# ARIMA preperation stationarity

Hello,

I am trying to predict a time series with ARIMA. In the first step I tested for heterosocedactiy and performed a BoxCox() transformation. In the next step I want to test if a differentiation is necessary. For this I wanted to test with Box.test(), adf.test() and kpss.test() whether this is necessary. Unfortunately the tests do not work properly with my data, because I am told once that I can accept stationarity and once that I can reject it. You can find the code enclosed. I am not sure what to do, cause when I use diff(bc_ts) adf.test() rejects H0 and kpss.test() accepts H0. Or can I ignore the test and do a differentiation anyway?

``````# Box-Ljung test (tests the null hypothesis of absence of serial correlation)

Box.test(bc_ts, type="Ljung")

#	Box-Ljung test
# data:  bc_ts
# X-squared = 55.029, df = 1, p-value = 1.188e-13

# ADF Test (non-stationary) (H0, Data is non-stationary: p-value < 0.05 -> differentiation necessary)

# Augmented Dickey-Fuller Test
# data:  bc_ts
# Dickey-Fuller = -6.2552, Lag order = 5, p-value = 0.01
# alternative hypothesis: stationary
# Warnmeldung:
# In adf.test(bc_ts) : p-value smaller than printed p-value

#KPSS Test (stationarity) (H0, Data is stationary: p-value < 0.05 -> differentiation necessary)

kpss.test(bc_ts, null = c("Level", "Trend"), lshort = TRUE)

# KPSS Test for Level Stationarity
# data:  bc_ts
# KPSS Level = 1.5496, Truncation lag parameter = 4, p-value = 0.01
# Warnmeldung:
# In kpss.test(bc_ts, null = c("Level", "Trend"), lshort = TRUE) : p-value smaller than printed p-value

kpss.test(diff(bc_ts), null = c("Level", "Trend"), lshort = TRUE)

#	KPSS Test for Level Stationarity

# data:  diff(bc_ts)
# KPSS Level = 0.039205, Truncation lag parameter = 4, p-value = 0.1

# Warnmeldung:
# In kpss.test(diff(bc_ts), null = c("Level", "Trend"), lshort = TRUE) : p-value greater than printed p-value

``````

Test for autocorrelation is useless for the question. For further help please read more on the adf test. Withouth data this task is impossible.

Thanks for your reply. Here you find the data attached. The Data is already boxcox transformed (jfyi)

``````4159,736784
4139,10144
4406,129537
4742,92508
4492,8339
4574,919274
4442,31201
4501,77024
4678,986623
5384,0532
5507,03267
4746,925865
3973,567359
3981,43785
4331,282031
4484,750553
4757,167814
5116,998925
5767,84162
4451,91307
4360,524935
4335,662705
4255,304826
4205,127983
4372,514219
4489,795853
4451,105289
4181,669069
4476,385998
4415,497234
4300,260156
4234,460839
4479,733531
4451,576511
4511,887421
4195,04822
4308,242813
4395,041319
4761,521673
4440,187112
4442,177123
4397,934878
4554,953067
4569,269721
4552,051826
4240,393137
5008,149339
5170,33007
5248,326884
6386,029867
5283,665085
3665,333588
2762,093421
3557,541761
4368,578196
4390,033055
4235,799349
4424,237617
4177,854556
4248,566234
4303,558979
4029,858821
4129,811868
4302,100837
4826,070687
5301,655234
4553,370781
3904,092939
4601,929367
4164,138831
4486,622262
4497,704214
4334,852413
5106,304364
3999,623625
3833,181797
4146,540963
3845,144106
4084,640589
4089,989184
4187,473865
4066,875232
4201,581289
4056,702188
3979,014805
4165,086683
3946,39627
4159,557749
3883,975019
4156,047243
4563,679588
4000,068953
4252,778996
4183,77104
4588,655266
4025,267579
4551,062381
3964,522983
4220,171071
4846,571722
5380,37402
5691,701648
4533,880682
2991,664069
3480,329185
4270,640901
4123,752576
4033,635178
4154,703221
4152,21125
4061,425666
4136,169002
4112,622713
4462,469242
4805,693846
5008,572475
3818,708333
3366,417587
3796,465909
3805,524701
4527,654189
4372,086547
4243,083936
4631,263288
3822,964739
3690,853786
3867,743057
3454,835885
3555,476187
3943,446081
3960,218428
3885,994899
4046,689399
3981,717345
3856,688896
3820,140516
3667,864785
3619,211367
3707,075466
4013,111828
3741,614261
3923,361324
4245,298719
3923,814546
4067,240736
3942,618915
4337,110543
3677,252447
4332,765704
3890,45049
4620,880758
4834,911151
5206,705745
5476,07854
4847,505952
1621,161639
3620,552842
3517,605993
3847,182589
3900,411113
4136,043026
3940,249335
3795,220241
3825,361899
4060,547259
4003,48163
3767,40694
4086,460556
4545,848058
4700,264884
4604,508198
4012,741825
3570,570946
3350,0931
3741,811465
3794,714082
4054,356893
3859,469523
4533,549682
3859,086097
3712,124019
4073,778193
3759,599705
3713,395107
3670,314108
3788,089399
3819,308361
3784,675509
3765,250639
3730,239241
3748,924195
3725,213102
3939,045241
3795,142375
4104,22099
3760,659846
4096,13037
3919,620416
4139,640946
3519,045351
4195,616681
3860,657923
4067,752391
4532,192352
5022,562909
5679,520658
4939,899398
2528,425406
``````

I provided the data below. Can you help me with that? I am not sure which test to use even they come to different results.

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