#time series data

week <- 1:6 #3independent variable - time
sales <- c(17,13,15,11,17,14) #dependent variable - sales


#niave method
forecast_a <- sales[length(sales)]
forecast_a
actual_a <-sales[-1]
actual_a
mse_a <- mean((actual_a - forecast_a)^2)
mse_a
mae_a <- mean(actual_a - forecast_a)
mae_a

#forcasting sales week 7 
forecast_wk6_a <- tail(sales, 1)
forecast_wk6_a

#average of all data forecast

cumulative_avg <- cumsum(sales[-length(sales)]) / (1:(length(sales) - 1))
cumulative_avg

forecast_b <- cumulative_avg
actual_b <- sales[-1]
mse_b <- mean((actual_b - forecast_b)^2)
mse_b

forecast_wk6_b <- mean(sales, 1)
forecast_wk6_b

Better_method <- ifelse(mse_a < mse_b, "most recent value", "avg of all data")

list(MSE_Most_Recent_Value = mse_a, forecast_wk7_Most_Recent = forecast_wk6_a,
     MSE_average = mse_b,
     Forecast_week11_avg = forecast_wk6_b,
     Better_method1 = Better_method)

##question 2 

library(dplyr)
library(zoo)

#time seris data 

df <- data.frame(Month=c(1,2,3,4,5,6,7,8,9,10,11,12),
                 sales=c(240,352,230,260,280,322,220,310,240,310,240,230))

summary(df)
#ave sales over 12 mo period is 269
plot(df$Month, df$sales, type = "o", col= "blue", xlab = "month", ylab = "sales,",
     main = "values of contracts")

df$avg_sales3 <- c(NA,NA,NA,
                   (df$sales[1] + df$sales[2] + df$sales[3]) / 3,
                   (df$sales[2] + df$sales[3] + df$sales[4]) / 3,
                   (df$sales[3] + df$sales[4] + df$sales[5]) / 3,
                   (df$sales[4] + df$sales[5] + df$sales[6]) / 3,
                   (df$sales[5] + df$sales[6] + df$sales[7]) / 3,
                   (df$sales[6] + df$sales[7] + df$sales[8]) / 3,
                   (df$sales[7] + df$sales[8] + df$sales[9]) / 3,
                   (df$sales[8] + df$sales[9] + df$sales[10]) / 3,
                   (df$sales[9] + df$sales[10] + df$sales[11]) / 3,
                   (df$sales[10] + df$sales[11]) / 3,
                   )
View(df)


library(readxl)
tax_df = read_excel(file.choose())
tax_df

plot(tax_df$Period, tax_df$Interest_Rate, type = "o", col= "blue", xlab = "period", ylab = "rate,",
     main = "tax rate")