X <- c(27.57, 28.43, 24.90, 27.10, 24.73, 34.67, 30.01, 31.55, 28.07, 26.58)

Y <- c(319, 147, 142, 161, 218, 242, 236, 223, 193, 166, 130, 133,
       129, 108, 82 , 98 ,180 ,213 ,223 ,213 ,194 ,179 ,142 ,101,
       79,   82,58  ,68  ,107 ,136 ,152 ,151 ,125 ,109 , 88 , 65,
       90,   91,95  ,87  ,131 ,165 ,178 ,189 ,164 ,147 ,125 , 73,
       52,   44,35  ,63  ,95  ,94  ,83  ,79  ,75  ,63  ,42  ,31,
       28,   16,11  ,14  ,55  ,82  ,88  ,85  ,93  ,101 ,126 ,104,
       103,  78, 67 , 79 ,130 ,147 ,168 ,165 ,151 ,119 , 96 , 77,
       118, 122,129 ,103 ,133 ,157 ,186 ,209 ,203 ,164 ,139 ,129,
       134, 137,156 ,198 ,282 ,311 ,311 ,307 ,290 ,265 ,230 ,216,
       215, 262,251 ,279 ,298 ,297 ,286 ,273 ,238 ,207 ,174 ,133)

X1 <- ts(X, start=1921,      freq=1)
Y1 <- ts(Y, start=c(1921,1), freq=12)

plot(X1)
plot(Y1)


#--- Take Annual Averages (Monthly Data) ---

  Aav1  <- ts(aggregate(c(Y1), list(year=floor(time(Y1))), mean)$x, start=start(Y1), freq=1)   #- Annual Average
  A.av1 <- ts(rep(Aav1, each=12), start=start(Y1), freq=12) #- Mtly Av as long as D1           #- Each month replaced with Ann Av


  #---------
  plot(X1)
  plot(Aav1)


  #---------
  plot(Y1)
  lines(A.av1, col="red")




#--- Take Monthly Averages (Monthly Data) ---

  D <- read.csv("http://gozips.uakron.edu/~nmimoto/pages/datasets/acci.txt", header=T)
  D1 <- ts(D, start=c(1973,1), freq=12)   #- Turn D into ts object with frequency

  plot(D1, type="o", ylab="num of accidents")


  Mav1  <- aggregate(c(D1), list(month=cycle(D1)), mean)$x           #- 1yr long Mtly Av $
  M.av1 <- ts(Mav1[cycle(D1)], start=start(D1), freq=frequency(D1))  #- Mtly Av as long as D1


  plot(Mav1)

  plot(D1, type="o")
  lines(M.av1, col="red")


  plot(D1-M.av1, type="o")   #- plot the difference