Time series analysis: Determine if trend is deterministic fluctuating/stable or stochastic I am analysing sales data of certain products and need to determine if the demand trend is  deterministic fluctuating or deterministic stable or stochastic. 
How do I do that in R / what approach is usually applied to do so?
Quarterly values would be for example:
2424,3030,3207,2943,2631,2863,2711,2837,2839,2876,3075,2886,2520,3136,3235,3071,2923,3237,
3054,3321,2856,3389,3092,3325
 A: Trends can be of the form
$$y(t)=a+bt+ct^2$$  OR
$$y(t)=y(t-1)+\theta_0$$ OR
$$Y(t)=a+b x_1+ c x_2$$
etc  where $x_1=1,2,3,4....t$ and $x_2=0,0,0,0,0,1,2,3,4$ thus one trend applies to observations $1-5$ and a second trend applies to observations $6$ to $t$.
if you wish you can post your data
EDIT after data was posted:
A plot of the ACF suggests that the series is stationary thus no trend is required. . This led directly to an AR(2) model /(2,0,0)(0,0,0) with a seasonal pulse reflecting consistent first quarter effect.  . The residual plot shows little structure thus randomness can be reasonably accepted. . This is confirmed by the ACF of the residuals  . The Actual/Fit/Forecast nicely summarizes the results 
A: Generally, in observational data it is difficult to distinguish the trend-stationary series from random walk. You called them deterministic and stochastic. 
The trend-stationary process is $x_t=\beta_0+\beta_tt+\varepsilon_t$, while RW is $x_t=x_{t-1}+\beta_0+\varepsilon_t$.
Consider a very well researched time series such as GDP. The economists are still debating whether it's trend-stationary or RW, e.g. see this paper on German GDP. You can also see how they try to determine if the series is RW or not.
