############# EMH Hypothesis: Autocorrelation & VR Tests & (Code #EMH) #############

########## Autocorrelation & VR Tests
## Need to install package vrtest 


###### Reading Monthly Data

EMH_da <- read.csv("http://www.bauer.uh.edu/rsusmel/4397/crsp_ew_vw_m.csv",head=TRUE,sep=",")

x_date <- EMH_da$DATE
lr_vw <- EMH_da$vwretd			# Value weighted CRSP Return (including distributions)
lr_ew <- EMH_da$ewretd			# Equal weighted CRSP Return (including distributions)
lr_sp <- EMH_da$sprtn			# SP500 total return

T <- length(lr_vw)


#### Descriptive stats and ACF
y <- lr_vw
summary(y)

SE_rho <- 1/sqrt(T)			# Asymptotic SE for rho’s: |rho| > 2 * SE => significant
SE_rho

y_acf <- acf(y)
y_acf


#### Q & LB Autocorrelation Tests & Q* Automatic Lag Selection Test

Box.test(y, lag = 4, type="Box-Pierce")
Box.test(y, lag = 12, type="Box-Pierce")
Box.test(y, lag = 4, type="Ljung-Box")
Box.test(y, lag = 12, type="Ljung-Box")

library(vrtest)
Auto.Q(y, 12)				# Q* test automatic selection of p



#### Q & LB Heteroscedasticity Tests
y2 <- y^2

Box.test(y2, lag = 12, type="Ljung-Box")
Box.test(y2, lag = 6, type="Ljung-Box")
Box.test(y2, lag = 3, type="Ljung-Box")


#### AR(1) Regression	
y_1 <- y[1:(T-1)]					# Estimation period data
y_0 <- y[2:T]						# Estimation period data

fit_ar1 <- lm(y_0 ~ y_1)
summary(fit_ar1)


#### AR(p) Regression
p_lag <- 12
y_lag <- matrix(0,T-p_lag,p_lag)
a <- 1
while (a <= p_lag) {
  za <- y[a:(T-p_lag+a-1)]
  y_lag[,a] <- za 
a <- a+1
}
y_lag[1:12,]

fit_ar_p <- lm(y[(p_lag+1):T] ~ y_lag)
summary(fit_ar_p)
b_ar_p <- fit_ar_p$coefficients

library(sandwich)
NW <- NeweyWest(fit_ar_p, lag = 12, prewhite = FALSE)	# with 12 lags
SE_NW <- diag(sqrt(abs(NW)))
t_NW <- b_ar_p/SE_NW

SE_NW
t_NW


#######  VR Tests with vrtest package (need to install it first)
kvec <- c(2,3,12)				# Vector with different q

vr_1 <- VR.minus.1(y, kvec)			# Stat should be close to 0 if RW
vr_1

sqrt(T*2)/sqrt(2)*vr_1$VR.kvec[1]		 # VR test for q=kvec[1] = 2 (Standard Normal dist)

sqrt(T*kvec)/sqrt(2*(kvec-1))*vr_1$VR.kvec	 # VR test for each q=kvec[i] (Standard Normal dist)


Auto.VR(y)					# VR Test with automatic q selection
AutoBoot.test(y, nboot=1000, wild="Normal",prob=c(0.025,0.975))	# Bootstrap for Auto.VR, as in Choi (1999)

Lo.Mac(y, kvec)					# Lo-MacKinlay's M1 and M2 tests
Boot.test(y, kvec, nboot=1000, wild="Normal", prob=c(0.025,0.975))	# Bootstrap for Lo.Mac M2 tests, as in Kim (2006)

Wald(y, kvec)					# RS Wald test

Chen.Deo(y, kvec)				# QP Wald test



###### Reading Daily Data

EMH_d_da <- read.csv("http://www.bauer.uh.edu/rsusmel/4397/crsp_ew_vw_d.csv",head=TRUE,sep=",")

lr_vw_d <- EMH_d_da$vwretd		# Value weighted CRSP returns (including distributions)
lr_ew_d <- EMH_d_da$ewretd		# Equal weighted CRSP returns (including distributions)
T <- length(lr_ew_d)

y <- lr_vw_d
kvec <- c(5,20,60)				# Vector with different q

vr_1 <- VR.minus.1(y, kvec)			# Stat should be close to 0 if RW
vr_1

sqrt(T*kvec)/sqrt(2*(kvec-1))*vr_1$VR.kvec	 # VR test for each q=kvec[i] (Standard Normal dist)

AutoBoot.test(y, nboot=1000, wild="Normal",prob=c(0.025,0.975))	# Bootstrap for Auto.VR, as in Choi (1999)

Lo.Mac(y, kvec)					# Lo-MacKinlay's M1 and M2 tests
Boot.test(y, kvec, nboot=1000, wild="Normal", prob=c(0.025,0.975))	# Bootstrap for Lo.Mac M2 tests, as in Kim (2006)

Wald(y, kvec)					# RS Wald test

Chen.Deo(y, kvec)				# QP Wald test



###### Reading Annual Data
EMH_d_a <- read.csv("http://www.bauer.uh.edu/rsusmel/4397/goyal-welch-a_27.csv",head=TRUE,sep=",")
names(EMH_d_a)

x_sp_a <- EMH_d_a$sp500index		# Value weighted CRSP returns (including distributions)
T <- length(x_sp)
lr_sp_a <- log(x_sp_a[-1]/x_sp_a[-T])

y <- lr_sp_a
kvec <- c(5,20,60)				# Vector with different q

vr_1 <- VR.minus.1(y, kvec)			# Stat should be close to 0 if RW
vr_1

sqrt(T*kvec)/sqrt(2*(kvec-1))*vr_1$VR.kvec	 # VR test for each q=kvec[i] (Standard Normal dist)

AutoBoot.test(y, nboot=1000, wild="Normal",prob=c(0.025,0.975))	# Bootstrap for Auto.VR, as in Choi (1999)


Lo.Mac(y, kvec)					# Lo-MacKinlay's M1 and M2 tests
Boot.test(y, kvec, nboot=1000, wild="Normal", prob=c(0.025,0.975))	# Bootstrap for Lo.Mac M2 tests, as in Kim (2006)