Class Exercise 16 Chapter 17

Question 1

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

#Most Recent Values as Forecast 
forecasts_a <- values[-length(values)] #exclude last value
actual_a <- values[-1] #exclude the first value
mse_a <- mean((actual_a - forecasts_a)^2)
mse_a
forecast_week_7_a <- tail(values, 1)
forecast_week_7_a

#Average of all the data as a forecast
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
forecast_week_7_BB <- mean(values, 1)
forecast_week_7_BB

mae_a <- mean(abs(actual_a - forecasts_a))
mae_a

Question 2

#Question 2: Time Series Plot 
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))
#Time Series Plot
plot(df$month, df$data, type = "o", col = "blue", xlab = "Month", ylab = "Value of Building Contracts",
     main = "Value of Alabama Building Contracts")

# Three-Month Moving Average 
df$avg_value <- c(NA, NA, NA,
                  (df$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)
 
#Calculate the squared errors 
df <- df %>%
  mutate(
    squared_error = ifelse(is.na(avg_value), NA, (data- avg_value)^2)
  )

#Compute MSE(excluding NA)
mse <- mean(df$squared_error, na.rm = TRUE)
mse #2040.44

#Exponential 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] + (1 - alpha) * exp_smooth[i-1]
}
mse_exp_smooth <- mean((df$data[2:12]- exp_smooth[2-12])^2)
mse_exp_smooth #2281.9

better_method <- ifelse(mse < mse_exp_smooth, "Three-month moving average", "Exponential Smoothing")
list(
  MSE_moving_average = mse,
  MSE_exponential_smoothing = mse_exp_smooth,
  Better_Method = better_method
) #Three Month Moving Average best because of smallest MSE 

Question 3

#Question 3: Linear Trend 
library(readxl)
library(ggplot2)
#Load the data
df1 <- read_excel(file.choose())

#Time Series Plot
ggplot(df1, aes(x = Period, y = "Interest_Rate")) +
  geom_line() +
  geom_point() + 
  xlab("Year") + 
  ylab("Revenue") +
  ggtitle("Time Series Plot of Fixed Mortgage Rate")

#Develop a linear trend equation 
model <- lm(Interest_Rate ~ Period, data = df1)
summary(model)
#Result - linear trend equation: Revenue = 6.7 - 0.13*Period

#Forecast for period 25 (2024)
forecast_period_25 <- predict(model, newdata = data.frame(Period = 25))
forecast_period_25
#3.47