Question 1

weeks <- 1:6
values <- c(17,13,15,11,17,14)

forecasts_a <- values[-length(values)]
actual_a <- values[-1]
mse_a <- mean((actual_a - forecasts_a)^2)
mse_a

mae <- abs(forecasts_a - actual_a)
mae
forecast_week_7 <- tail(values, 1)
forecast_week_7

cumulative_averages <- cumsum(values[-length(values)])/(1:(length(values)-1))
forecasts_b <- cumulative_averages
actual_b <- values[-1]
mse_b <- mean((actual_b - forecasts_b)^2)
mse_b

Question 2

install.packages("dplyr")
install.packages("zoo")

library(dplyr)
library(zoo)

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))

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

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

View(df)

mse <- mean((df$squared_error), na.rm = TRUE)
mse


alpha = 0.2
exp_smooth <- rep(NA, length(df$data))
exp_smooth[1] <- df$data[1]
for(i in 2:length(df$data)){
  exp_smooth[i] <- alpha * df$data[i-1] + (1-alpha) * exp_smooth[i-1]
}

mse_exp <- mean((df$data[2:12] - exp_smooth[2:12]) ^ 2)
mse_exp

Question 3 - 5

library(readxl)
library(ggplot2)

df1 <- read_excel(file.choose())
View(df1)

ggplot(df1, aes(x = Period, y = Interest_Rate)) + geom_line() + geom_point() + xlab("Year") + ylab("Interest Rate") + ggtitle("Time Series plot of Interest Rates")


model <- lm(Interest_Rate ~ Period, data = df1)
summary(model)


forecast_per_25 <- predict(model, newdata = data.frame(Period = 25))
forecast_per_25