laholmes · December 19, 2016 15:16
diff --git a/cointegration.R b/cointegration.R
 library('zoo')
 library('urca')

 prices <- read.zoo('./priceData.csv', sep=',', FUN = as.yearmon, format='%Y-%m', header=TRUE)

 # taking into account short term behaviour, derive the minimum variance hedge by fitting
 # a linear model that explains changes in B prices by changes in A prices
 # beta coefficient of the regression is the optimal hedge ratio

 # intercept is zero as no cash holdings
 simple_mod <- lm(diff(prices$B) ~ diff(prices$A) + 0)
 summary(simple_mod)
 # if hedge ratio <1, not a perfect hedge - the resulting hedged portfolio is still risky

 # try to improve on hedge ratio by using existing long-run relationship between levels
 # plot to get initial view on existence of such a relationship
 plot(prices$B, main='A and B prices', xlab='Date', ylab='USD')
 lines(prices$A, col='red')

 # using Engle and Granger's two-step estimation technique for cointegration

 # first test both time series for a unit root (non-stationarity), using augmented 
 # Dickey-Fuller test
 b_adf <- ur.df(prices$B, type='drift')
 summary(b_adf)
 # the null hypothesis of non-stationarity - time series contains a unit root, cannot be 
 # rejected at the 1% level id test statistic is not < 1% critical val

 # same is true for A prices?
 a_adf <- ur.df(prices$A, type='drift')
 summary(a_adf)

 # estimate the static equilibrium model + test residuals for a stationary
 # time series using augmented dickey fuller test
 # different critical values must be used as the series is an estimated one
 mod_static <- summary(lm(prices$B ~ prices$A))
 error <- residuals(mod_static)
 error_cadf <- ur.df(error, type='none')
 summary(error_cadf)
                          
 # if test stat < 1% crit value -> reject null hyp of non-stationarity

 # -> we have discovered two cointegrated variables, and can proceed
 # with specification of an error-correction model (ECM)
 # ECM represents a dynamic model of how (and how fast) the system moves back
 # to the static equilibrium estiamted earlier

 db <- diff(prices$B)
 da <- diff(prices$A)
 error_lag <- lag(error, k=-1)
 mod_ecm <- lm(db ~ da + error_lag + 0)
 summary(mod_ecm)

 # by taking into account existence of long-run relationship between 
 # A and A prices (cointegration), hedge ratio is now slightly higher
 # coefficient of the error term is negative - large deviations between the two
 # prices are going to be corrected and prices move closer to their 
 # long-run stable relationship
	library('zoo')
	library('urca')

	prices <- read.zoo('./priceData.csv', sep=',', FUN = as.yearmon, format='%Y-%m', header=TRUE)

	# taking into account short term behaviour, derive the minimum variance hedge by fitting
	# a linear model that explains changes in B prices by changes in A prices
	# beta coefficient of the regression is the optimal hedge ratio

	# intercept is zero as no cash holdings
	simple_mod <- lm(diff(prices$B) ~ diff(prices$A) + 0)
	summary(simple_mod)
	# if hedge ratio <1, not a perfect hedge - the resulting hedged portfolio is still risky

	# try to improve on hedge ratio by using existing long-run relationship between levels
	# plot to get initial view on existence of such a relationship
	plot(prices$B, main='A and B prices', xlab='Date', ylab='USD')
	lines(prices$A, col='red')

	# using Engle and Granger's two-step estimation technique for cointegration

	# first test both time series for a unit root (non-stationarity), using augmented
	# Dickey-Fuller test
	b_adf <- ur.df(prices$B, type='drift')
	summary(b_adf)
	# the null hypothesis of non-stationarity - time series contains a unit root, cannot be
	# rejected at the 1% level id test statistic is not < 1% critical val

	# same is true for A prices?
	a_adf <- ur.df(prices$A, type='drift')
	summary(a_adf)

	# estimate the static equilibrium model + test residuals for a stationary
	# time series using augmented dickey fuller test
	# different critical values must be used as the series is an estimated one
	mod_static <- summary(lm(prices$B ~ prices$A))
	error <- residuals(mod_static)
	error_cadf <- ur.df(error, type='none')
	summary(error_cadf)

	# if test stat < 1% crit value -> reject null hyp of non-stationarity

	# -> we have discovered two cointegrated variables, and can proceed
	# with specification of an error-correction model (ECM)
	# ECM represents a dynamic model of how (and how fast) the system moves back
	# to the static equilibrium estiamted earlier

	db <- diff(prices$B)
	da <- diff(prices$A)
	error_lag <- lag(error, k=-1)
	mod_ecm <- lm(db ~ da + error_lag + 0)
	summary(mod_ecm)

	# by taking into account existence of long-run relationship between
	# A and A prices (cointegration), hedge ratio is now slightly higher
	# coefficient of the error term is negative - large deviations between the two
	# prices are going to be corrected and prices move closer to their
	# long-run stable relationship