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results.pci.R
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library(data.table)
library(lubridate)
library(ggplot2)
library(patchwork)
library(PerformanceAnalytics)
library(future.apply)
library(partialCI)
library(xts)
library(AzureStor)
options(future.globals.maxSize = 4000 * 1024^2) # 2GB
# DATA --------------------------------------------------------------------
# Daily prives
prices = fread("F:/strategies/statsarb/pci/prices.csv")
# Reshape prices to make below function faster
prices = as.xts.data.table(dcast(prices, date ~ symbol, value.var = "close"))
# Import pci tests
files = list.files("F:/strategies/statsarb/pci/output_pci", full.names = TRUE)
pci_tests = lapply(files, fread)
pci_tests = rbindlist(pci_tests, fill = TRUE)
# Check for missing values
pci_tests[, .(pvmr_miss = sum(is.na(pvmr)),
rho_miss = sum(is.na(rho)),
p_rw_miss = sum(is.na(p_rw)),
p_ar_miss = sum(is.na(p_ar)),
negloglik_miss = sum(is.na(negloglik)))]
pci_tests = na.omit(pci_tests, cols = c("pvmr", "rho", "p_rw", "p_ar", "negloglik"))
# Check one meta row
pci_test[search_type == "lasso" & maxfact == 1 & train_size == 24]
pci_test[search_type == "lasso" & maxfact == 1 & train_size == 24] |>
_[pvmr > 0.5 & rho > 0.5 & p_rw < 0.05 & p_ar < 0.05 &
negloglik <= quantile(negloglik, probs = 0.25)]
# FILTER PAIRS ------------------------------------------------------------
# Apply restrictions to the universe
# 1) pairs with a half-life of mean-reversion of one day or less - thereby avoiding to select
#where trading gains are largely attributable to bid-ask bounce
# 2) pvmr > 0.5 ensures pairs more reliable parameter estimates
# 3) p_rw < 0.05 & p_ar < 0.05. A time series is classified as partially cointegrated,
# if and only if the random walk as well as the AR(1)-hypotheses are rejected
# 3) my condition: MR p value should be lower than 0.05 because this test confirms mean reverting component
# 4) restriction to same sector I DON'T WANT APPLY THIS FOR NOW
# 5) 25% lowest by neLog
# 6) possible to add additional fundamental matching
pci_tests_eligible = pci_tests[pvmr > 0.5 & rho > 0.5 & p_rw < 0.05 & p_ar < 0.05]
pci_tests_eligible[, nq := quantile(negloglik, probs = 0.25),
by = .(search_type, maxfact, train_size, train_start)]
pci_tests_eligible = pci_tests_eligible[negloglik <= nq]
# TODO: Later try with maxfact 2
pci_tests_eligible = pci_tests_eligible[maxfact == 1]
# remove same pairs
pci_tests_eligible = pci_tests_eligible[
, .SD[!(series_2 %in% series_1)],
by = .(search_type, maxfact, train_size, train_start)]
# PAIRS STRATEGY FUNCTION -------------------------------------------------
# Function to generate zscore
generate_signal_zscore = function(Z_score, threshold_long, threshold_short) {
signal = Z_score
colnames(signal) = "signal"
signal[] = NA
# initial position
signal[1] = 0
if (Z_score[1] <= threshold_long[1]) {
signal[1] = 1
} else if (Z_score[1] >= threshold_short[1])
signal[1] = -1
# loop
for (t in 2:nrow(Z_score)) {
if (signal[t-1] == 0) { # if we were in no position
if (Z_score[t] <= threshold_long[t]) {
signal[t] = 1
} else if(Z_score[t] >= threshold_short[t]) {
signal[t] = -1
} else signal[t] = 0
} else if (signal[t-1] == 1) { #if we were in a long position
if (Z_score[t] >= 0) signal[t] = 0
else signal[t] = signal[t-1]
} else { #if we were in a short position
if (Z_score[t] <= 0) signal[t] = 0
else signal[t] = signal[t-1]
}
}
return(signal)
}
# main function to analyse pairs
pairs_trading_pci = function(train_start, train_end,
test_start = train_end + 1,
test_end = ceiling_date(test_start, unit = "month")-1,
ticker_1, ticker_2, ...,
std_entry = 1,
plot_pnl = TRUE) {
# Debug
# n_ = 9
# pci_tests_eligible[n_]
# ticker_1 = pci_tests_eligible[n_, series_1]
# ticker_2 = pci_tests_eligible[n_, series_2]
# train_start = pci_tests_eligible[n_, train_start]
# train_end = pci_tests_eligible[n_, train_end]
# test_start = pci_tests_eligible[n_, train_end + 1]
# test_end = pci_tests_eligible[n_, ceiling_date(test_start, unit = "month")-1]
# Define train and test sets
y1_train = prices[paste0(train_start, "/", train_end), ticker_1]
y2_train = prices[paste0(train_start, "/", train_end), ticker_2]
y1_test = prices[paste0(test_start, "/", test_end), ticker_1]
y2_test = prices[paste0(test_start, "/", test_end), ticker_2]
# get spreads
fit_pci = fit.pci(y1_train, y2_train)
hs_train = statehistory.pci(fit_pci)
hs_test = statehistory.pci(fit_pci, data = y1_test, basis = y2_test)
hs = rbind(hs_train, hs_test)
spread_train = xts(hs_train[, 4], as.Date(rownames(hs_train)))
spread = xts(hs[, 4], as.Date(rownames(hs)))
# z-score
spread_var = sd(spread_train)
Z_score_M = spread/spread_var
# generate signals with z scored
threshold_long = threshold_short = Z_score_M
threshold_short[] = std_entry
threshold_long[] = -std_entry
# get and plot signals
signal = generate_signal_zscore(Z_score_M, threshold_long, threshold_short)
# let's compute the PnL directly from the signal and spread
spread_return = diff(Z_score_M)
traded_return = spread_return * lag(signal) # NOTE THE LAG!!
