ClassEX Forecasting Problems

Objective

To understand different types of forecasting methods 

Question 1: Naive Forecasting

Step 1: Import data for time series

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

Step 2: Naive Forecasting

forcasts_a <- values[-length(values)] #exclude the last value 
actual_a <- values[-1] #exclude the first value
mse_a <- mean((actual_a - forcasts_a)^2)
mse_a #results: 16.2

## [1] 16.2

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

## [1] 14

Finding the Mean Absloute Error

MAE <- mean(abs((actual_a - forecast_week_7_a)/(actual_a)))
MAE #Result: 0.12

## [1] 0.1185575

MAE*100 #Result: 11.86

## [1] 11.85575

Problem 2: Building Contracts

#Packages:

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

library(dplyr)

## Warning: package 'dplyr' was built under R version 4.3.3

## 
## 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 4.3.3

## 
## Attaching package: 'zoo'

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

##Import Data Frame

df <- data.frame(month=c(1,2,3,4,5,6,7,8,9,10,11,12),
                 data = c(2.40,3.52,2.30,2.60,2.80,3.22,2.20,3.10,2.40,3.10,2.40,2.30))

##Time-Series Plot

plot(df$month, df$data, type= "o", col = "blue", xlab = "Month",
     ylab = "Building Contracts ($100 Millions)", main = "Monthly Values of Building Contracts")

#Interpretation:The time-series plot exhibits a horizontal pattern

##Part B: Three-Month Moving Average

df$avg_forecast <- c(NA, NA, NA,
                     (df$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)
                     
                     
#Calulate the squared errors (only for the months available)
df <- df %>%
  mutate(
    squared_error = ifelse(is.na(avg_forecast), NA, (data - avg_forecast)^2)
  )

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

## [1] 0.2040444

#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 #Result: 4.85

## [1] 4.849183

Problem 3: Mortgage Interest Rate

#Packages:

library(readxl)
library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.3.3

##Data:

df1 <- read_excel(file.choose())

#Part A: Time-Series Plot

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

#Interpretation: We observe a decreasing a pattern in the majority of the graph 
#with a sharp increase in after year 20 or 2021-2023. 

#Part B. Develop a linear trend equation

model1 <- lm(Interest_Rate ~ Period, data = df1)
summary(model1)

## 
## Call:
## lm(formula = Interest_Rate ~ Period, data = df1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.3622 -0.7212 -0.2823  0.5015  3.1847 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.69541    0.43776  15.295 3.32e-13 ***
## Period      -0.12890    0.03064  -4.207 0.000364 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.039 on 22 degrees of freedom
## Multiple R-squared:  0.4459, Adjusted R-squared:  0.4207 
## F-statistic:  17.7 on 1 and 22 DF,  p-value: 0.0003637

#Results - Equation: Interest Rate = 6.70 - 0.13*(Period)

#Part C. Forecast for period 25

forecast_period_25 <- predict(model1, newdata = data.frame(Period = 25))
forecast_period_25 # Results = 3.47

##        1 
## 3.472942

#Interpeatation: There is a forecasted decrease in the year 2024 in the fixed mortgage interest rate.