raw data stationary but still can see trend and seaonality is stl So I am looking at unit sales data. I am doing a univariate time series analysis. My data is weekly sales numbers figures, spanning 2012- 2014 (obviously no till end 2014). I first ploted my response var against time.

I suspected trend and seasonality which would make sense. So I did a seasonal trend decompose with loess (STL). Here is the result.

However when I did a stationarity test on my original dataset, it gives me stationarity. And I tried Box-Ljung Philips-Perron unit root test augmented dicky fuller test with stationary and explosive as alternative both and kpss. Stationary. So why is it that my trend and sesonality not significant?
I assigned to every observation a month index and did boxplot(sales~month, data=???)
Here is the result:

Then asked myself if differences in mean were significant, they were not. I tried aov pairwise.t.test and TuckeyHD. even if difference in mean for some means was important, overall not. Could I say then that no significant trend and seasonality appears in the dataset and model with an ARIMA? Also I have only 156 observations in my dataset.

Here is the acf and pacf what ARMA would you specify? if ARMA at all.
I am really at loss it is the first time I see a staionary raw sales figure.
 A: In the spirit of  Christmas and a sincere respect for the persistence of the OP for an answer to his reasonable question I have taken the 152 weekly observations ( nearly 3 years of data) and used AUTOBOX in a totally automatic hands-free mode, a piece of software that I have helped develop , to give what I think is a more  complete  and comprehensive answer. One could use any flexible analysis system to duplicate my results with some requisite programming required to accomplish some technical advances.  @javlacalle (previously reported results) concluded that although the residual ACF ( at period ) suggested a cyclic effect but he failed to provide a complete solution although he had some clues to what was wrong with his well-intentioned approach.  He I believe didn’t have the facility to seamlessly integrate a set of weekly dummies into his model. The problem here is very straight-forward : the identification of a significant  lag at period 52 in the acf can be evidence of either the need for an ARIMA augmentation OR the need for a deterministic seasonal dummy augmentation .  Before Box and Jenkins and their army of zealots (of which I was a leader!) limited there approach to ARIMA (memory based) solutions a rich history of deterministic models (i.e. seasonal dummies ) was in vogue and apparently has been ignored  . Developments in integrating deterministic  seasonal  structure  in the presence of. ARIMA structure and empirically identified interventions in the presence of time varying coefficients and time varying error variance are now routinely available. In this case the toolkit  used by @javlacalle whose scholarship I generally respect was not robust enough in my opinion to correctly and fully solve the problem suggested by the data. The simplistic approach to use  initial ARIMA model identification assuming among other things that there were no anomalies, no deterministic seasonal dummies, no deterministic trends prior to Intervention Detection , which assumes a “good  ARIMA model”, seems to have failed as the series has a significant upwards trend in the data and contains strong deterministic weekly effects. His  Intervention  Detection schemes yielded a mixed bag of results as the tentative set of residuals data was strongly affected by the  unspecified i.e. explicitly omitted/ needed weekly dummies and a time trend.
I have posted my complete results on the web at http://www.autobox.com/stack/weekly.zip . The final model included an AR(1) coefficient  value .606 curiously close to the reported .617  and 48 weekly dummies (missing weeks 1,18 and 33) , a trend value of 5.54 and some 5 Additive Outliers (AO) at periods 12,14,65,42, and 39. The final model statistics showing an MSE of 44800 a reduction of 50% from the previously reported 88411 emphasizes the differences in the models. Following is a plot of the residuals suggesting randomness . The final ACF of the residuals , noticeably free of any lag 52 effect  is available in weekly.zip as finalacf.txt . A plot of the final model residuals is shown here. It is important to notice that the range of the errors is dramatically reduced as compared to the the previously reported results.  The fit/forecast graph nicely presents the essence of the model and is shown here.   The Cleansed Data graph nicely highlights the parsimonious identification of  5 anomalies.  The incorporation of weekly dummies requires additional parameters (needed in my opinion as they are statistically significant) although I can already hear the gasps of some readers who look askance at the utilization of so many parameters.
The Actual/Fit and Forecast graph is also useful in the understanding of these powerful results.  While all models are wrong, this model seems particularly useful in explaining the past and predicting the next 52 weeks. 
In summary while the ARIMA structures are the same, the models differ significantly in terms of trend and seasonal components with a reduction of nearly 50% in the estimated error variance. Restated the reported results have a 100% larger error variance than my suggested model. I feel sure that if it were somehow possible to automatically integrate the weekly dummies the results would still suggest a deficit. The trend and seasonality visually evident to the OP are now safely reflected in the model and the forecast. Finally a cyclical model is not necessarily an auto-regressive (memory ) model it could be a seasonal dummy model as in this case. QED 
