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I have a project about time series analysis. My data are not stationary and they have daily seasonality as shown in figure below. Is it correct to do the following steps?

  • Decompose Time serie into season, trend , residuals
  • Model residuals using ARIMA
  • Then add back seasonality and trend

Should i model seasonality and trends too?

enter image description here

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12
18
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
25
39
63
163
190
219
289
416
600
679
705
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807
720
544
603
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419
333
336
424
290
369
273
342
269
297
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331
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357
185
301
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399
342
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293
452
331
545
390
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362
385
443
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400
594
405
551
355
407
324
391
206
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223
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194
163
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119
126
91
71
9
37
45
23
33
9
27
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
18
45
60
138
157
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272
395
556
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553
811
702
630
507
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349
309
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309
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139
87
56
37
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25
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26
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1
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15
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40
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568
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728
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309
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144
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222
108
88
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31
31
38
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41
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  • 1
    $\begingroup$ What is the seasonality for the Data above ? It it 7 ? $\endgroup$ – forecaster Jul 21 '18 at 14:11
  • $\begingroup$ The time serie contains 3 days of data every 15 minutes. So i think saesonality is 96. $\endgroup$ – Karou Jul 21 '18 at 14:56
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    $\begingroup$ I will try and help you .. Please post the data in a csv file. As an overview comment ...pure SARIMA implies that the model structure is all endogenous whereas if there are hourly effects deterministic structure may be needed. Only uour data knows for sure ..so lets listen to it. $\endgroup$ – IrishStat Jul 21 '18 at 15:01
  • $\begingroup$ So you think making the time series stationary using decomposition is wrong? $\endgroup$ – Karou Jul 21 '18 at 15:27
  • $\begingroup$ I didn't say that .... $\endgroup$ – IrishStat Jul 21 '18 at 16:04
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The strong relationship is not within day but across days . You have 3 samples i.e. 3 days . For example your first reading per day is more related to the first reading on the previous day than the last reading of the previous day ( ala an ar(1) ). Memory or predictability is across similar time periods for previous days. Those who suggest arima/sarima have swallowed the pill/poison ! As a recovering arima addict , I fully understand the symptoms.

In my opinion ( after looking at your data with AUTOBOX ) you are probably wasting you time trying to use arima or sarima .. I suggest that you extend your data from 3 to many more days ..and then employ developing daily forecasts and using daily totals and predictions as a driver to predict each of the 96 slices ... then roll the forecasts up and reconcile them with the daily forecasts. We have successfully done this for half-hour call center forecasting data here http://demand-planning.com/2010/03/18/can-forecasting-help-me-staff-a-specific-hewlett-packard-call-center-at-1030-am-on-a-friday/ and are currently looking at using 15 minute time slices (96 per day ) for Taco Bell.

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  • $\begingroup$ Thanks for wasting your time to help me. I will have access to more data soon but they will be unfortunately max 20 days. The main goal of the project was to compare linear models like ARIMA with Neural networks in time series forecasting. $\endgroup$ – Karou Jul 21 '18 at 20:35
  • $\begingroup$ Why would you say "wasting my time" when you can just upvote my answer to show your true appreciation for my valuable time. 20 days would do just fine .... $\endgroup$ – IrishStat Jul 21 '18 at 20:39
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For me, this seems a good approach but you can do better by comparing the results you obtain (e.g. h-step ahead forecasting error) using this approach with the results you obtain with a seasonal ARIMA (or SARIMA) model in order to decide which one is "the best".

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  • $\begingroup$ Sarima works with non-stationary data? One problem with sarima is that period is too high (96) and my program crashes. $\endgroup$ – Karou Jul 21 '18 at 14:58
  • $\begingroup$ SARIMA includes a classical differencing (the "I" of SARIMA) and a seasonal one (the "S" of SARIMA). $\endgroup$ – paf Jul 21 '18 at 15:35
  • $\begingroup$ I uploaded my data above so which value D for sarima should take? $\endgroup$ – Karou Jul 21 '18 at 15:51
  • $\begingroup$ In general, D should be 0 or 1 (so probably 1 is a good choice in your case). But auto.arima function in R chooses D automatically. $\endgroup$ – paf Jul 21 '18 at 17:36
  • $\begingroup$ I am working in python but i will give it a try and compare the results as you said. Do you have any paper for decomposotion and forecasting to use it as reference? Thanks for everything. $\endgroup$ – Karou Jul 21 '18 at 18:02

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