Basic Time Series Forecasting
#Problem 1
#Insert Time Series Data
weeks <- 1:6
values <- c(17,13,15,11,17,14)#Part A
forecasts_a <- values[-length(values)] #exclude last value
actual_a <- values[-1] #exlude first value
mse_a <- mean((actual_a - forecasts_a)^2)
mse_a #Result: 16.20## [1] 16.2mae_a <- mean(abs(actual_a - forecasts_a))
forecast_month_7_a <- tail(values, 1)
forecast_month_7_a #Result: 14## [1] 14#Part B
cumulative_averages <- cumsum(values[-length(values)]) / (1:(length(values)-1))
cumulative_averages## [1] 17.0 15.0 15.0 14.0 14.6forecasts_b <- cumulative_averages
actual_b <- values[-1] #exclude first value
mse_b <- mean((actual_b - forecasts_b)^2)
mse_b #Result: 8.27## [1] 8.272forecast_month_7_b <- tail(values, 1) #avg of all months
forecast_month_7_b #Result: 14.5 ## [1] 14#Part C
better_method <- ifelse(mse_a < mse_b, "Most Recent value", "Average of All Data")
list(
MSE_most_recent_value = mse_a,
forecast_month_7_most_recent = forecast_month_7_a,
MSE.average_of_all_data = mse_b,
forecast_month_7_average = forecast_month_7_b,
Better_method = better_method
)## $MSE_most_recent_value
## [1] 16.2
##
## $forecast_month_7_most_recent
## [1] 14
##
## $MSE.average_of_all_data
## [1] 8.272
##
## $forecast_month_7_average
## [1] 14
##
## $Better_method
## [1] "Average of All Data"Result: The better method is the “Average of ALl Data”
#Problem 2 #Install Packages and Load required libraries
#install.packages("dplyr")
#install.packages("zoo")
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(zoo)##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric#Enter Data and Build Time Series Plot
df <- data.frame(month=c(1,2,3,4,5,6,7,8,9,10,11,12),
data=c(240, 352, 230, 260, 280, 322, 220, 310, 240, 310, 240, 230))
plot(df$month, df$data, type = "o", col = "blue",xlab = "Month", ylab = "contracts built",
main = "Monthly Percentage of Contracts Built")
#Three Month Moving Avg # Three month moving avg
df$avg_value <- 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$data[11]) / 3)#Calculate Squared Error
df <- df %>%
mutate(
squared_error = ifelse(is.na(avg_value), NA, (data - avg_value)^2)
)#Calculate MSE fror Three Month Moving Avg
mse <- mean(df$squared_error,na.rm = TRUE)#Do Exponential Smoothing Approach
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]#Calculate MSE for Exponential Smoothing Approach
mse_exp_smooth <- mean((df$data[2:12] - exp_smooth[2:12])^2)
mse_exp_smooth #Result : 2593.76 ## [1] 2593.762#Compare which Approach Is Better
better_method <- ifelse(mse < mse_exp_smooth, "three month moving avg", "exponential smoothing")
list(
MSE_avg = mse,
MSE_exp_smoothing = mse_exp_smooth,
Better_method = better_method
)## $MSE_avg
## [1] 2040.444
##
## $MSE_exp_smoothing
## [1] 2593.762
##
## $Better_method
## [1] "three month moving avg"#Result: The Three Month Moving Approach is better because it gives a lower MSE
#Problem 3 #Load Library and Data
library(readxl)
library(ggplot2)
df1 <- read_excel("/Users/yashgor/Downloads/R markdown /Mortgage.xlsx")#Construct Time Series Plot #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 Fixed Mortgage Rate")
#Questions 4 and 5- Build Trend Equation and Forecast Future Period 25
#Build Trend Equation
model <- lm(Interest_Rate ~ Period, data = df1)
summary(model) #Result: 6.7 + (-0.13)*Period##
## 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#Forecast Future Period 25 forecast_period_25 <- predict(model, newdata = data.frame(Period = 25)) forecast_period_25