threebuys

cc_sim = function(seed, tran, debug=FALSE) {
  # Does a simulation from a list of transition coefficients
  # and initial state.
  #
  # Args:
  #   seed: the initial state
  #   tran: a list of transition coefficients
  n = length(tran)
  lst = rep(1,n)

  if (debug) {
    print(seed)
    print(tran[1])
  }

  for (i in 1:n) {
    lst[i] = seed * tran[i] + seed
    seed = lst[i]
  }
  lst
}

Bcc_sim = function(seed, prev, tran, debug=FALSE) {
  # Does a simulation from a list of transition coefficients
  # and initial state.
  #
  # Args:
  #   seed: the initial state
  #   tran: a list of transition coefficients
  n = length(tran)
  lst = rep(1,n)
  twodaysample = .7*seed + .3*(prev*tran[n] + prev)
  seed = twodaysample
 
  if (debug) {
    print(seed)
    print(tran[1])
  }

 for (i in 1:n) {
    lst[i] = seed * tran[i] + seed
    seed = lst[i]
  }
  lst
}

rotate = function(lst) {
  # Rotates a list by one element e.g. [1, 2, 3] --> [2, 3, 1]
  #
  # Args:
  #   lst: the list to rotate
  n = length(lst)
  tmp = rep(0, n)
  end = lst[1]
  for (i in 1:n-1) {
    tmp[i] = lst[i + 1]
  }
  tmp[n] = end
  tmp
}

errors = function(y_hat, y) {
  n = length(y)
  errs = rep(0, n)
  for (i in 1:n) {
    errs[i] = abs(1 - y_hat[i]/y[i])
  }
  mean(errs)
}

###################################################

setwd('~/threebuys/')
setwd('C:/Users/josh/Desktop/threebuys')
data = droplevels(read.csv('10755.csv', header=TRUE))

tran10755 = rep(c(-.0025,-.0531,.0925,.0457,.0011,-.0626,.0145), 4)
tran10111 = rep(c(-.0025,-.0531,.0925,.0457,.0011,-.0626,.0145), 4)

###################################################

dist = seq(-.2,.2, by=.0001) # percent distance from true value
N = length(data$Cost.Clicks) - 7 # exclude the last week
m = length(dist)
n = N - 7 # number of days 
Y = matrix(nrow=m, ncol=n) # err at dist by day matrix

# Y matrix example:
#      1/17  1/18
#      ----- ----
# -  1|  .5   .8
# - .9|  .3   .1

# Check convergence
tmp = tran10755
for (j in 1:length(dist)) {
  tmp = tran10755
  for (i in 8:N) { # exclude the first week
    q = i + 1
    p = i + 7
    a = cc_sim(data$Cost.Clicks[i+1] * dist[j] + data$Cost.Clicks[i+1], tmp)
    Y[j, i - 7] = errors(a, data$Cost.Clicks[q:p])
    tmp = rotate(tmp)
  }
}

daily_errs = rep(0, m)
for (i in 1:m) {
  daily_errs[i]=mean(Y[i,])
}

plot(dist,daily_errs*100, col='blue', type='l', ylab='mean 7 day error %', xlab='% from true value', 
     main='Mean 7 day error )
best = which.min(daily_errs)
dist[best]

###################################################

# Original method
tmp = tran10755
for (i in 8:N) { # exclude the first week
  print(rep('=',10))
  print(droplevels(data$Date[i+1]))
  print(cc_sim(data$Cost.Clicks[i], tmp))
  tmp = rotate(tmp)
}

# Bill's method
tmp = tran10755
for (i in 8:N) { # exclude the first week
  print(rep('=',10))
  print(droplevels(data$Date[i+1]))
  print(Bcc_sim(data$Cost.Clicks[i], data$Cost.Clicks[i-1], tmp))
  tmp = rotate(tmp)
}