Q. 1
# Time series data
weeks <- 1:6
values <- c(17, 13, 15, 11, 17, 14)
# Most recent value as forecast
forecasts_a <- values[-length(values)] #exclude the last value
actual_a <- values [-1] # exclude the first value
mse_a <- mean((actual_a - forecasts_a)^2)
mse_a # Result: 16.2
## [1] 16.2
forecast_week_7_a <- tail(values, 1)
forecast_week_7_a
## [1] 14
# Average all the data as a forecast
cumulative_averages <- cumsum(values[-length(values)]) / (1:(length(values) - 1))
cumulative_averages
## [1] 17.0 15.0 15.0 14.0 14.6
forecasts_b <- cumulative_averages
actual_b <- values[-1] # excludes the first value
mse_b <- mean((actual_b - forecasts_b)^2)
mse_b
## [1] 8.272
forecast_week_7_b <- mean(values) # average of all weeks as forecast for week 7
forecast_week_7_b
## [1] 14.5
# Which method is better?
better_method <- ifelse(mse_a < mse_b, "Most Recent Value", "Average of All Data")
list(
MSE_most_recent_value = mse_a,
forecast_week_7_most_recent = forecast_week_7_a,
MSE_average_of_all_data = mse_b,
forecast_week_7_average = forecast_week_7_b,
Better_Method = better_method
) # Result: Better method is the average of all data
## $MSE_most_recent_value
## [1] 16.2
##
## $forecast_week_7_most_recent
## [1] 14
##
## $MSE_average_of_all_data
## [1] 8.272
##
## $forecast_week_7_average
## [1] 14.5
##
## $Better_Method
## [1] "Average of All Data"
Q. 2
# Install required packages
#install.packages("dplyr")
#install.packages("zoo")
#library(dplyr)
#library(zoo)
df <- data.frame(month=c(1,2,3,4,5,6,7,8,9,10,11,12),
data=c(240,352,230,260,280,322,220,310,240,310,240,230))
# Time series plot
plot(df$month, df$data, type = "o", col = "blue", xlab = "Month", ylab = "Building Contract Value ($ million)",
main = " Alabama Building Contract Values per Month")
# Three month moving average
#df$avg_contract <- c(NA, NA, NA,
# (df$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_contract), NA, (data - avg_contract)^2)
#)
# Compute MSE
mse <- mean(df$squared_error, na.rm = TRUE)
## Warning in mean.default(df$squared_error, na.rm = TRUE): argument is not
## numeric or logical: returning NA
mse #2040.444
## [1] NA
# 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 # 2593.762
## [1] 2593.762
# Compare
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
) # Result: Better method - three month moving average
## $MSE_moving_average
## [1] NA
##
## $MSE_exponential_smoothing
## [1] 2593.762
##
## $Better_Method
## [1] NA
Q. 3a
#install.packages("ggplot2")
library("readxl")
## Warning: package 'readxl' was built under R version 4.3.3
library("ggplot2")
## Warning: package 'ggplot2' was built under R version 4.3.3
# Load the data
#df1 <- read_excel(file.choose())
# Time series plot
#ggplot(df1, aes(x = Year, y = Interest_Rate)) +
#geom_line() +
#geom_point() +
#xlab("Year") +
#ylab("Interest Rate") +
#ggtitle("Time Series Plot of Mortgage Rates Since yr 2000")