTION OF NON-ZERO RETURNS TO GET A BETTER OVERVIEW?
rawreturnsSPY <- list()
rawreturnsTLT <- list()
for (i in 1:length(dataTLT)){
rawreturnsSPY[[i]] <- diff(log(dataSPY[[i]]))[-1]
rawreturnsTLT[[i]] <- diff(log(dataTLT[[i]]))[-1]
}
TLT_1sec <- list()
TLT_5sec <- list()
SPY_1sec <- list()
SPY_5sec <- list()
for(i in 1:length(dataTLT)){
TLT_1sec[[i]] <- diff(log(aggregatets(dataTLT[[i]], on = "seconds", k=1)))[-1]
TLT_5sec[[i]] <- diff(log(aggregatets(dataTLT[[i]], on = "seconds", k=5)))[-1]
SPY_1sec[[i]] <- diff(log(aggregatets(dataSPY[[i]], on = "seconds", k=1)))[-1]
SPY_5sec[[i]] <- diff(log(aggregatets(dataSPY[[i]], on = "seconds", k=5)))[-1]
}
nonzeroSPY <- vector()
nonzeroSPY_1sec <- vector()
nonzeroSPY_5sec <- vector()
nonzeroTLT <- vector()
nonzeroTLT_1sec <- vector()
nonzeroTLT_5sec <- vector()
SPYtotal <- numeric()
TLTtotal <- numeric()
SPYtotal_1sec <- numeric()
TLTtotal_1sec<- numeric()
SPYtotal_5sec <- numeric()
TLTtotal_5sec <- numeric()
for (i in 1:length(dataTLT)){
nonzeroSPY[i] <- apply(rawreturnsSPY[[i]], 2, function(c)sum(c!=0))
nonzeroSPY_1sec[i] <- apply(SPY_1sec[[i]], 2, function(c)sum(c!=0))
nonzeroSPY_5sec[i] <- apply(SPY_5sec[[i]], 2, function(c)sum(c!=0))
nonzeroTLT[i] <- apply(rawreturnsTLT[[i]], 2, function(c)sum(c!=0))
nonzeroTLT_1sec[i] <- apply(TLT_1sec[[i]], 2, function(c)sum(c!=0))
nonzeroTLT_5sec[i] <- apply(TLT_5sec[[i]], 2, function(c)sum(c!=0))
SPYtotal[i] <- dim(rawreturnsSPY[[i]])[1]
SPYtotal_1sec[i] <- dim(SPY_1sec[[i]])[1]
SPYtotal_5sec[i] <- dim(SPY_5sec[[i]])[1]
TLTtotal[i] <- dim(rawreturnsTLT[[i]])[1]
TLTtotal_1sec[i] <- dim(TLT_1sec[[i]])[1]
TLTtotal_5sec[i] <- dim(TLT_5sec[[i]])[1]
print(sprintf("iteration %s", i))
}
#(daily) average nonzero trade returns.