traded_return[is.na(traded_return)] = 0
colnames(traded_return) = "traded spread"
# plot PnL
if (plot_pnl) {
# plot Pnl
data_plot = as.data.table(traded_return)
setnames(data_plot, c("date", "spread"))
g1 = ggplot(as.data.table(Z_score_M), aes(x = index, y = V1)) + geom_line() +
geom_hline(yintercept = 0, color = "red") +
geom_hline(yintercept = 1, color = "blue") +
geom_hline(yintercept = -1, color = "blue") +
geom_vline(xintercept = test_start, color = "blue")
g2 = ggplot(data_plot, aes(date, y = 1 + cumsum(spread))) +
geom_line() +
geom_vline(xintercept = test_start, color = "blue")
print(g1 / g2)
}
# data for QC
qc_data = cbind(date = rownames(hs_test), as.data.table(hs_test))
qc_data[, Z_score_M := M / spread_var]
qc_data[, symbol_1 := ticker_1]
qc_data[, symbol_2 := ticker_2]
qc_data[, beta := fit_pci$beta]
cols = colnames(qc_data)[2:ncol(qc_data)]
qc_data[, (cols) := lapply(.SD, shift), .SDcols = cols]
qc_data = na.omit(qc_data)
return(qc_data)
}
# example
n_ = sample(seq_along(files), 1)
pairs_trading_pci(
train_start = pci_tests_eligible[n_, train_start],
train_end = pci_tests_eligible[n_, train_end],
# test_end = ceiling_date(test_start, unit = "month")-1
test_end = pci_tests_eligible[n_, train_end] + 125,
ticker_1 = pci_tests_eligible[n_, series_1],
ticker_2 = pci_tests_eligible[n_, series_2],
std_entry = 1,
plot_pnl = TRUE
)
# PAIRS TRADING FUNCION SIMPLE --------------------------------------------
# main function to analyse pairs
pairs_trading_pci_performance = function(train_start,
train_end,
test_start = train_end + 1,
test_end = ceiling_date(test_start, unit = "month") -1,
ticker_1, ticker_2,
std_entry = 1,
set = c("test", "train", "both")) {
# Debug
# n_ = 1
# pci_tests_eligible[n_]
# ticker_1 = pci_tests_eligible[n_, series_1]
# ticker_2 = pci_tests_eligible[n_, series_2]
# train_start = pci_tests_eligible[n_, train_start]
# train_end = pci_tests_eligible[n_, train_end]
# test_start = pci_tests_eligible[n_, train_end + 1]
# test_end = pci_tests_eligible[n_, ceiling_date(test_start, unit = "month")-1]
# Arguments
set = match.arg(set)
# Define train and test sets
y1_train = prices[paste0(train_start, "/", train_end), ticker_1]
y2_train = prices[paste0(train_start, "/", train_end), ticker_2]
y1_test = prices[paste0(test_start, "/", test_end), ticker_1]
y2_test = prices[paste0(test_start, "/", test_end), ticker_2]
# get spreads
fit_pci = fit.pci(y1_train, y2_train)
hs_train = statehistory.pci(fit_pci)
hs_test = statehistory.pci(fit_pci, data = y1_test, basis = y2_test)
hs = rbind(hs_train, hs_test)
spread_train = xts(hs_train[, 4], as.Date(rownames(hs_train)))
spread = xts(hs[, 4], as.Date(rownames(hs)))
# z-score
spread_var = sd(spread_train)
if (spread_var == 0) {
print("Spread variance is zero")
return(NULL)
}
Z_score_M = spread/spread_var
# generate signals with z scored
threshold_long = threshold_short = Z_score_M
threshold_short[] = std_entry
threshold_long[] = -std_entry
# get and plot signals
signal = tryCatch(
generate_signal_zscore(Z_score_M, threshold_long, threshold_short),
error = function(e) NULL)
if (is.null(signal)) {
print("Error in signal generation")
return(NULL)
}
# let's compute the PnL directly from the signal and spread
spread_return = diff(Z_score_M)
traded_return = spread_return * lag(signal) # NOTE THE LAG!!
