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#
# WARNING - NOT YET UPDATED TO R 2.4.0, THIS MAY RESULT IN ERRORS
#
# Examples from the Monograph:
# "Rmetrics - Financial Engineering and Computational Finance"
# written by Diethelm Wuertz
# ISBN to be published
#
# Details:
# Chapter 1.4
# Stylized Facts, Structures and Dependencies
#
# List of Examples, Exercises and Code Snippets:
#
# * Example: Plot Autocorrelation and Partial Autocorrelations
# 1.4.1 Example: Short-Term Autocorrelations
# 1.4.2 Example: Short-Term Partial Autocorrelations
# 1.4.3 Example: Long Memory Autocorrelation Function
# 1.4.5 Example: Display the Taylor Effect
# 1.4.6 Example: Compare with Normal Rvs and AR Model
# 1.4.7 Example: Absolute Value Scaling
#
# Author:
# (C) 1997-2005, Diethelm Wuertz, GPL
# www.rmetrics.org
# www.itp.phys.ethz.ch
# www.finance.ch
#
################################################################################
### Load Packages:
# require(fBasics)
###
# ------------------------------------------------------------------------------
### Example: Plot Autocorrelation and Partial Autocorrelations
# This example plots the autocorrelation function and the
# partial autocorrelation function using acf() and pacf()
# functions from R's base package - The pedestrian way ...
# Settings:
data(nyse)
class(nyse)
head(nyse)
###
# Autocorrelations and Partial Autocorrelations:
# ACF and PACF of NYSE log Returns - Use the second column
# of the data frame which is the data column
par(mfrow = c(2, 2), cex = 0.7)
acf(diff(log(nyse[, 2])))
pacf(diff(log(nyse[, 2])))
###
# ------------------------------------------------------------------------------
### 1.4.1 Example: Short-Term Autocorrelations
# Plot the autocorrelation function for USDDEM FX BID returns
# for 30 min lags. The demo data file "usddem30u" contains the
# FX BID and ASK Rates.
# Graph Frame:
par(mfrow = c(2, 2), cex = 0.7)
###
# Load 30m USDDEM Data in Business Time:
USDDEM.RET = returnSeries(as.timeSeries(data(usddem30u)))
###
# Plot the ACF of the Return Series:
acfPlot(USDDEM.RET[, "BID"], lag.max = 8, ylim = c(-0.05, 0.20),
labels = FALSE)
title(main = "Short Term ACF\n30 Minutes USDDEM",
xlab = "30 min Lags", ylab = "ACF")
###
# ------------------------------------------------------------------------------
### 1.4.1 Example: Short-Term Autocorrelations
# Plot the PACF of the Return Series:
pacfPlot(USDDEM.RET[, "BID"], lag.max = 8, ylim = c(-0.05, 0.20),
labels = FALSE)
title(main = "Short Term PACF\n30 Minutes USDDEM", xlab = "30 min Lags",
ylab = "ACF")
###
# Show the range of the data
start(USDDEM.RET)
end(USDDEM.RET)
###
# ------------------------------------------------------------------------------
### 1.4.2 Example: Long Memory Autocorrelation Function
# Make a simple plot which displays the long-memory behavior of
# the 30 min USDDEM returns.
# Graphics Frame:
par(mfrow = c(2, 2), cex = 0.7)
###
# 30m USDDEM Exchange Rates in Business Time:
USDDEM.RET = returnSeries(as.timeSeries(data(usddem30u)))
# Volatility Series of Bid Prices:
USDDEM.RET = USDDEM.RET[, "BID"]
lmacfPlot(USDDEM.RET, lag.max = 48*14)
# Output:
# Long Memory Autocorrelation Function:
# Maximum Lag 672
# Cut-Off ConfLevel 0.006853398
# Plot-Intercept -1.65672
# Plot-Slope -0.1892507
# Hurst Exponent 0.9053746
###
# Daily NYSE Composite Index Series:
NYSE.RET = returnSeries(as.timeSeries(data(nyse)))
# Remove Return Value from Index Redefinition:
NYSE.RET = outlier(NYSE.RET)
lmacfPlot(NYSE.RET, lag.max = 63, type = "acf")
title(main = "\n\nNYSE INDEX")
grid()
lmacfPlot(NYSE.RET, lag.max = 63, type = "hurst")
title(main = "\n\nNYSE INDEX")
grid()
# Output:
# Long Memory Autocorrelation Function:
# Maximum Lag 63
# Cut-Off ConfLevel 0.01978551
# Plot-Intercept -1.280071
# Plot-Slope -0.2805422
# Hurst Exponent 0.8597289
###
# ------------------------------------------------------------------------------
### 1.4.3 Example: Plot USDDEM and NYSE Lagged Correlations
# Graph Frame:
par(mfrow = c(2, 2), cex = 0.7)
###
# Load USDDEM Data, Convert to 'timeSeries' Object
URL = "http://www.itp.phys.ethz.ch/econophysics/R/data/textbooks/"
SRC = "Wuertz/data/usddem30u.csv"
DATA = paste(URL, SRC, sep = "")
download.file(DATA, destfile = "usddem30u.csv")
USDDEM = readSeries("usddem30u.csv")
print(USDDEM[1,])