nonzerotrades20102012SPY <- sum(nonzeroSPY[1:504])/(sum(SPYtotal[1:504]))
nonzerotrades20122014SPY <- sum(nonzeroSPY[505:1006])/(sum(SPYtotal[505:1006]))
nonzerotrades20142016SPY <- sum(nonzeroSPY[1007:1510])/(sum(SPYtotal[1007:1510]))
nonzerotrades20162018SPY <- sum(nonzeroSPY[1511:2013])/(sum(SPYtotal[1511:2013]))
nonzerotrades20182020SPY <- sum(nonzeroSPY[2014:2516])/(sum(SPYtotal[2014:2516]))
nonzerotrades20102012TLT <- sum(nonzeroTLT[1:504])/(sum(TLTtotal[1:504]))
nonzerotrades20122014TLT <- sum(nonzeroTLT[505:1006])/(sum(TLTtotal[505:1006]))
nonzerotrades20142016TLT <- sum(nonzeroTLT[1007:1510])/(sum(TLTtotal[1007:1510]))
nonzerotrades20162018TLT <- sum(nonzeroTLT[1511:2013])/(sum(TLTtotal[1511:2013]))
nonzerotrades20182020TLT <- sum(nonzeroTLT[2014:2516])/(sum(TLTtotal[2014:2516]))
# 1 sec
nonzerotrades20102012SPY_1sec <- sum(nonzeroSPY_1sec[1:504])/(sum(SPYtotal_1sec[1:504]))
nonzerotrades20122014SPY_1sec <- sum(nonzeroSPY_1sec[505:1006])/(sum(SPYtotal_1sec[505:1006]))
nonzerotrades20142016SPY_1sec <- sum(nonzeroSPY_1sec[1007:1510])/(sum(SPYtotal_1sec[1007:1510]))
nonzerotrades20162018SPY_1sec <- sum(nonzeroSPY_1sec[1511:2013])/(sum(SPYtotal_1sec[1511:2013]))
nonzerotrades20182020SPY_1sec <- sum(nonzeroSPY_1sec[2014:2516])/(sum(SPYtotal_1sec[2014:2516]))
nonzerotrades20102012TLT_1sec <- sum(nonzeroTLT_1sec[1:504])/(sum(TLTtotal_1sec[1:504]))
nonzerotrades20122014TLT_1sec <- sum(nonzeroTLT_1sec[505:1006])/(sum(TLTtotal_1sec[505:1006]))
nonzerotrades20142016TLT_1sec <- sum(nonzeroTLT_1sec[1007:1510])/(sum(TLTtotal_1sec[1007:1510]))
nonzerotrades20162018TLT_1sec <- sum(nonzeroTLT_1sec[1511:2013])/(sum(TLTtotal_1sec[1511:2013]))
nonzerotrades20182020TLT_1sec <- sum(nonzeroTLT_1sec[2014:2516])/(sum(TLTtotal_1sec[2014:2516]))
# 5 sec
nonzerotrades20102012SPY_5sec <- sum(nonzeroSPY_5sec[1:504])/(sum(SPYtotal_5sec[1:504]))
nonzerotrades20122014SPY_5sec <- sum(nonzeroSPY_5sec[505:1006])/(sum(SPYtotal_5sec[505:1006]))
nonzerotrades20142016SPY_5sec <- sum(nonzeroSPY_5sec[1007:1510])/(sum(SPYtotal_5sec[1007:1510]))
nonzerotrades20162018SPY_5sec <- sum(nonzeroSPY_5sec[1511:2013])/(sum(SPYtotal_5sec[1511:2013]))
nonzerotrades20182020SPY_5sec <- sum(nonzeroSPY_5sec[2014:2516])/(sum(SPYtotal_5sec[2014:2516]))
nonzerotrades20102012TLT_5sec <- sum(nonzeroTLT_5sec[1:504])/(sum(TLTtotal_5sec[1:504]))
nonzerotrades20122014TLT_5sec <- sum(nonzeroTLT_5sec[505:1006])/(sum(TLTtotal_5sec[505:1006]))
nonzerotrades20142016TLT_5sec <- sum(nonzeroTLT_5sec[1007:1510])/(sum(TLTtotal_5sec[1007:1510]))
nonzerotrades20162018TLT_5sec <- sum(nonzeroTLT_5sec[1511:2013])/(sum(TLTtotal_5sec[1511:2013]))
nonzerotrades20182020TLT_5sec <- sum(nonzeroTLT_5sec[2014:2516])/(sum(TLTtotal_5sec[2014:2516]))
#total
(sum(nonzeroSPY) / sum(SPYtotal))
(sum(nonzeroTLT) / sum(TLTtotal))
nonzerotradeSPY_1sec <- sum(nonzeroSPY_1sec)/(sum(SPYtotal_1sec))
nonzerotradeTLT_1sec <- sum(nonzeroTLT_1sec)/(sum(TLTtotal_1sec))
nonzerotradeSPY_5sec <- sum(nonzeroSPY_5sec)/(sum(SPYtotal_5sec))
nonzerotradeTLT_5sec <- sum(nonzeroTLT_5sec)/(sum(TLTtotal_5sec))
#--------------------------------------------------NOISE ESTIMATOR-----------------------------------
#This is based on based on TRTS employing all transactions.
