#**Class Exercise 16: Chapter 17 ### Question1 ## Time series forecasting ## Part A.
week <- 1:6
values <- c(17, 13, 15, 11, 17, 14)
forecasts_a <- values[-length(values)]
actual_a <- values[-1]
mse_a <- mean((actual_a - forecasts_a)^2)
mse_a## [1] 16.2forecast_week_7_a <- tail(values,1)
forecast_week_7_a## [1] 14Part B
cumulative_averages <- cumsum(values[-length(values)]) / (1:(length(values)-1))
cumulative_averages## [1] 17.0 15.0 15.0 14.0 14.6forecast_b <- cumulative_averages
actual_b <- values[-1]
mse_b <- mean((actual_b - forecast_b)^2)
mse_b## [1] 8.272forecast_week_7_b <- tail(values)
forecast_week_7_b## [1] 17 13 15 11 17 14Part C
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,
Bettter_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
##
## $Bettter_Method
## [1] "Average of All Data"Q2
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(zoo)##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericdf <- data.frame(month=c(1,2,3,4,5,6,7,8,9,10,11,12),
data=c(240, 352, 230, 260, 280, 322, 220, 310, 240, 310, 240, 230))
plot(df$month, df$data, type = "o", col= "red", xlab = "Month", ylab = "Contratcs",
main = "Monthly Contracts")
## Q2b
df$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$data[11])/3)
df<- df %>%
mutate(
sqaured_error= ifelse(is.na(avg_contracts), NA, (data - avg_contracts)^2)
)
mse <- mean(df$sqaured_error, na.rm = TRUE)
mse## [1] 2040.444alpha = 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] 2593.762better_method <- ifelse(mse < mse_exp_smooth, "Three Month 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 average"Q3
library(readxl)
library(ggplot2)
df1 <- read_excel("/Users/leo/Desktop/Rrr/Mortgage.xlsx")
ggplot(df1, aes(x = Period, y = Interest_Rate)) +
geom_line() +
geom_point() +
xlab ("year") +
ylab("Interest Rate") +
ggtitle("Times Series Plot of Interest Rate on Mortage")
model <- lm(Interest_Rate ~ Period, data = df1)
summary(model)##
## 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: 0.0003637forecast_period_25 <- predict(model, newdata = data.frame(Period = 25))
forecast_period_25## 1
## 3.472942