Class Exercise: Chapter 17
Chapter 17: Time Series Forecasting
Explain The Time Series Patterns and Forecasting Methods such as
Naïve Forecasting, Moving Averages, and Exponential Smoothing.Question 1: The Naive Method
Add Time Series Data
week <- 1:6
value <- c(17,13,15,11,17,14)Part A: Mean absolute error
forecast_a <- value[-length(value)]
actual_a <- value[-1]
mae <- mean(abs(actual_a - forecast_a ))
mae## [1] 3.8Part B. Most recent value as forecast
mse <- mean((actual_a - forecast_a)^2)
mse ## [1] 16.2Part C: Mean absolute percentage error
MAPE <- mean(abs ((actual_a - forecast_a) /actual_a) *100)
MAPE## [1] 27.43778Part: Forecast the value for week 7
forecast_week7_a <- tail(value, 1)
forecast_week7_a## [1] 14Interpretation: the value for week 7 is 14Question 2: Exponential Smoothing and Moving Averages Methods
Install and load required libraries
#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, unionlibrary(zoo)##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericTime Series Data; import the data
df <- data.frame(month=c(1:12),
data=c(240, 352, 230, 260, 280, 322, 220, 310, 240, 310, 240,
230))Descriptive statistics
summary(df)## month data
## Min. : 1.00 Min. :220.0
## 1st Qu.: 3.75 1st Qu.:237.5
## Median : 6.50 Median :250.0
## Mean : 6.50 Mean :269.5
## 3rd Qu.: 9.25 3rd Qu.:310.0
## Max. :12.00 Max. :352.0Interpretation: the avreage value for the 12 month is 250Time Series Plot
plot(df$month,df$data, type = "o", col = "blue", xlab = "Month", ylab = "data",
main = "Alabama building contracts plot")
Interpretation:the type of pattern exists in the data is a seasonal pattern.Moving Averages Method
df$avg_data3 <- c(NA, NA, NA,
df$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 error
df <- df %>%
mutate(
squared_error = ifelse(is.na(avg_data3), NA, (data - avg_data3)^2))Compute MSE
mse <- mean(df$squared_error, na.rm = TRUE)
mse ## [1] 143065.2The output of MSE is 143065.2###Exponential smoothing
alpha <- 0.2
exp_smooth <- rep(NA, length(df$data))
exp_smooth[1] <- df$data[1]
for(i in 2: length(df$data)) {
exp_smooth[i] <- alpha * df$data[i-1] + (1 - alpha) * exp_smooth[i-1]
}
mse_exp_smooth <- mean((df$data[2:12] - exp_smooth[2:12])^2)
mse_exp_smooth ## [1] 2593.762The output of MSE is 2593.76Comparison
better_method <- ifelse(mse < mse_exp_smooth, "Three-Month Moving Average",
"Exponential Smoothing")Results
list(
MSE_Moving_Average = mse,
MSE_Exponential_Smoothing = mse_exp_smooth,
Better_Method = better_method
)## $MSE_Moving_Average
## [1] 143065.2
##
## $MSE_Exponential_Smoothing
## [1] 2593.762
##
## $Better_Method
## [1] "Exponential Smoothing"##Question 3: The Tinear Trend
Install and load required libraries
#install package
#install.packages("ggplot2")
#load the libraries
library(readxl)
library(ggplot2)Load The Data
df_m <- read_excel("~/Desktop/untitled folder 2/Mortgage.xlsx")
summary(df_m)## Year Period Interest_Rate
## Min. :2000-01-01 00:00:00 Min. : 1.00 Min. :2.958
## 1st Qu.:2005-10-01 18:00:00 1st Qu.: 6.75 1st Qu.:3.966
## Median :2011-07-02 12:00:00 Median :12.50 Median :4.863
## Mean :2011-07-02 18:00:00 Mean :12.50 Mean :5.084
## 3rd Qu.:2017-04-02 06:00:00 3rd Qu.:18.25 3rd Qu.:6.105
## Max. :2023-01-01 00:00:00 Max. :24.00 Max. :8.053Time Series Plot
ggplot(df_m, aes(x = Period, y = Interest_Rate)) +
geom_line() +
geom_point() +
xlab("period") +
ylab("Interest_Rate") +
ggtitle("Time Series Plot")
Question 4: The Linear Trend Equation
model <- lm(Interest_Rate ~ Period, data = df_m)
summary(model)##
## Call:
## lm(formula = Interest_Rate ~ Period, data = df_m)
##
## 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: 0.0003637The linear trend equation for this time series is "Tt = 6.70 - 0.13* period"