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rm(list = ls())
ptf <- "~/Documents/isye_6501/homework/week_3/week 3 Homework-Summer21-1/week 3 data-summer/temps.txt"
df <- read.delim(ptf)

# make full time series of all days and plot it
all_d_ts <- ts(as.vector(unlist(df[,2:21])), frequency=nrow(df), start=1996)

# create es using Holt Winters and plot it
hw <- HoltWinters(all_d_ts, seasonal="multiplicative")
plot(hw)

# get seasonality factors from fitted hw model
seas <- matrix(hw$fitted[,4], nrow=nrow(df))
colnames(seas) <- colnames(df[,3:21])

# plot the seasonal factors
seas_by_year <- vector()
for (i in 1:ncol(seas)) {
  seas_by_year[i] = mean(seas[,i])
}
plot(1997:2015, seas_by_year)

# def cusum func
cusum <- function(d, mu, t, c) {
  res <- list()
  s_t <- 0
  row_iter <- 1
  while (row_iter <= nrow(d)) {
    x <- d[row_iter,]
    s_t <- max(0, s_t + (mu - x - c))
    if (s_t >= t) {
      res <- row_iter
      break
    }
    row_iter <- row_iter + 1
    if (row_iter >= nrow(d)) {
      res <- NA
      break
    }
  }
  return (res)
}

# execute cusum on seasonality factors by year
t <- sd(seas[,1]) * 2
c <- 0

change_idxs <- vector()
for (i in 1:ncol(seas)) {
  change_idxs[i] <- cusum(as.matrix(seas[,i]), 1, t, c)
}

change_df <- data.frame(year=1997:2015, change_day=df[change_idxs,1])
as.matrix(change_df)

      year   change_day
 [1,] "1997" "20-Sep"  
 [2,] "1998" "21-Sep"  
 [3,] "1999" "22-Sep"  
 [4,] "2000" "21-Sep"  
 [5,] "2001" "21-Sep"  
 [6,] "2002" "21-Sep"  
 [7,] "2003" "22-Sep"  
 [8,] "2004" "22-Sep"  
 [9,] "2005" "22-Sep"  
[10,] "2006" "22-Sep"  
[11,] "2007" "23-Sep"  
[12,] "2008" "24-Sep"  
[13,] "2009" "24-Sep"  
[14,] "2010" "25-Sep"  
[15,] "2011" "25-Sep"  
[16,] "2012" "26-Sep"  
[17,] "2013" "25-Sep"  
[18,] "2014" "24-Sep"  
[19,] "2015" "24-Sep"