Class Exercise 16: Chapter 17 Time Series
Project Objective
To practice various time series problemsQuestion 1: Using Naive Method as Forecast
Step 1: Create Time Series Data
weekl <- 1:6 #this is the independent variable
values <- c(17, 13, 15, 11, 17, 14) #dependent variableStep 2: Create actual and forecast variables
forecast <- values[-length(values)] #exclude the last variable
actual <- values[-1] #exclude the first saleQuestion 1A: Calculate Mean Absolute Error
mae_a <- mean(abs(actual - forecast))
mae_a## [1] 3.8Interpretation: The Mean absolute Error is 3.80Question 1B: Calculate Mean Squared Error
mse_b <- mean((actual - forecast)^2)
mse_b## [1] 16.2Interpretation: The Mean Squared Error is 16.20Question 1C: Calculate Absolute Percentage Error
mape_c <- 100 * mean((actual - forecast) / actual)
mape_c## [1] -7.986798Interpretation: The Absolute Percentage Error is -7.97%Question 1D: Forecast the values for week 7
forecast_week7_a <- tail(values, 1)
forecast_week7_a## [1] 14Interpretation: The value projected for week 7 is 14.Question 2A. Constructing a Time Series Plot
Step 1: Install and Load Packages
install.packages("dplyr", repos = "http://cran.us.r-project.org")## Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.4'
## (as 'lib' is unspecified)## package 'dplyr' successfully unpacked and MD5 sums checked## Warning: cannot remove prior installation of package 'dplyr'## Warning in file.copy(savedcopy, lib, recursive = TRUE): problem copying
## C:\Users\Admin\AppData\Local\R\win-library\4.4\00LOCK\dplyr\libs\x64\dplyr.dll
## to C:\Users\Admin\AppData\Local\R\win-library\4.4\dplyr\libs\x64\dplyr.dll:
## Permission denied## Warning: restored 'dplyr'##
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## C:\Users\Admin\AppData\Local\Temp\Rtmp8u3uLA\downloaded_packagesinstall.packages("zoo", repos = "http://cran.us.r-project.org")## Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.4'
## (as 'lib' is unspecified)## package 'zoo' successfully unpacked and MD5 sums checked## Warning: cannot remove prior installation of package 'zoo'## Warning in file.copy(savedcopy, lib, recursive = TRUE): problem copying
## C:\Users\Admin\AppData\Local\R\win-library\4.4\00LOCK\zoo\libs\x64\zoo.dll to
## C:\Users\Admin\AppData\Local\R\win-library\4.4\zoo\libs\x64\zoo.dll: Permission
## denied## Warning: restored 'zoo'##
## The downloaded binary packages are in
## C:\Users\Admin\AppData\Local\Temp\Rtmp8u3uLA\downloaded_packageslibrary(dplyr)## Warning: package 'dplyr' was built under R version 4.4.2##
## 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)## Warning: package 'zoo' was built under R version 4.4.2##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericStep 2: Create the Time Series Plot
df <- data.frame(month=c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12),
contracts=c(240, 352, 230, 260, 280, 322, 220, 310, 240, 310, 240, 230))
plot(df$month, df$contracts, type = "o", col = "blue", xlab = "Month", ylab = "Contract",
main = "Alabama Building Contracts Plot")
Interpretation: The average contract price over a 12 month period is $269.5 million dollarsQuestion 2B. Comparing the Three-Month Moving Average with the Exponential Smoothing Average
Step 1: Manually calculate the Three-Month Moving Average
df$avg_contract3 <- c(NA, NA, NA,
(df$contracts[1] + df$contracts[2] + df$contracts[3]) / 3,
(df$contracts[2] + df$contracts[3] + df$contracts[4]) / 3,
(df$contracts[3] + df$contracts[4] + df$contracts[5]) / 3,
(df$contracts[4] + df$contracts[5] + df$contracts[6]) / 3,
(df$contracts[5] + df$contracts[6] + df$contracts[7]) / 3,
(df$contracts[6] + df$contracts[7] + df$contracts[8]) / 3,
(df$contracts[7] + df$contracts[8] + df$contracts[9]) / 3,
(df$contracts[8] + df$contracts[9] + df$contracts[10]) / 3,
(df$contracts[9] + df$contracts[10] + df$contracts[11]) / 3)Step 2: Calculate the square errors
df <- df %>%
mutate(
squared_error = ifelse(is.na(avg_contract3), NA, (contracts - avg_contract3)^2)
)Step 3: Compute the MSE
mse <- mean(df$squared_error, na.rm = TRUE)
mse # Output the MSE - 2040.44## [1] 2040.444Step 4: Compute the MSE using Exponential Smoothing
alpha <- 0.2
exp_smooth <- rep(NA, length(df$contracts))
exp_smooth[1] <- df$contracts[1] # Starting point
for(i in 2: length(df$contracts)) {
exp_smooth[i] <- alpha * df$contracts[i-1] + (1 - alpha) * exp_smooth[i-1]
}
mse_exp_smooth <- mean((df$contracts[2:12] - exp_smooth[2:12])^2)
mse_exp_smooth # Output the MSE - 2593.76## [1] 2593.762Step 5: Compare the Results
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: The Three-Month Moving Average had a smaller error than Exponential Smoothing so it has more accurate forecasts.Question 3A: Constructing the Time Series Plot
Step 1: Install and Load Packages
install.packages("ggplot2", repos = "http://cran.us.r-project.org")## Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.4'
## (as 'lib' is unspecified)## package 'ggplot2' successfully unpacked and MD5 sums checked
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## The downloaded binary packages are in
## C:\Users\Admin\AppData\Local\Temp\Rtmp8u3uLA\downloaded_packageslibrary(readxl)
library(ggplot2)## Warning: package 'ggplot2' was built under R version 4.4.2df <- read_excel(file.choose())
df## # A tibble: 24 × 3
## Year Period Interest_Rate
## <dttm> <dbl> <dbl>
## 1 2000-01-01 00:00:00 1 8.05
## 2 2001-01-01 00:00:00 2 6.97
## 3 2002-01-01 00:00:00 3 6.54
## 4 2003-01-01 00:00:00 4 5.83
## 5 2004-01-01 00:00:00 5 5.84
## 6 2005-01-01 00:00:00 6 5.87
## 7 2006-01-01 00:00:00 7 6.41
## 8 2007-01-01 00:00:00 8 6.34
## 9 2008-01-01 00:00:00 9 6.03
## 10 2009-01-01 00:00:00 10 5.04
## # ℹ 14 more rowsStep 2: Construct a Time Series Plot
ggplot(df, aes(x = Period, y = Interest_Rate)) +
geom_line() +
geom_point() +
xlab("Period") +
ylab("Interest Rate") +
ggtitle("Time Series Plot of Interest Rate")
Interpretation: We observe a decreasing pattern in the time series plot.Question 3B: Develop the linear trend equation
model <- lm(Interest_Rate ~ Period, data = df)
summary(model)##
## Call:
## lm(formula = Interest_Rate ~ Period, data = df)
##
## 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: 0.0003637Result - estimated linear trend equation: Interest_Rate = 6.70 - 0.13*PeriodQuestion 3C: Forecast Interest Rate for Period = 25
forecast_period_25 <- predict(model, newdata = data.frame(Period = 25))
forecast_period_25## 1
## 3.472942