traded_return[is.na(traded_return)] = 0
colnames(traded_return) = paste0(ticker_1, "_", ticker_2)
# Keep only test or train
if (set == "test") {
traded_return = traded_return[paste0(test_start, "/", test_end)]
} else if (set == "train") {
traded_return = traded_return[paste0(train_start, "/", train_end)]
}
return(traded_return)
}
# example
n_ = sample(seq_along(files), 1)
pairs_trading_pci_performance(
train_start = pci_tests_eligible[n_, train_start],
train_end = pci_tests_eligible[n_, train_end],
ticker_1 = pci_tests_eligible[n_, series_1],
ticker_2 = pci_tests_eligible[n_, series_2],
std_entry = 1
)
# Define all parameters
params = expand.grid(
train_start = meta,
train_end = pci_tests_eligible[, train_end],
ticker_1 = pci_tests_eligible[, series_1],
ticker_2 = pci_tests_eligible[, series_2],
std_entry = 1
)
# Generate for all pairs for all meta rows
plan(multisession, workers = 8L)
params = CJ(search_type = pci_tests[, unique(search_type)],
maxfact = pci_tests[, unique(maxfact)],
train_size = pci_tests[, unique(train_size)])
pnl_by_i_l = list()
for (i in 1:nrow(params)) {
# Extract params
p = params[i, ]
# print(p)
# sample pci pairs
pci_tests_eligible_sample = pci_tests_eligible[
search_type == p$search_type &
maxfact == p$maxfact &
train_size == p$train_size
]
# Return portfolio return
s = Sys.time()
pnl_by_i = future_lapply(1:nrow(pci_tests_eligible_sample), function(j) {
print(j)
pairs_trading_pci_performance(
train_start = pci_tests_eligible[j, train_start],
train_end = pci_tests_eligible[j, train_end],
ticker_1 = pci_tests_eligible[j, series_1],
ticker_2 = pci_tests_eligible[j, series_2],
std_entry = 1
)
})
e = Sys.time()
e - s
# save
test = do.call(merge, c(pnl_by_i[1:500], fill = NA))
names(test)
# Merge across date and symbol
pnl_dt = lapply(pnl_by_i, function(x) {
if (is.null(x)) return(NULL)
dt = data.table(date = index(x), value = coredata(x)[,1])
dt[, symbol := colnames(x)[1]]
return(dt)
})
pnl_dt = rbindlist(pnl_dt)
pnl_dt = dcast(pnl_dt, date ~ symbol, value.var = "value")
setorder(pnl_dt, date)
dim(pnl_dt)
pnl_dt[, 1:5]
# Calculate portfolio returns
charts.PerformanceSummary(Return.portfolio(pnl_dt)[100:150])
}
pnl_by_i = do.call(cbind, pnl_by_i)
Return.portfolio(pnl_by_i)
charts.PerformanceSummary(Return.portfolio(pnl_by_i))
# DATA FOR QC -------------------------------------------------------------
# Choose best parameters
param_search_type_qc = "lasso"
param_maxfact_qc = 1
param_train_size_qc = 24
# Function to extract data for QC
pairs_trading_pci_qc = function(train_start,
train_end,
test_start = train_end + 1,
test_end = ceiling_date(test_start, unit = "month") - 1,
ticker_1,
ticker_2,
std_entry = 1) {
# Debug
# n_ = 13
# pci_tests_eligible[n_]
# ticker_1 = pci_eligible_qc[n_, series_1]
# ticker_2 = pci_eligible_qc[n_, series_2]
# train_start = pci_eligible_qc[n_, train_start]
# train_end = pci_eligible_qc[n_, train_end]
# test_start = pci_eligible_qc[n_, train_end + 1]
# test_end = pci_eligible_qc[n_, ceiling_date(test_start, unit = "month")-1]
# Define train and test sets
y1_train = prices[paste0(train_start, "/", train_end), ticker_1]
y2_train = prices[paste0(train_start, "/", train_end), ticker_2]
y1_test = prices[paste0(test_start, "/", test_end), ticker_1]
y2_test = prices[paste0(test_start, "/", test_end), ticker_2]
# get spreads
fit_pci = fit.pci(y1_train, y2_train)
hs_train = statehistory.pci(fit_pci)
hs_test = statehistory.pci(fit_pci, data = y1_test, basis = y2_test)
hs = rbind(hs_train, hs_test)
spread_train = xts(hs_train[, 4], as.Date(rownames(hs_train)))
spread = xts(hs[, 4], as.Date(rownames(hs)))
# Calculate sd of train spread to get z-score below
spread_var = sd(spread_train)
if (spread_var == 0) {
print("Spread variance is zero")
return(NULL)
}
# data for QC
qc_data = cbind(date = rownames(hs_test), as.data.table(hs_test))
qc_data[, Z_score_M := M / spread_var]
qc_data[, symbol_1 := ticker_1]
qc_data[, symbol_2 := ticker_2]
qc_data[, beta := fit_pci$beta]
qc_data = na.omit(qc_data)
return(qc_data)
}
# Get dat for QC
pci_eligible_qc = pci_tests_eligible[
search_type == param_search_type_qc &
maxfact == param_maxfact_qc &
train_size == param_train_size_qc
]
setorder(pci_eligible_qc, train_start)
# Example
n_ = sample(seq_along(pci_eligible_qc), 1)
pairs_trading_pci_qc(
train_start = pci_eligible_qc[n_, train_start],
train_end = pci_eligible_qc[n_, train_end],
ticker_1 = pci_eligible_qc[n_, series_1],
ticker_2 = pci_eligible_qc[n_, series_2],
std_entry = 1,
)[]
# Get all data for QC
plan(multisession, workers = 8L)
# qc_data = lapply(1:nrow(pci_eligible_qc), function(j) {
qc_data = future_lapply(1:nrow(pci_eligible_qc), function(j) {
pairs_trading_pci_qc(
train_start = pci_eligible_qc[j, train_start],
train_end = pci_eligible_qc[j, train_end],
ticker_1 = pci_eligible_qc[j, series_1],
ticker_2 = pci_eligible_qc[j, series_2],
std_entry = 1
)
})
qc_data = rbindlist(qc_data)
setorder(qc_data, date, symbol_1)
# Save locally and to Azure blob
fwrite(qc_data, "F:/strategies/statsarb/pci/qc_data.csv")
bl_endp_key = storage_endpoint(Sys.getenv("BLOB-ENDPOINT"),
Sys.getenv("BLOB-KEY"))
cont = storage_container(bl_endp_key, "qc-backtest")
sample_ = qc_data[date > as.Date("2020-01-01")]
sample_[, date := paste0(date, " 15:59:00")]
storage_write_csv(sample_, cont, "pci.csv", col_names = FALSE)
# # save data to QC
# bl_endp_key = storage_endpoint(Sys.getenv("BLOB-ENDPOINT"),
# Sys.getenv("BLOB-KEY"))
# cont <- storage_container(bl_endp_key, "qc-backtest")
# time_ <- format.POSIXct(Sys.time(), format = "%Y%m%d%H%M%S")
# lapply(unique(pairs_results$symbol_1), function(s) {
# sample_ <- pairs_results[symbol_1 == s]
# sample_[, date := paste0(date, " 15:59:00")]
# file_name <- paste0("pairs_pci_", s, "_", sample_[1, symbol_2], "_", time_, ".csv")
# print(file_name)
# print(sample_)
# storage_write_csv(sample_, cont, file_name, col_names = FALSE)
# })
# WARNING: QC DATA is not shifted as before in function
cols = colnames(qc_data)[2:ncol(qc_data)]
qc_data[, (cols) := lapply(.SD, shift), .SDcols = cols]
# # example of partially cointegrated pairs
# pairs = unlist(pci_tests_eligible[1, 1:2])
# plot(log(train[, pairs]), main = paste0(pairs[1], " - ", pairs[2])) # log prices series of first pair
# # EQIX - Equinix, Inc. je američka multinacionalna tvrtka sa sjedištem u Redwood Cityju, Kalifornija,
# # specijalizirana za internetske veze i podatkovne centre.
# # AMT - American Tower Corporation je američka zaklada za ulaganje u nekretnine te vlasnik i operater bežične i
# # televizijske komunikacijske infrastrukture u nekoliko zemalja
# pairs <- unlist(pci_tests_eligible[2, 1:2])
# plot(log(train[, pairs]), main = paste0(pairs[1], " - ", pairs[2])) # log prices series of second pair
# # DOV - američki je konglomerat proizvođača industrijskih proizvod
# # APH - glavni proizvođač elektroničkih i optičkih konektora, kabelskih i interkonektnih sustava kao što su koaksijalni kabeli
