#############  Testing in the CLM: Nested and Non-Nested Formulations (Code #7) #############

SFX_da <- read.csv("http://www.bauer.uh.edu/rsusmel/4397/Stocks_FX_1973.csv",head=TRUE,sep=",")
names(SFX_da)
x_sp <- SFX_da$SP500
x_ibm <- SFX_da$IBM
x_Mkt_RF<- SFX_da$Mkt_RF
x_SMB <- SFX_da$SMB
x_HML <- SFX_da$HML
x_RF <- SFX_da$RF

T <- length(x_ibm)
lr_ibm <- log(x_ibm[-1]/x_ibm[-T])
lr_sp <- log(x_sp[-1]/x_sp[-T])
x0 <- matrix(1,T-1,1)
 Mkt_RF <- x_Mkt_RF[-1]/100
 SMB <- x_SMB[-1]/100
 HML <- x_HML[-1]/100
 RF <- x_RF[-1]/100

ibm_x <- lr_ibm - RF

####  Testing Linear Hypothesis in the Fama-French 3 factor Linear Model
ibm_x <- lr_ibm - RF
x <- cbind(x0, Mkt_RF, SMB, HML)
k <- ncol(x)

# OLS results
fit_ibm_ff3 <- lm(ibm_x ~ Mkt_RF + SMB + HML)
summary(fit_ibm_ff3)


## Test Linear Restrictions using R package "car"
install.packages("car")
library(car)

linearHypothesis(fit_ibm_ff3, c("SMB = 0.2","HML = 0.6"), test="F")	# Exact F test
linearHypothesis(fit_ibm_ff3, c("SMB = 0.2","HML = 0.6"), test="Chisq")	# Asymptotic F-test

linearHypothesis(fit_ibm_ff3, c("SMB = HML"), test="F")	# testing beta_SMB = beta_HMB

linearHypothesis(fit_ibm_ff3, c("SMB + HML = 1"), test="F")	# testing beta_SMB + beta_HMB = 1



####  Goodness of Fit Model
y <- ibm_x
T <- length(y)
x0 <- matrix(1,T,1)
x <- cbind(x0, Mkt_RF, SMB, HML)
k <- ncol(x)					# Unrestricted k
e <- fit_ibm_ff3$residuals			# we could have used e <- y - x%*%b
RSS <- sum(e^2)					# If using e <- y - x%*%b you should use RSS <- as.numeric(t(e)%*%e)
R2 <- 1 - RSS/sum(y^2)				# R-squared
R2 
summary(fit_ibm_ff3)$r.squared			# extracting R-squared from fit_ibm_ff3

F_goodfit <- (R2/(k-1))/((1-R2)/(T-k))		#F-test of goodness of fit.
F_goodfit



####  Testing with Unrestricted and Restricted Estimations
x_r <- cbind(x0,Mkt_RF)				# Restricted X vector
k_r <- ncol(x_r)

fit_ibm_ff3_R <- lm(y ~ Mkt_RF)			# CAPM estimation
summary(fit_ibm_ff3_R)
eR <- fit_ibm_ff3_R$residuals			# extracting Restricted residuals

RSSR <- as.numeric(t(eR)%*%eR)
J <- k - k_r				# J = degrees of freedom of numerator 
F_test <- ((RSSR - RSS)/J)/(RSS/(T-k))
F_test

qf(.95, df1=J, df2=(T - k)) 			# exact distribution (F-dist) if e normal
p_val <- 1 - pf(F_test, df1=J, df2=(T - k)) 	# p-value(F_t) under e normal
p_val


###  Testing with package lmtest
install.packages("lmtest")
library(lmtest)
fit_wU <- lm (y ~ Mkt_RF + SMB + HML)
fit_wR <- lm (y ~ Mkt_RF)
waldtest(fit_wU, fit_wR)


##### Testing for Structural Change (Chow Test): Dot.com Bubble (T_sb = 347)
## Pooled RSS  (1973 - 2023)
e_p <- fit_ibm_ff3$residuals			# extract residuals from pooled FF regression
RSS_p <- sum(e_p^2)

## Before T_sb RSS  (1973 - 2001)
T_sb <- 347
y1 <- y[1:T_sb]
x1 <- x[1:T_sb,] 
fit_ibm_ff3_1 <- lm(y1 ~ x1 -1)			# Add -1 inside lm() so no constant is added to regressors
summary(fit_ibm_ff3_1)
e_1 <- fit_ibm_ff3_1$residuals			# extract residuals from pooled FF regression
RSS_1 <- sum(e_1^2)

## After T_sb RSS  (2002 - 2023)
T2 <- T_sb + 1
y2 <- y[T2:T]
x2 <- x[T2:T,] 
fit_ibm_ff3_2 <- lm(y2 ~ x2 -1)			# Add -1 inside lm() so no constant is added to regressors
summary(fit_ibm_ff3_2)
e_2 <- fit_ibm_ff3_2$residuals			# extract residuals from pooled FF regression
RSS_2 <- sum(e_2^2)

## Compute Chow test
F_chow_t <- ((RSS_p - (RSS_1 + RSS_2))/k) / ((RSS_1 + RSS_2)/(T-2*k))		# Chow test (F-test) 
F_chow_t
p_val <- 1 - pf(F_chow_t, df1=k, df2=(T - 2*k)) 	# p-value(F_t) under e normal
p_val

## Compute Chow test with R package strucchange
library(strucchange)
sctest(ibm_x ~ Mkt_RF + SMB + HML, type = "Chow", point = t_s)