Hw2

library(readxl)
library(moments)

file_path <- "Data1930-2018.xlsx"
df <- read_excel(file_path)

## New names:
## • `` -> `...1`

colnames(df)[1] <- "Date"

df$Date <- as.numeric(df$Date)
midpoint <- nrow(df) %/% 2  
df_first_half <- df[1:midpoint, ]
df_second_half <- df[(midpoint + 1):nrow(df), ]

compute_stats <- function(data) {
  stats <- data.frame(
    Mean = colMeans(data, na.rm = TRUE),   # Calculate mean
    SD = apply(data, 2, sd, na.rm = TRUE), # Calculate standard deviation
    Skewness = apply(data, 2, skewness, na.rm = TRUE), # Calculate skewness
    Kurtosis = apply(data, 2, kurtosis, na.rm = TRUE)  # Calculate kurtosis
  )
  return(stats)
}
df_first_half_numeric <- df_first_half[, -1]
df_second_half_numeric <- df_second_half[, -1]
stats_first_half <- compute_stats(df_first_half_numeric)
stats_second_half <- compute_stats(df_second_half_numeric)

print("Summary statistics for the 1st half:")

## [1] "Summary statistics for the 1st half:"

print(stats_first_half)

##                 Mean        SD  Skewness  Kurtosis
## SMALL LoBM 0.9797676  8.211286 1.1852484 12.022978
## ME1 BM2    1.1645060  8.398445 1.6200903 15.900982
## SMALL HiBM 1.4797768 10.164258 2.3471818 20.526106
## BIG LoBM   0.7670809  5.706153 0.1649981  9.985251
## ME2 BM2    0.8096833  6.720350 1.7538693 20.724012
## BIG HiBM   1.1905485  8.894354 1.7614099 17.444886

print("Summary statistics for the 2nd half:")

## [1] "Summary statistics for the 2nd half:"

print(stats_second_half)

##                 Mean       SD   Skewness Kurtosis
## SMALL LoBM 1.0019195 6.706768 -0.4116903 5.097896
## ME1 BM2    1.3557365 5.301609 -0.5451070 6.447590
## SMALL HiBM 1.4331846 5.520672 -0.4717360 7.298135
## BIG LoBM   0.9786109 4.700148 -0.3329533 4.982457
## ME2 BM2    1.0632631 4.330084 -0.4586522 5.579832
## BIG HiBM   1.1273446 4.926489 -0.5464995 5.840161

comparison <- stats_first_half - stats_second_half
print("Difference in statistics (First Half - Second Half):")

## [1] "Difference in statistics (First Half - Second Half):"

print(comparison)

##                   Mean       SD  Skewness  Kurtosis
## SMALL LoBM -0.02215187 1.504518 1.5969387  6.925082
## ME1 BM2    -0.19123052 3.096836 2.1651973  9.453393
## SMALL HiBM  0.04659213 4.643586 2.8189177 13.227971
## BIG LoBM   -0.21152996 1.006005 0.4979513  5.002794
## ME2 BM2    -0.25357978 2.390266 2.2125215 15.144180
## BIG HiBM    0.06320393 3.967865 2.3079094 11.604725

#The study compares the statistical differences between the first and second halves of a dataset to determine if returns come from the same distribution over the entire period. The mean returns are relatively stable, with minor differences. The first half shows higher volatility, extreme deviations, and positive skewness, while the second half shows lower volatility, less extreme movements, and negative skewness. The differences in standard deviation, skewness, and kurtosis suggest that returns does not come from the same distribution over the entire period. These results suggest a structural change in the return distribution, possibly due to economic, financial, or policy changes over time.