Creating a Time Series Data: Naive Method

Project Objective

To investigate the value for the forecast for a selected week. 

Forcast week 7

##Part A: Insert Data

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

##Part B: 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 # results: 16.2

## [1] 16.2

forecast_week_7_a <- tail(values, 1)
forecast_week_7_a #results: 14

## [1] 14

Interpretation: The mean square of value a is 16.2. 

##Part C: Average all of the data as forecast

cumulative_avg <- cumsum(values[-length(values)]) / (1:(length(values) - 1))
cumulative_avg

## [1] 17.0 15.0 15.0 14.0 14.6

forecasts_b <- cumulative_avg
actual_b <- values[-1] #exclude the first value 
mse_b <- mean((actual_b - forecasts_b)^2)
mse_b

## [1] 8.272

forecast_week_7_b <- tail(values) #average of all weeks as forecast for week 7
forecast_week_7_b

## [1] 17 13 15 11 17 14

Interpretation: The mean square of value b is 8.27

Part D: 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
) 

## $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] 17 13 15 11 17 14
## 
## $Better_Method
## [1] "Average of All Data"

Interpretation: Better method is Average of All Data.

###Example 2: Alabama Contracts

##Part A: Install and load packages

#install.packages("dplyr")
#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)

## 
## Attaching package: 'zoo'

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

##Part B: Time Series Plot

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 = "Monthly Percentages of All Alabama Contracts")

Interpretation: The time-series plot exhibits a horizontal pattern 

##Part C: Three-month moving average

df$avg_contracts <- c(NA, NA, NA,
                      (df$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)

##Part D: Calculate the squared errors (only for the months where moving average is available)

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

##Part E: Compute MSE (excluding the initial months with NA)

mse <- mean(df$squared_error, na.rm = TRUE) 
mse #results: 2040.44                    

## [1] 2040.444

# 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 #results: 2593.76

## [1] 2593.762

##Part F: Better Method

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
) 

## $MSE_moving_average
## [1] 2040.444
## 
## $MSE_exponential_smoothing
## [1] 2593.762
## 
## $Better_Method
## [1] "Three-month moving average"

Interpretation: Better method is Three-month moving average