## TESTING FOR STRUCTURAL CHANGE ----

## There appears to be structural differences in valuation during the 1920's and 1930's and then again in the last 60's
## and early 70's. Run a version of the Chow Test with dummy variables to determine if there were structural breaks.

## Define dummy variables for 20's & 30's and 60's & 70's separately. We are creating two dummy variables as we don't
## know if the nature of the structural change is the same or different for the two time periods.

df.3$D1 <- NA

df.3$D2 <- NA

for(i in 1:length(df.3$Dates)){
        
        if(df.3$Dates[i] < 1940){
                
                df.3$D1[i] <- 1
                
        } else {
                
                df.3$D1[i] <- 0
                
        }
        
        if(df.3$Dates[i] > 1965 & df.3$Dates[i] < 1975){
                
                df.3$D2[i] <- 1
                
        } else {
                
                df.3$D2[i] <- 0
        }
        
}

## Create Interaction terms between dummy variables and CAPE Ratio.

df.3$I1 <- df.3$CAPE*df.3$D1

df.3$I2 <- df.3$CAPE*df.3$D2

## Chow Test Model

chow_model <- lm(df.3$Annualized ~., data = df.3[ ,c(-2,-3)])

summary(chow_model)