#
#
#We use a slightly modified function other than the previous year. Ie, we use a sparse sampled (5-min) bipower variation
#as the estimator for IV instead of the MLRV proposed in the podolskij hautsch paper.
#
#
#
source("Previous functions/projectfunctions.R")
TLT_raw <- list()
SPY_raw <- list()
TLT_1min <- list()
SPY_1min <- list()
for(i in 1:length(dataTLT)){
TLT_raw[[i]] <- diff(log(dataTLT[[i]]))[-1]
SPY_raw[[i]] <- diff(log(dataSPY[[i]]))[-1]
TLT_1min[[i]] <- diff(log(aggregatets(dataTLT[[i]], on="minutes",k=1)))[-1]
SPY_1min[[i]] <- diff(log(aggregatets(dataSPY[[i]], on="minutes", k=1)))[-1]
}
library(highfrequency)
#only univariate lists
noisetosignal2 <- function(list,sparse_data, names = NULL){
n <- as.vector(sapply(list, length))
#IVest <- MLRV(list, names)
IVest <- matrix(0L, nrow = length(list), ncol = 1)
for(i in 1:length(list)){
IVest[i] <- preavBPCOV(sparse_data[[i]], F, F, F, theta = 1)
}
#a bar calculations
condition <- as.numeric(vector())
#sum only takes numeric vectors, therefore saving in list object.
ret <- list()
for ( i in 1:length(list)){
ret[[i]] <- as.vector(list[[i]])
}
for (i in 1:length(list)){
condition[i] <- t(ret[[i]][2:n[i]]) %*% ret[[i]][1:(n[i]-1)]
}
abar <- matrix(0L, nrow = length(list), ncol=1)
for(i in 1:length(list)){
if(condition[i] < 0){
abar[i, 1] <- -1/(n[i]-1) * t(ret[[i]][1:(n[i]-1)]) %*% ret[[i]][2:n[i]]
}
else{
abar[i, 1] <- (1/(2*n[i]) * realCov(ret[[i]]))
}
}
#eps <- abar %*% 1/(IVest %*% 1/n)
eps <- abar / (IVest / n)
return(eps)
}
dailynoiseTLT <- noisetosignal2(TLT_raw, TLT_1min)
dailynoiseTLTMLRV <- noisetosignal(TLT_raw)
noiseTLT20102012 <- mean(dailynoiseTLT[1:504])
noiseTLT20122014 <- mean(dailynoiseTLT[505:1006])
noiseTLT20142016 <- mean(dailynoiseTLT[1007:1510])
noiseTLT20162018 <- mean(dailynoiseTLT[1511:2013])
noiseTLT20182020 <- mean(dailynoiseTLT[2014:2516])
noiseTLT20102012
noiseTLT20122014
noiseTLT20142016
noiseTLT20162018
noiseTLT20182020
#Total
mean(dailynoiseTLT)
mean(dailynoiseTLTMLRV)
dailynoiseSPY <- noisetosignal2(SPY_raw, SPY_1min)
dailynoiseSPYMLRV <- noisetosignal(SPY_raw)
#729
noisetosignal2(list(SPY_raw[[729]]), list(SPY_5min[[729]]))
noisetosignal2(list(SPY_raw[[100]]), list(SPY_5min[[100]]))
noiseSPY20102012 <- mean(dailynoiseSPY[1:504])
noiseSPY20122014 <- mean(dailynoiseSPY[505:1006])
noiseSPY20142016 <- mean(dailynoiseSPY[1007:1510])
noiseSPY20162018 <- mean(dailynoiseSPY[1511:2013])
noiseSPY20182020 <- mean(dailynoiseSPY[2014:2516])
noiseSPY20102012
noiseSPY20122014
noiseSPY20142016
noiseSPY20162018
noiseSPY20182020
mean(dailynoiseSPY)
mean(dailynoiseSPYMLRV)
#---------------------------------exhanges--------------------------------------------
extlt <- read.csv("ExchangeStatistics_TLT.csv")
exspy <- read.csv("ExchangeStatistics_SPY.csv")
#TLT
#construct ad-hoc function that gives me the results for 2 year increments.
