
I have non-stationary time series. It has evident trend in means and seasonality. These raw data are measured every second. On the plot of original series I see trend and seasonality about 80,81 (after each 80 second we can see new growth). It is possible that I will never obtain model with white noise? I have tried first difference and first seasonal difference on 80 and second seasonal difference with 81 pediod, and twice of 81. And stiil I have regular data in residuals! It is possible??


I have used R. I have tried different ways: step-by-step, ARIMA with different settings for differences, auto.arima. I do not know why I cannot receive white noise in the residuals. I look on ACF of residuals.


Has the task got solution?


Below I present my data.



```
3785
4542
4542
4542
4542
4542
4542
4542
4731
4731
4731
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5772
8043
8516
8516
8516
8516
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8516
8516
8516
8516
8516
8516
8516
8516
8705
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8800
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8989
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10314
12585
13058
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13247
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14288
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18073
21101
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21574
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25359
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26021
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29333
30090
30090
30090
30090
30090
30090
30090
30090
30090
30090
30090
30090
30090
30090
30090
30090
30279
30279
30279

```


[ARIMA with difficult seasonality in R](/questions/80710/arima-with-difficult-seasonality-in-r)
===============================================================================================



I'm not sure if ARIMA would be able to decompose the data into interprettable/decomposed time series. 


I used [Proc UCM](http://support.sas.com/documentation/cdl/en/etsug/60372/HTML/default/viewer.htm#etsug_ucm_sect006.htm) in SAS which is a state space model. Following is the code of a basic structural model. The data is decomposed into Trend (level+slope) + Seasonal and White noise (Irregular). There is not much white noise left after you model. I'm assuming this is what you were looking for. The model fits the data like a glove. If you have access to SAS, you can try running the following code, you can get the decomposed series.


Level + Slope+ Seasonal + Irregular (not Shown).


![enter image description here](https://i.stack.imgur.com/1dyFK.png)


![Forecast Output which is comination of level+slope+season:](https://i.stack.imgur.com/j23yi.png)


![enter image description here](https://i.stack.imgur.com/UglD2.png)


You could also try `STL decomposition` in R.


ods graphics on;
 proc ucm data = data;



```
      id date interval = second; 
      model value;
      irregular plot = smooth;
      level ;
      slope variance = 0 noest;
      season length = 80 ;
       dep lags = 2;
      forecast plot=(forecasts decomp) lead = 80 outfor=forecast; 
   run ; 
ods graphics off ;

```

Hope this is helpful.