print(end(USDDEM))
# Extract Bid Series:
USDDEM.BID = USDDEM[, "BID"]
###
# Plot Lagged Correlations:
lacfPlot(USDDEM.BID, n = 6, lag.max = 15)
title(main = "\n\nUSDDEM: 30 min - 3 Business hours")
lacfPlot(USDDEM.BID, n = 22, lag.max = 15)
title(main = "\n\nUSDDEM 30 min day - 1 Business Day")
###
# Load NYSE Data and Convert to timeSeries Object:
NYSE = as.timeSeries(data(nyse))
# Use only Data Before the Index Definition was Changed:
NYSE = cut(NYSE, "1966-01-01", "2002-12-31")
###
# Plot Lagged Correlations:
lacfPlot(NYSE, n = 5, lag.max = 15)
title(main = "\n\nNYSE: 1 day - 1 week")
lacfPlot(NYSE, n = 20, lag.max = 15)
title(main = "\n\nNYSE: 1 day - 1 month")
###
# ------------------------------------------------------------------------------
### 1.4.3 Example: Plot Lagged Correlations from Simulated Series
# Graph Frame:
par(mfrow = c(2, 2), cex = 0.7)
###
# Load NYSE Data and Convert to timeSeries Object:
NYSE = as.timeSeries(data(nyse))
# Use only Data Before the Index Definition was Changed:
NYSE = cut(NYSE, "1966-01-01", "2002-12-31")
###
# Simulate Index by Normal Series:
set.seed(4711)
nyse.ret = as.vector(returnSeries(NYSE))
Mean = mean(nyse.ret)
SD = sd(nyse.ret)
nyse.norm = rnorm(length(nyse.ret), mean = Mean, sd = SD)
nyse.norm = exp(cumsum(nyse.norm))
lacfPlot(nyse.norm, n = 5, lag.max = 15)
title(main = "\n\nNormal Series: 1 day - 1 week")
###
# Simulate Index by AR(1) autoregresssive Series:
set.seed(4711)
ar = pacf(nyse.ret, plot = FALSE)$acf[1]
nyse.ar = arima.sim(length(nyse.ret), model = list(ar = ar))
nyse.ar = ((nyse.ar-mean(nyse.ar))/sd(nyse.ar) ) * SD + Mean
nyse.ar = exp(cumsum(nyse.ar))
lacfPlot(nyse.ar, n = 5, lag.max = 15)
title(main = "\n\nAR(1) Series: 1 day - 1 week")
###
# ------------------------------------------------------------------------------
### 1.4.4 Example: Display the Taylor Effect
# Graph Frame:
par(mfrow = c(2, 2), cex = 0.7)
###
# Taylor Effect - NYSE Data:
NYSE = as.timeSeries(data(nyse))
NYSE.RET = outlier(returnSeries(NYSE))
teffectPlot(NYSE.RET, deltas = seq(from = 0.2, to = 3, by = 0.1))
title(main = "\n\nNYSE Composite Index", cex = 0.5)
###
# Taylor Effect - USDCHF Data:
USDCHF.RET = returnSeries(as.timeSeries(data(usdchf)))
teffectPlot(USDCHF.RET, deltas = seq(from = 0.2, to = 3, by = 0.1))
title(main = "\n\nUSDCHF Exchange Rate", cex = 0.5)
###
# ------------------------------------------------------------------------------
### 1.4.5 Example: Compare with Normal Rvs and AR Model
# Normal RVs:
Mean = mean(as.vector(NYSE.RET)); SD = sd(as.vector(NYSE.RET))
RNORM = rnorm(9813, mean = Mean, sd = SD)
teffectPlot(RNORM, deltas = seq(from = 0.2, to = 3, by = 0.1))
title(main = "\n\nNYSE - Normal RVs", cex = 0.5)
###
# Simulated AR Model - Standardised :
AR = arima.sim(9813, model = list(ar = c(0.124, -0.033)))
AR = ( (AR-mean(AR))/sd(AR) ) * SD + Mean
teffectPlot(AR, deltas = seq(from = 0.2, to = 3, by = 0.1))
title(main = "\n\nNYSE - AR Model", cex = 0.5)
###
# ------------------------------------------------------------------------------
### 1.4.6 Example: Absolute Value Scaling
# Absolute Value Scaling of daily NYSE Index:
NYSE = outlier(returnSeries(as.timeSeries(data(nyse))))
scalinglawPlot(NYSE, span = 6)$fit$coefficients
title(main = "\n\nNYSE")
# Output:
# Intercept X
# 4.1767239 0.5277384
###
# Absolute Value Scaling of 30m USDCHF Rates:
USDCHF = returnSeries(as.timeSeries(data(usdchf)))
scalinglawPlot(x = USDCHF, span = 6)$fit$coefficients
title(main = "\n\nUSDCHF")
# Output:
# Intercept X
# 3.7083449 0.5225638
###
# ------------------------------------------------------------------------------
### CodeSnippet: 'scalinglawPlot' Function
# Function:
.scalinglawPlot = function (x, span = 6)
{
# We expect a Return series from the Input:
x = as.vector(x); y = (x - mean(x))
logprices = cumsum(y)
# Internal Scaling Function - Absolute Value Scaling:
scale = function(n, logprices) {
sum(abs(diff(logprices, lag = (2^n)))) }
# Aggregate on log(2) Scale:
x = (0:span) * log(2)
y = log(apply(matrix(0:span), 1, scale, logprices))
# Fit a straight Line:
fit = lsfit(x, y)$coefficient[[2]]
# Return Value:
c(d = fit, alpha = 1/fit)
}
###
# Try:
.scalinglawPlot(x = NYSE)
# Output:
# d alpha
# 0.5277384 1.8948784
###
################################################################################
|