# pairs = unlist(pci_tests_eligible[3, 1:2])
# plot(log(train[, pairs]), main = paste0(pairs[1], " - ", pairs[2])) # log prices series of third pair
# # O - investicijski fond za nekretnine
# # CPT - investicijski fond za nekretnine
#
#
# # TRADING STRATEGY FOR ONE PAIR ----------------------------------------------------
# # preparedata for pci estimation
# n_ = 1 # GOOD: 1,3,4,6,7,10 FLAT: 2,8,9 BAD: 5
# cat("symbols are", unlist(pci_tests_eligible[n_, 1]), " and ",
# unlist(pci_tests_eligible[n_, 2]))
# y1_train = train[, unlist(pci_tests_eligible[n_, 1])]
# y2_train = train[, unlist(pci_tests_eligible[n_, 2])]
# y1_test = test[, unlist(pci_tests_eligible[n_, 1])]
# y2_test = test[, unlist(pci_tests_eligible[n_, 2])]
# y1 = X["2019-01-01/2022-01-01", unlist(pci_tests_eligible[n_, 1])]
# y2 = X["2019-01-01/2022-01-01", unlist(pci_tests_eligible[n_, 2])]
#
# # get spreads
# fit_pci = fit.pci(y1_train, y2_train)
# plot(fit_pci)
# hs_train = statehistory.pci(fit_pci)
# hs_test = statehistory.pci(fit_pci, data = y1_test, basis = y2_test)
# hs = rbind(hs_train, hs_test)
# spread_train = xts(hs_train[, 4], as.Date(rownames(hs_train)))
# spread = xts(hs[, 4], as.Date(rownames(hs)))
# ggplot(as.data.table(spread), aes(x = index, y = V1)) +
# geom_line() +
# geom_vline(xintercept = as.Date("2021-01-01"), color = "blue")
#
# # understand calculation
# cat("Price data ", head(hs_test$Y))
# cat("Price X1 ", head(y1_test)) # AEE
# cat("Price X0 ", head(y2_test)) # XEL
# cat("Beta ", fit_pci$beta)
# cat("Y hat calculation", head(y2_train %*% fit_pci$beta))
# print("Hidden states:")
# head(hs_train)
#
# # calculate std of spread an plot it
# spread_var = sd(spread_train)
# ggplot(as.data.table(spread), aes(x = index)) +
# geom_line(aes(y = V1)) +
# geom_hline(aes(yintercept = spread_var), color = "red") +
# geom_hline(aes(yintercept = -spread_var), color = "red") +
# geom_hline(aes(yintercept = spread_var*2), color = "green") +
# geom_hline(aes(yintercept = -spread_var*2), color = "green") +
# geom_vline(xintercept = as.Date("2017-01-01"), color = "blue")
#
# # plot spread and thresholdswith z-score
# Z_score_M = spread/sd(spread_train)
# plot(Z_score_M)
# ggplot(as.data.table(Z_score_M), aes(x = index, y = V1)) + geom_line() +
# geom_hline(yintercept = 0, color = "red") +
# geom_hline(yintercept = 1, color = "blue") +
# geom_hline(yintercept = -1, color = "blue") +
# geom_vline(xintercept = as.Date("2017-01-01"), color = "blue")
#
# # trading signal
# threshold = spread_var # in the paper authors uses theta = 1 (probbably -1 also) as the entry threshold
# threshold_long = threshold_short = spread
# threshold_short[] = spread_var
# threshold_long[] = -spread_var
# # Z_score_M <- spread
# generate_signal = function(Z_score_M, threshold_long, threshold_short) {
# signal = Z_score_M
# colnames(signal) = "signal"
# signal[] = NA
#
# # initial position
# signal[1] = 0
# if (Z_score_M[1] <= threshold_long[1]) {
# signal[1] = 1
# } else if (Z_score_M[1] >= threshold_short[1])
# signal[1] = -1
#
# # loop
# for (t in 2:nrow(Z_score_M)) {
# if (signal[t-1] == 0) { # if we were in no position
# if (Z_score_M[t] <= threshold_long[t]) {
# signal[t] <- 1
# } else if(Z_score_M[t] >= threshold_short[t]) {
# signal[t] <- -1
# } else signal[t] <- 0
# } else if (signal[t-1] == 1) { # if we were in a long position
# if (Z_score_M[t] >= (0.5 * spread_var)) signal[t] <- 0
# else signal[t] <- signal[t-1]
# } else { # if we were in a short position
# if (Z_score_M[t] <= -(0.5 * spread_var)) signal[t] <- 0
# else signal[t] <- signal[t-1]
# }
# }
# return(signal)
# }
#
# # get and plot signals
# signal = generate_signal(spread, threshold_long, threshold_short)
# ggplot(as.data.table(cbind(spread, signal)), aes(x = index)) +
# geom_line(aes(y = spread)) +
# geom_line(aes(y = signal), color = "red")
#
# # generate signals with z scored
# threshold_long = threshold_short <- Z_score_M
# threshold_short[] = 1
# threshold_long[] = -1
# generate_signal_zscore <- function(Z_score, threshold_long, threshold_short) {
# signal <- Z_score
# colnames(signal) <- "signal"
# signal[] <- NA
#
# #initial position
# signal[1] <- 0
# if (Z_score[1] <= threshold_long[1]) {
# signal[1] <- 1
# } else if (Z_score[1] >= threshold_short[1])
# signal[1] <- -1
#
# # loop
# for (t in 2:nrow(Z_score)) {
# if (signal[t-1] == 0) { #if we were in no position
# if (Z_score[t] <= threshold_long[t]) {
# signal[t] <- 1
# } else if(Z_score[t] >= threshold_short[t]) {
# signal[t] <- -1
# } else signal[t] <- 0
# } else if (signal[t-1] == 1) { #if we were in a long position
# if (Z_score[t] >= 0) signal[t] <- 0
# else signal[t] <- signal[t-1]
# } else { #if we were in a short position
# if (Z_score[t] <= 0) signal[t] <- 0
# else signal[t] <- signal[t-1]
# }
# }
# return(signal)
# }
#
# # get and plot signals
# signal <- generate_signal(Z_score_M, threshold_long, threshold_short)
# ggplot(as.data.table(cbind(Z_score_M, signal)), aes(x = index)) +
# geom_line(aes(y = Z_score_M)) +
# geom_line(aes(y = signal), color = "red") +
# geom_vline(xintercept = as.Date("2021-01-01"), color = "blue")
#
#
# # let's compute the PnL directly from the signal and spread
# spread_return <- diff(Z_score_M)
# traded_return <- spread_return * lag(signal) # NOTE THE LAG!!
# traded_return[is.na(traded_return)] <- 0
# colnames(traded_return) <- "traded spread"
#
# # plot Pnl
# data_plot <- as.data.table(traded_return)
# setnames(data_plot, c("date", "spread"))
# ggplot(data_plot, aes(date, y = 1 + cumsum(spread))) +
# geom_line() +
# geom_vline(xintercept = as.Date("2021-01-01"), color = "blue")
#
#
# # PAIRS STRATEGY FUNCTION -------------------------------------------------
# # main function to analyse pairs
# pairs_trading_pci <- function(y1_train, y2_train, y1_test, y2_test,
# std_entry = 1, plot_pnl = TRUE) {
#
# # symbols
# symb1 <- colnames(y1_train)
# symb2 <- colnames(y2_train)
#
# # get spreads
# fit_pci <- fit.pci(y1_train, y2_train)
# hs_train <- statehistory.pci(fit_pci)
# hs_test <- statehistory.pci(fit_pci, data = y1_test, basis = y2_test)
# hs <- rbind(hs_train, hs_test)
# spread_train <- xts(hs_train[, 4], as.Date(rownames(hs_train)))
# spread <- xts(hs[, 4], as.Date(rownames(hs)))
#
# # z-score
# spread_var <- sd(spread_train)
# Z_score_M <- spread/spread_var
#
# # generate signals with z scored
# threshold_long <- threshold_short <- Z_score_M
# threshold_short[] <- std_entry
# threshold_long[] <- -std_entry
# generate_signal_zscore <- function(Z_score, threshold_long, threshold_short) {
# signal <- Z_score
# colnames(signal) <- "signal"
# signal[] <- NA
#
# #initial position
# signal[1] <- 0
# if (Z_score[1] <= threshold_long[1]) {
# signal[1] <- 1
# } else if (Z_score[1] >= threshold_short[1])
# signal[1] <- -1
#
# # loop
# for (t in 2:nrow(Z_score)) {
# if (signal[t-1] == 0) { #if we were in no position
# if (Z_score[t] <= threshold_long[t]) {
# signal[t] <- 1
# } else if(Z_score[t] >= threshold_short[t]) {
# signal[t] <- -1
# } else signal[t] <- 0
# } else if (signal[t-1] == 1) { #if we were in a long position
# if (Z_score[t] >= 0) signal[t] <- 0
# else signal[t] <- signal[t-1]
# } else { #if we were in a short position
# if (Z_score[t] <= 0) signal[t] <- 0
# else signal[t] <- signal[t-1]
# }
# }
# return(signal)
# }
#
#
# # get and plot signals
# signal <- generate_signal_zscore(Z_score_M, threshold_long, threshold_short)
#
# # let's compute the PnL directly from the signal and spread
# spread_return <- diff(Z_score_M)
# traded_return <- spread_return * lag(signal) # NOTE THE LAG!!
