I need an example for pure deterministic time series which is not just dependent on time but on previous values, i.e $Y(t) = βY(t-1) + f(t). It should not have stochastic trends in it. I need this for academic purpose.
Looking for an example of actual data, where I can explain the terms comparing to real world
Exponential Decay formula would work.
is the remaining amout of material of the decay cycle is complete.
If you start with 100 grams of x this is your
If your decay rate is 2% this is your r.
If you do 1 second increments that would be your t.
The remaining amount becomes your new initial amount and you
Initial Amount Time Decay Rate Remaining Amount
100 grams 1 sec 2% 98.0198673307 grams
96.0789438852 grams 1 sec 2% 94.1764532455 grams
94.1764532455 grams 1 sec 2% 92.3116344834 grams
92.3116344834 grams 1 sec 2% 90.4837411776 grams
It would take 230.258509299 seconds to only have 1 gram of material left.
Actual examples of academic research, you can find at Exponential decay--Applications and examples
Edit: In my opinion another way of calling what you want would be a non-stochastic iterative time series.