#Years are changing at, 252, 504, 754, 1006, 1258, 1510, 1762, 2013, 2264, 2516(end)
main.ExchangesTLT <- function(sequence){
tqtlt <- length(grep("T Q", extlt[sequence,1])) + length(grep("T Q", extlt[sequence,2])) +
length(grep("T Q", extlt[sequence,3]))
wyjktlt <- length(grep("W Y J K", extlt[sequence,1])) + length(grep("W Y J K", extlt[sequence,2])) +
length(grep("W Y J K", extlt[sequence,3]))
ptlt <- length(grep("P", extlt[sequence,1])) + length(grep("P", extlt[sequence,2])) +
length(grep("P", extlt[sequence,3]))
ztlt <- length(grep("Z", extlt[sequence,1])) + length(grep("Z", extlt[sequence,2])) +
length(grep("Z", extlt[sequence,3]))
dtlt <- length(grep("D", extlt[sequence,1])) + length(grep("D", extlt[sequence,2])) +
length(grep("D", extlt[sequence,3]))
btlt <- length(grep("B", extlt[sequence,1])) + length(grep("B", extlt[sequence,2])) +
length(grep("B", extlt[sequence,3]))
res <- matrix(c(tqtlt, wyjktlt, ptlt, ztlt, dtlt, btlt), ncol = 6, nrow = 1)
colnames(res) <- c("tqtlt", "wyjktlt", "ptlt", "ztlt", "dtlt", "btlt")
return(res)
}
main.ExchangesTLT(1:504)
main.ExchangesTLT(505:1006)
main.ExchangesTLT(1007:1510)
main.ExchangesTLT(1511:2013)
main.ExchangesTLT(2014:2516)
#total
main.ExchangesTLT(1:2516)
#SPY
main.ExchangesSPY <- function(sequence){
tqspy <- length(grep("T Q", exspy[sequence,1])) + length(grep("T Q", exspy[sequence,2])) +
length(grep("T Q", exspy[sequence,3]))
wyjkspy <- length(grep("W Y J K", exspy[sequence,1])) + length(grep("W Y J K", exspy[sequence,2])) +
length(grep("W Y J K", exspy[sequence,3]))
pspy <- length(grep("P", exspy[sequence,1])) + length(grep("P", exspy[sequence,2])) +
length(grep("P", exspy[sequence,3]))
zspy <- length(grep("Z", exspy[sequence,1])) + length(grep("Z", exspy[sequence,2])) +
length(grep("Z", exspy[sequence,3]))
dspy <- length(grep("D", exspy[sequence,1])) + length(grep("D", exspy[sequence,2])) +
length(grep("D", exspy[sequence,3]))
bspy <- length(grep("B", exspy[sequence,1])) + length(grep("B", exspy[sequence,2])) +
length(grep("B", exspy[sequence,3]))
res <- matrix(c(tqspy, wyjkspy, pspy, zspy, dspy, bspy), ncol=6, nrow = 1)
colnames(res) <- c("tqspy", "wyjkspy", "pspy", "zspy", "dspy", "bspy")
return(res)
}
main.ExchangesSPY(1:504)
main.ExchangesSPY(505:1006)
main.ExchangesSPY(1007:1510)
main.ExchangesSPY(1511:2013)
main.ExchangesSPY(2014:2516)
#total
main.ExchangesSPY(1:2516)