# traded_return[is.na(traded_return)] <- 0
# colnames(traded_return) <- "traded spread"
#
# # plot PnL
# if (plot_pnl) {
# # plot Pnl
# data_plot <- as.data.table(traded_return)
# setnames(data_plot, c("date", "spread"))
# g1 <- ggplot(as.data.table(Z_score_M), aes(x = index, y = V1)) + geom_line() +
# geom_hline(yintercept = 0, color = "red") +
# geom_hline(yintercept = 1, color = "blue") +
# geom_hline(yintercept = -1, color = "blue") +
# geom_vline(xintercept = as.Date("2017-01-01"), color = "blue")
# g2 <- ggplot(data_plot, aes(date, y = 1 + cumsum(spread))) +
# geom_line() +
# geom_vline(xintercept = as.Date("2021-01-01"), color = "blue")
# print(g1 / g2)
# }
#
# # data for QC
# qc_data <- cbind(date = rownames(hs_test), as.data.table(hs_test))
# qc_data[, Z_score_M := M / spread_var]
# qc_data[, symbol_1 := symb1]
# qc_data[, symbol_2 := symb2]
# qc_data[, beta := fit_pci$beta]
# cols <- colnames(qc_data)[2:ncol(qc_data)]
# qc_data[, (cols) := lapply(.SD, shift), .SDcols = cols]
# qc_data <- na.omit(qc_data)
#
# return(qc_data)
# }
#
# # example
# n_ = 6
# pairs_trading_pci(
# y1_train = train[, unlist(pci_tests_eligible[n_, 1])],
# y2_train = train[, unlist(pci_tests_eligible[n_, 2])],
# y1_test = test[, unlist(pci_tests_eligible[n_, 1])],
# y2_test = test[, unlist(pci_tests_eligible[n_, 2])],
# std_entry = 1,
# plot_pnl = TRUE
# )
#
# # all pairs
# pairs_results_l <- lapply(1:nrow(pci_tests_eligible), function(n_) {
# pairs_trading_pci(
# y1_train = train[, unlist(pci_tests_eligible[n_, 1])],
# y2_train = train[, unlist(pci_tests_eligible[n_, 2])],
# y1_test = test[, unlist(pci_tests_eligible[n_, 1])],
# y2_test = test[, unlist(pci_tests_eligible[n_, 2])],
# std_entry = 1,
# plot_pnl = FALSE
# )
# })
# pairs_results <- rbindlist(pairs_results_l)
#
#
#
# # SAVE FOR QC BACKTEST ----------------------------------------------------
# # save data to QC
# bl_endp_key = storage_endpoint(Sys.getenv("BLOB-ENDPOINT"),
# Sys.getenv("BLOB-KEY"))
# cont <- storage_container(bl_endp_key, "qc-backtest")
# time_ <- format.POSIXct(Sys.time(), format = "%Y%m%d%H%M%S")
# lapply(unique(pairs_results$symbol_1), function(s) {
# sample_ <- pairs_results[symbol_1 == s]
# sample_[, date := paste0(date, " 15:59:00")]
# file_name <- paste0("pairs_pci_", s, "_", sample_[1, symbol_2], "_", time_, ".csv")
# print(file_name)
# print(sample_)
# storage_write_csv(sample_, cont, file_name, col_names = FALSE)
# })
#
# # # simulate quantities and prices
# # A = 10000
# # aee = 4.2
# # xel = 3.8
# # share = 0.2
# # A_ = 2000
# # q_xel = floor(A_ / xel)
# # q_aee = q_xel * fit_pci$beta
# #
# # q_xel * xel
# # q_aee * aee
# #
# # q_aee = A_ / (aee %*% fit_pci$beta)
# # q_xel * fit_pci$beta
# #
# # (xel / aee) * fit_pci$beta
# #
# #
# # 61.657137504 * 323
# # 69.145082055 * 312
#
#
#
#
# # PAPER TRADING ----------------------------------------------------------
# # sp500 universe
# fmp = FMP$new()
# symbols <- fmp$get_sp500_symbols()
#
# # get daily market data for sp500 stocks
# start_date_test <- as.Date(format.Date(Sys.Date(), format = "%Y-%m-01")) - 30
# start_date <- start_date_test - (365 * 3)
# arr <- tiledb_array("D:/equity-usa-daily-fmp",
# as.data.frame = TRUE,
# query_layout = "UNORDERED",
# selected_ranges = list(symbol = cbind(symbols, symbols))
# # selected_ranges = list(date = cbind(start_date, Sys.Date()),
# # symbol = cbind(symbols, symbols))
# )
# system.time(prices_new <- arr[])
# tiledb_array_close(arr)
# prices_dt_new <- as.data.table(prices_new)
# setorder(prices_dt_new, symbol, date)
#
# # cleaning steps with explanations
# prices_dt_new <- prices_dt_new[isBusinessDay(date)] # keep only trading days
# prices_dt_new <- prices_dt_new[open > 0 & high > 0 & low > 0 & close > 0 & adjClose > 0] # remove rows with prices <= 0
