##### Exam 2 - Answers (Code) ######

######## QUESTION 3 ########
RE_da <- read.csv("http://www.bauer.uh.edu/rsusmel/4397/Real_Estate_2023.csv", head=TRUE, sep=",")
summary(RE_da)

x_date <- RE_da$DATE
x_sf <- RE_da$SF_c
x_sd <- RE_da$SD_c
x_usa <- RE_da$USA_c
u_sf <- RE_da$SF_u
u_sd <- RE_da$SD_u
x_tech <- RE_da$Tech_c 
Cind <- RE_da$Cind_c
Nind <- RE_da$Nind_c
x_Mkt <- RE_da$Mkt_RF
x_SMB <- RE_da$SMB
x_HML <- RE_da$HML
x_RMW <- RE_da$RMW
x_CMA <- RE_da$CMA
x_RF <- RE_da$RF
Mkt_RF <- x_Mkt/100
SMB <- x_SMB/100
HML <- x_HML/100
RMW <- x_RMW/100
CMA <- x_CMA/100
RF <- x_RF/100
oil <- RE_da$Oil
gold <- RE_da$Gold

zz <- x_sf
T <- length(x_sd)
T_sb <- 224
T_end_reg2 <- T - T_sb
Fin_c0 <- rep(0,T_sb)
Fin_c1 <- rep(1,T_end_reg2)
Fin_c <- c(Fin_c0,Fin_c1)								# Create 2008 Financial crisis dummy
Feb1 <- rep(c(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (length(zz)/12+1))	# Create January dummy
Mar1 <- rep(c(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (length(zz)/12+1))	# Create March dummy
Apr1 <- rep(c(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (length(zz)/12+1))	# Create April dummy
May1 <- rep(c(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (length(zz)/12+1))	# Create May dummy
Jun1 <- rep(c(0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0), (length(zz)/12+1))	# Create June dummy
Jul1 <- rep(c(0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0), (length(zz)/12+1))	# Create Jul dummy
Aug1 <- rep(c(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0), (length(zz)/12+1))	# Create Aug dummy
Sep1 <- rep(c(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0), (length(zz)/12+1))	# Create Sep dummy
Oct1 <- rep(c(0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0), (length(zz)/12+1))	# Create Oct dummy
Nov1 <- rep(c(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0), (length(zz)/12+1))	# Create Oct dummy
Dec1 <- rep(c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0), (length(zz)/12+1))	# Create Oct dummy
Feb <- Feb1[1:T]
Mar <- Mar1[1:T]
Apr <- Apr1[1:T]
May <- May1[1:T]
Jun <- Jun1[1:T]
Jul <- Jul1[1:T]
Aug <- Aug1[1:T]
Sep <- Sep1[1:T]
Oct <- Oct1[1:T]
Nov <- Nov1[1:T]
Dec <- Dec1[1:T]
Spring <- Mar + Apr + May
Summ <- Jun + Jul + Aug
Fall <- Sep + Oct + Nov
u_sf2 <- u_sf^2
x_usa2 <- x_usa^2
x_tech2 <- x_tech^2
Cind2 <- Cind^2
u_sf_Cind <- u_sf*Cind
u_sf_tech <- u_sf*x_tech
u_sf_Spring <- u_sf*Spring
u_sf_Summ <- u_sf*Summ
u_sf_Fall <- u_sf*Fall
Cind_Spring <- Cind*Spring
Cind_Summ <- Cind*Summ
Cind_Fall <- Cind*Fall
tech_Spring <- x_tech*Spring
tech_Summ <- x_tech*Summ
tech_Fall <- x_tech*Fall
u_sf_Finc <- u_sf*Fin_c
Cind_Finc <- Cind*Fin_c
tech_Finc <- x_tech*Fin_c
Finc_Spring <- Fin_c*Spring
Finc_Summ <- Fin_c*Summ
Finc_Fall <- Fin_c*Fall


## 1.a - Report GUM 

fit_sf_gum <- lm(formula = x_sf ~ x_usa + u_sf + x_tech + Cind + + Mkt_RF + SMB + HML + RMW + CMA + gold + oil + x_usa2 +
                   u_sf2 + Cind2 + x_tech2 + Spring + Summ + Fall + Fin_c + u_sf_Cind + u_sf_tech + u_sf_Spring + 
                   u_sf_Summ + u_sf_Fall + Cind_Spring + Cind_Summ + Cind_Fall + 
                   tech_Spring + tech_Summ + tech_Fall + u_sf_Finc + Cind_Finc + 
                   tech_Finc + Finc_Spring + Finc_Summ + Finc_Fall)

summary(fit_sf_gum)


## 1.b Use p-value = 0.05. Report reduced model
fit_sf_red <- lm(x_sf ~ x_usa + u_sf + x_usa2 +  Fin_c + Cind_Spring + u_sf_Finc + Cind_Fall)
summary(fit_sf_red)

## 1,c Report R2
# R2 = 70.67% (70.67% of variability of sf changes in prices explained by factors in reduced model)

## 1.d -  Drivers (variables with significant t-stats a)
# Drivers: x_usa, u_sf, x_usa2, Financial crisis, interactions terms with Financial crisis and Economic Conditions with Spring & Falll

## 1.e - Evidence of Seasonality?
# None of the seasonal dummies shows up as significant directly, but the indirect effect of Spring with Economic Conditions is very significant in the Reduced Model.

