Part 2 Boston

plot(boston, ylab=" Boston crime data", xlab= "Time")

#Time series seem to have homogeneous variance upon visual inspection

#Q2
#Trend looks linear in the plot, so for trend differencing operator take d=1
newboston= as.numeric(unlist(boston))
xdiff = diff(newboston)
plot(xdiff)

#Q3
#ADF
library(tseries)
adf.test(xdiff)

#From the result, alternative hypothesis is stationary so null hypothesis is rejected

#KPSS test
install.packages('fpp3', dependencies = TRUE)

library ( fpp3 )

unitroot_kpss(xdiff)

#the p-value is >0.05, so fail to reject null hypothesis for KPSS

#Q4
library(astsa)
acf2(xdiff, max.lag = 50)

model1 = sarima(xdiff, p, 1, q)

So this is what I have tried so far. I am quite new to R and so do be kind if my workings make little sense. For context, Boston is the data I imported from an excel, that is simply a column of x axis data. Firstly, I am trying to do Q4, but I am not sure how I would go about to find p and q. Second, I am unsure whether what I did in Q2 to detrend my data is correct in the first place.

Here is the output of dput(boston)

dput(boston)
structure(list(x = c(41, 39, 50, 40, 43, 38, 44, 35, 39, 35, 
29, 49, 50, 59, 63, 32, 39, 47, 53, 60, 57, 52, 70, 90, 74, 62, 
55, 84, 94, 70, 108, 139, 120, 97, 126, 149, 158, 124, 140, 109, 
114, 77, 120, 133, 110, 92, 97, 78, 99, 107, 112, 90, 98, 125, 
155, 190, 236, 189, 174, 178, 136, 161, 171, 149, 184, 155, 276, 
224, 213, 279, 268, 287, 238, 213, 257, 293, 212, 246, 353, 339, 
308, 247, 257, 322, 298, 273, 312, 249, 286, 279, 309, 401, 309, 
328, 353, 354, 327, 324, 285, 243, 241, 287, 355, 460, 364, 487, 
452, 391, 500, 451, 375, 372, 302, 316, 398, 394, 431, 431), 
    y = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 
    16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 
    31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 
    46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 
    61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 
    76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 
    91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 
    105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 
    117, 118)), class = c("tbl_df", "tbl", "data.frame"), row.names = c(NA, 
-118L))