# prices_dt_new <- prices_dt_new[, .(symbol, date, adjClose )] # keep only columns we need
# prices_dt_new <- unique(prices_dt_new, by = c("symbol", "date")) # remove duplicates
# prices_dt_new <- na.omit(prices_dt_new) # remove missing values
# setorder(prices_dt_new, "symbol", "date") # order for returns calculation
# prices_dt_new[, returns := adjClose / data.table::shift(adjClose, 1, type = "lag") - 1, by = symbol]
# prices_dt_new <- prices_dt_new[returns < 1] # TODO:: better outlier detection mechanism
# prices_dt_new <- dcast(prices_dt_new, date ~ symbol, value.var = "adjClose")
#
# # remove columns with NA values
# keep_cols <- names(which(colMeans(!is.na(prices_dt_new)) > 0.99))
# prices_dt_new <- prices_dt_new[, .SD, .SDcols = keep_cols]
# X <- as.xts.data.table(prices_dt_new)
# X <- X[, colSums(!is.na(X)) == max(colSums(!is.na(X)))]
# X <- log(X)
# dim(X)
#
# # split in train and test set
# train_dates <- paste(start_date, start_date_test, sep = "/")
# train <- X[train_dates]
# test_dates <- paste(start_date_test, Sys.Date(), sep = "/")
# test <- X[test_dates]
#
# # choose best pairs using hedge.pci function and maxfact = 1 (only one factor possible)
# pci_tests_new_i <- list()
# for (i in 1:ncol(train)) {
#
# # DEBUG
# print(i)
#
# # quasi multivariate pairs
# hedge <- tryCatch(hedge.pci(train[, i], train[, -i], maxfact = 1, use.multicore = FALSE),
# error = function(e) NULL)
# if (is.null(hedge)) {
# pci_tests_i[[i]] <- NULL
# next()
# }
#
# # pci fit
# test_pci <- test.pci(train[, i], hedge$pci$basis)
#
# # summary table
# results <- data.table(series1 = hedge$pci$target_name, series2 = hedge$index_names)
# metrics <- c(hedge$pci$beta, hedge$pci$rho, hedge$pci$sigma_M, hedge$pci$sigma_R,
# hedge$pci$M0, hedge$pci$R0, hedge$pci$beta.se, hedge$pci$rho.se,
# hedge$pci$sigma_M.se, hedge$pci$sigma_R.se, hedge$pci$M0.se,
# hedge$pci$R0.se, hedge$pci$negloglik, hedge$pci$pvmr)
# names(metrics)[c(1, 7:12)] <- c("beta", "beta_se", "rho_se", "sigma_M_se", "sigma_R_se",
# "M0_se", "R0_se")
# metrics <- as.data.table(as.list(metrics))
# results <- cbind(results, metrics)
# pci_tests_new_i[[i]] <- cbind(results, p_rw = test_pci$p.value[1], p_ar = test_pci$p.value[2])
# }
# pci_tests_new <- rbindlist(pci_tests_new_i, fill = TRUE)
#
# # Apply restrictions to the universe
# pci_tests_eligible_new <- pci_tests_new[pvmr > 0.5 &
# rho > 0.5 &
# p_rw < 0.05 &
# p_ar < 0.05 &
# negloglik <= quantile(negloglik, probs = 0.25)]
#
# # remove same pairs
# pci_tests_eligible_new <- pci_tests_eligible_new[!(series2 %in% series1)]
#
# # example of partially cointegrated pairs
# pairs <- unlist(pci_tests_eligible_new[1, 1:2])
# plot(log(train[, pairs]), main = paste0(pairs[1], " - ", pairs[2]))
# # ACN - IT usluge i savjete
# # GOOG - Google!
# pairs <- unlist(pci_tests_eligible_new[2, 1:2])
# plot(log(train[, pairs]), main = paste0(pairs[1], " - ", pairs[2])) # log prices series of second pair
# # AEP - električna tvrtka
# # ED - energetskih tvrtki
# pairs <- unlist(pci_tests_eligible_new[3, 1:2])
# plot(log(train[, pairs]), main = paste0(pairs[1], " - ", pairs[2])) # log prices series of second pair
# # ALL - osiguravajuća tvrtka
# # AFL - pružatelj dopunskog osiguranja
#
# # all pairs
# pairs_results_l <- lapply(1:nrow(pci_tests_eligible_new), function(n_) {
# pairs_trading_pci(
# y1_train = train[, unlist(pci_tests_eligible_new[n_, 1])],
# y2_train = train[, unlist(pci_tests_eligible_new[n_, 2])],
# y1_test = test[, unlist(pci_tests_eligible_new[n_, 1])],
# y2_test = test[, unlist(pci_tests_eligible_new[n_, 2])],
# std_entry = 1,
# plot_pnl = FALSE
# )
# })
# pairs_results_new <- rbindlist(pairs_results_l)
# pairs_results_new[, date := as.Date(date)]