## 1.f - LM Tests for autocorrelation (DW & BG) and Heteroscedasticity (GQ & BP)
dwtest(fit_sf_red)
bgtest(fit_sf_red, order=4)

## 1.g - LM Tests for autocorrelation (DW & BG) and Heteroscedasticity (GQ & BP)
gqtest(fit_sf_red)
bptest(fit_sf_red)

## 1.h - White and NW SE
# At 5% level, we have evidence of both heteroscedasticiy & autocorrelation. Then, use NW SE.
Var_NW <- NeweyWest(fit_sf_red, lag = 12)
SE_NW <- sqrt(diag(Var_NW))
b_sf_red <- fit_sf_red$coefficients
t_b_NW <- b_sf_red/SE_NW
t_b_NW

# Once, we take into account autocorrelation and heteroscedasticity the signficance at 5% level not affected


######## QUESTION 2 ########

## 2.a Model For Dependent Variable	(y = x_sf)
y <- x_sf
T1 <- 396	

xx <- cbind(x_usa, u_sf)						# Independent Variables
y1 <- y[1:T1]						    # Estimation period data
xx1 <- xx[1:T1,]						    # Estimation period data
fit_y <- lm(y ~ xx)						# Estimation Period Regression for SF_c
b_y <- fit_y$coefficients
summary(fit_y)

## 2.b Model Forecast p_t+1 = (SF_c_t+1)
k_for <- T-T1
xx_cons <- rep(1,T_for)
T_val <- T1 + 1
y_f0 <-  cbind(xx_cons,xx[T1:(T-1)])%*% b_y1		# b_est coefficients from estimation period regresssion
e_f0 <- y_f0 - y[T_val:T]				# Forecasat error
mse_e_f0 <- sum(e_f0^2)/k_for				# MSE
mse_e_f0						# MSE(2)	=> et(2)


## 2.c RW Forecast p_t+1 = (SF_c_t+1)
e_rw_f0 <- y[T_val:T] - y[T1:(T-1)]			# Error for RW model =>  et (1) 	
mse_e_rw_f0 <- sum(e_rw_f0^2)/k_for	
mse_e_rw_f0

## 2.d Testing Equality of MSE: Model vs RW
z_mgn <- e_rw_f0 + e_f0 
x_mgn <- e_rw_f0 - e_f0 
fit_mgn <- lm(z_mgn ~ x_mgn)	
summary(fit_mgn)    


######## QUESTION 3 ########
SFX_da <- read.csv("http://www.bauer.uh.edu/rsusmel/4397/Stocks_FX_1973.csv",head=TRUE,sep=",")
names(SFX_da)
x_dat <- SFX_da$Date
x_unp <- SFX_da$UNP
x_xom <- SFX_da$XOM
x_Mkt_RF<- SFX_da$Mkt_RF
x_SMB <- SFX_da$SMB
x_HML <- SFX_da$HML
x_CMA <- SFX_da$CMA
x_RMW <- SFX_da$RMW
x_RF <- SFX_da$RF

T <- length(x_SMB)
lr_unp <- log(x_unp[-1]/x_unp[-T])
Mkt_RF <- x_Mkt_RF[-1]/100
SMB <- x_SMB[-1]/100
HML <- x_HML[-1]/100
CMA <- x_CMA[-1]/100
RMW <- x_RMW[-1]/100
RF <- x_RF[-1]/100

unp_x <- lr_unp - RF			# UNP excess returns 

## 3.a
fit1 <- lm(unp_x ~ Mkt_RF + SMB + HML)		# Model 1
summary(fit1)

fit2 <- lm(unp_x ~ Mkt_RF + CMA + RMW) 		# Model 2
summary(fit2)


## 3.b
library(lmtest)
jtest(fit1,fit2)

## 3.c
fit_enc <- lm( unp_x ~ Mkt_RF + SMB + HML + lr_cs + CMA + RMW)
summary(fit_enc)

encomptest(fit1,fit2)


######## QUESTION 4 - THEORY REVIEW ######
# 4.a. False. IF there is endogeneity -i.e., X is related to error term-, OLS is inconsistent.
# 4.b. True. NWSE are not efficient. Estimators that incorporate the true model for (A3) will be efficient.
# 4.c. False. The reverse is true.
# 4.d. True. The asymptotic distribution gives an approximation to the small sample distribution (hopefully, a good one)
# 4.e. False. Type I and Type II errors make this task impossible for GETS.