### Method 2: Moving Average and Exponential Smoothing Approach

### Part A: Moving Average
#install.packages('zoo')
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(zoo)

## Warning: package 'zoo' was built under R version 4.4.2

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

#Time Series Data
df <- data.frame(month=c(1,2,3,4,5,6,7,8,9,10,11,12),
                 data=c(240, 352, 230, 260, 280, 322, 220, 310, 240, 310, 240, 230))

#Descriptive statistics
summary(df)

##      month            data      
##  Min.   : 1.00   Min.   :220.0  
##  1st Qu.: 3.75   1st Qu.:237.5  
##  Median : 6.50   Median :250.0  
##  Mean   : 6.50   Mean   :269.5  
##  3rd Qu.: 9.25   3rd Qu.:310.0  
##  Max.   :12.00   Max.   :352.0

#Interpretation: The average of sales over a 12 month period is 269.5

#Time series plot
plot(df$month, df$data, type = "o", col = "blue", xlab = "Month", ylab = "Contracts",
     main = "Alabama Building Contracts")

# Interpretation: The timeseries plot shows a horizontal pattern

# Mannually calculate the Three-Month Moving Average
df$avg_data3 <- c(NA, NA,
                  (df$data[1] + df$data[2] + df$data[3]) / 3,
                  (df$data[2] + df$data[3] + df$data[4]) / 3,
                  (df$data[3] + df$data[4] + df$data[5]) / 3,
                  (df$data[4] + df$data[5] + df$data[6]) / 3,
                  (df$data[5] + df$data[6] + df$data[7]) / 3,
                  (df$data[6] + df$data[7] + df$data[8]) / 3,
                  (df$data[7] + df$data[8] + df$data[9]) / 3,
                  (df$data[8] + df$data[9] + df$data[10]) / 3,
                  (df$data[9] + df$data[10] + df$data[11]) / 3,
                  (df$data[10] + df$data[11] + df$data[12]) / 3
)

df <- df %>%
  mutate(
    squared_error = ifelse(is.na(avg_data3), NA, (data - avg_data3)^2)
  )

#Compute MSE (excluding the intial weeks with NA)
mse <- mean(df$squared_error, na.rm = TRUE)
mse

## [1] 996.8

###Part B: Expontential Smoothing

alpha <- 0.2
exp_smooth <- rep(NA, length(df$data))
exp_smooth[1] <- df$data[1] #Starting point
for (i in 2:length(df$data)) {
  exp_smooth[i] <- alpha * df$data[i] + (1 - alpha) * exp_smooth[i-1]
}
mse_exp_smooth <- mean((df$data[2:length(df$data)] - exp_smooth[2:length(exp_smooth)])^2)
mse_exp_smooth

## [1] 1660.007

###Part C: Comparison
better_method <- ifelse(mse < mse_exp_smooth, "Moving Average", "Exponential Smoothing")
#Results
list(
  MSE_Moving_Average = mse,
  MSE_Expontential_Smoothing = mse_exp_smooth,
  Better_Method = better_method
)

## $MSE_Moving_Average
## [1] 996.8
## 
## $MSE_Expontential_Smoothing
## [1] 1660.007
## 
## $Better_Method
## [1] "Moving Average"