#
# # spread all plots
# plots <- list()
# symbols_1 <- unique(pairs_results_new$symbol_1)
# for (i in seq_along(symbols_1)) { # seq_along(symbols_1)
# data_ <- pairs_results_new[symbol_1 == symbols_1[i]]
# plots[[i]] <- ggplot(data_, aes(x = date, y = Z_score_M)) +
# geom_line() +
# geom_hline(yintercept = c(1, -1), color = "red") +
# ggtitle(paste0(data_$symbol_1[1], " - ", data_$symbol_2[2])) +
# theme(plot.title = element_text(size = 10),
# axis.title.y = element_blank())
# }
# wrap_plots(plots)
#
# # spread plots to trade
# plots <- list()
# # symbols_1 <- pairs_results_new[, tail(.SD, 1), by = symbol_1][Z_score_M >= 1 | Z_score_M <= -1, symbol_1]
# symbols_1 <- unique(pairs_results_new[, any(Z_score_M >= 1) | any(Z_score_M <= -1), by = symbol_1][V1 == TRUE][[1]])
# for (i in seq_along(symbols_1)) { # seq_along(symbols_1)
# data_ <- pairs_results_new[symbol_1 == symbols_1[i]]
# plots[[i]] <- ggplot(data_, aes(x = date, y = Z_score_M)) +
# geom_line() +
# geom_hline(yintercept = c(1, -1), color = "red") +
# ggtitle(paste0(data_$symbol_1[1], " - ", data_$symbol_2[2])) +
# theme(plot.title = element_text(size = 10),
# axis.title.y = element_blank())
# }
# wrap_plots(plots)
#
#
#
#
# # PORTFOLIO ---------------------------------------------------------------
# # sp500 universe
# fmp = FMP$new()
# symbols <- fmp$get_sp500_symbols()
#
# # import daily market data
# arr <- tiledb_array("D:/equity-usa-daily-fmp",
# as.data.frame = TRUE,
# query_layout = "UNORDERED",
# selected_ranges = list(symbol = cbind(symbols, symbols))
# )
# system.time(prices <- arr[])
# tiledb_array_close(arr)
# prices_dt <- as.data.table(prices)
#
# # cleaning steps with explanations
# prices_dt <- prices_dt[isBusinessDay(date)] # keep only trading days
# prices_dt <- prices_dt[open > 0 & high > 0 & low > 0 & close > 0 & adjClose > 0] # remove rows with prices <= 0
# prices_dt <- prices_dt[, .(symbol, date, adjClose )] # keep only columns we need
# prices_dt <- unique(prices_dt, by = c("symbol", "date")) # remove duplicates
# prices_dt <- na.omit(prices_dt) # remove missing values
# setorder(prices_dt, "symbol", "date") # order for returns calculation
# prices_dt[, returns := adjClose / data.table::shift(adjClose, 1, type = "lag") - 1, by = symbol]
# prices_dt <- prices_dt[returns < 1] # TODO: better outlier detection mechanism
#
# # define train period
# test_period_start <- seq.Date(Sys.Date() - 7000, Sys.Date(), by = 1)
# test_period_start <- unique(format.Date(test_period_start, format = "%Y-%m-01"))
# test_period_start <- as.Date(test_period_start)
# train_start <- test_period_start - (365 * 3)
# train_stop <- test_period_start - 1
#
# # find best pairs for every trainset
# bl_endp_key <- storage_endpoint(Sys.getenv("BLOB-ENDPOINT-SNP"),
# Sys.getenv("BLOB-KEY-SNP"))
# cont <- storage_container(bl_endp_key, "qc-backtest")
# train_start = train_start[which(test_period_start == as.Date("2004-06-01")):length(test_period_start)]
# train_stop = train_stop[which(test_period_start == as.Date("2004-06-01")):length(test_period_start)]
# test_period_start = test_period_start[which(test_period_start == as.Date("2004-06-01")):length(test_period_start)]
# # best_pairs <- list()
# for (i in seq_along(train_start)) {
#
# # sample
# sample_dt <- prices_dt[date %between% c(train_start[i], train_stop[i])]
# sample_dt <- dcast(sample_dt, date ~ symbol, value.var = "adjClose")
#
# # remove columns with NA values
# X <- as.xts.data.table(sample_dt)
# X <- X[,colSums(!(is.na(X))) == nrow(X)]
# X <- log(X)
#
# # choose best pairs using hedge.pci function and maxfact = 1 (only one factor possible)
# pci_tests_i <- list()
# for (j in 1:ncol(X)) {
#
# # quasi multivariate pairs
# print(j)