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#
# Examples:
# A Compendium for R and Rmetrics users to the book
# "The Econometric Modelling of Financial Time Series"
# written by T.C. Mills
# ISBN 0-521-62492-4
#
# Description:
# See Chapter 2 of the book.
#
# Author:
# (C) Rmetrics 1997-2005, Diethelm Wuertz, GPL
# www.rmetrics.org
# www.itp.phys.ethz.ch
# www.finance.ch
#
################################################################################
### Mills 2.1:
# Load Data:
data(SP500R)
x = SP500R[,1]
# Sample Autocorrelation Function:
rk = round(acf(x, 12)$acf[,,1][-1], 3)
names(rk) = paste("lag", 1:12, sep = "")
rk
# 95% Confidence Interval:
ci95 = round(2/sqrt(length(x)), 3)
ci95
# Q(k) Statistics:
Qk = NULL
for (lag in 1:12 )
Qk = c(Qk, Box.test(x, lag, "Ljung-Box")$statistic)
names(Qk) = paste("lag", 1:12, sep = "")
round(Qk, 2)
# ------------------------------------------------------------------------------
### Mills 2.2
# Time Series Data:
data(R20); data(RS)
x = (R20-RS)[, 1]
time = 1952+(1:length(x))/12
plot(time, x, type = "o", pch = 19, cex = 0.5)
# Parameter Estimation:
fit = armaFit(x ~ ar(2), "ols")@fit
# Estimated Parameters and Standard Errors:
round(rbind(coef = fit$coef, se.coef = fit$se.coef), 3)
# sigma:
round(sqrt(fit$sigma2[[1]]), 3)
# Compute Sample ACF and Sample PACF:
N = length(x)
ACF = acf(x, lag.max = 12)$acf[,,1]
seACF = sqrt(1/N)
for (k in 2:12) seACF =
c(seACF, sqrt((1+2*sum(ACF[2:k]^2))/N))
PACF = pacf(x, lag.max = 12)$acf[,,1]
sePACF = rep(sqrt(1/N), times = 12)
# Reproduce Table 2.2 in Mills' Textbook:
data.frame(round(cbind(
"r_k" = ACF[-1], "se" = seACF,
"phi_kk" = PACF, "se" = sePACF ), 3) )
# Create Graphs:
par(mfrow = c(2,2), cex = 0.7)
acfPlot(x, 12, main = "ACF: UK IR Spread" )
points(0:12, c(0,seACF), pch=19, col = "steelblue")
pacfPlot(x, 12,main = "PACF: UK IR Spread")
# ------------------------------------------------------------------------------
### Mills 2.3
# Load Data:
data(FTARET)
x = FTARET[,1]
# Sample Autocorrelation Function:
round(acf(x, 12)$acf[,,1], 3)[-1]
# IC Statistics:
N = length(x)
n = 4
BIC = AIC = matrix(rep(0, n^2), n)
for (p in 0:(n-1) ) {
for (q in 0:(n-1) ) {
Formula = paste("x ~arima(", p, ",0,", q, ")", sep = "")
fit = armaFit(as.formula(Formula), method = "ML")@fit
AIC[p+1, q+1] = log(fit$sigma2) + 2*(p+q) / N
BIC[p+1, q+1] = log(fit$sigma2) + log(N)*(p+q) / N
}
}
rownames(AIC) = colnames(AIC) = as.character(0:(n-1))
print(round(max(AIC) - AIC, 3))
rownames(BIC) = colnames(BIC) = as.character(0:(n-1))
print(round(max(BIC) - BIC, 3))
# ------------------------------------------------------------------------------
### Mills 2.4: Modelling the UK Spread as an Integrated Process
# Load Data:
data(R20); data(RS)
x = diff((R20-RS)[, 1])
# Sample ACF and Sample PACF:
data.frame(round(rbind(
"r(k)" = acf(x, lag.max = 12)$acf[,,1][-1],
"phi(kk)" = pacf(x, lag.max = 12)$acf[,,1]), 3))
# Fit AR(1):
fit = arima(x, order = c(1, 0, 0))
fit
# Portmanteau Statistic of Q(12):
Box.test(x = fit$residuals, lag = 12, "Ljung-Box")$statistic
# ------------------------------------------------------------------------------
### Mills 2.5: Modelling the Dollar/Sterling Exchange Rate
par (mfrow = c(2, 2), cex = 0.7)
data(EXCHD)
x = EXCHD[,1]
ts.plot(x)
x = diff(x)
plot(x, type = "l", ylim = c(-0.1, 0.1))
grid()
# ------------------------------------------------------------------------------
### Mills 2.6: Modelling the FTA ALL Share Index
data(FTAPRICE)
x = FTAPRICE[,1]
par (mfrow = c(2, 2), cex = 0.7)
ts.plot(x)
ts.plot(x, log = "y")
x = diff(log(x))
arima(x, order = c(3, 0, 0))
# Sample ACF and Sample PACF:
data.frame(round(rbind(
"r(k)" = acf(x, lag.max = 12)$acf[,,1][-1],
"phi(kk)" = pacf(x, lag.max = 12)$acf[,,1]), 3))
# ------------------------------------------------------------------------------
### Mills 2.7: ARIMA Forecasting of Financial Time Series
# Time Series Data:
data(R20); data(RS)
x = (R20-RS)[, 1]
x[525:526]
fit = armaFit(x ~ ar(2), "ols", include.mean = FALSE)
pred = predict(fit, 5)
fit = armaFit(x ~ ar(2), "ols", include.mean = TRUE)
pred = predict(fit, 5)
################################################################################
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