Right terminology for time series associated to a variable

I am in the process of writing a paper and I have a doubt. I am not sure that this is the best stackexchange site where to post since it is more a terminology problem than a mathematical one. Please point me to the right site if I am wrong.

During my experiments, I am acquiring a set of kinematic variables (angles) which we can call $$x_i$$ and I have a set of 5 outputs $$y_i$$. To each variable is associated a time-series.
Therefore, I wanted to denote the variables introduced above in the following way, but I am not sure if it is the best one.

(I need to introduce explicitly the time series because in the paper I talk about the correlation of the two time-series.)

I will write:

We denote with $$\mathbf{x}=\{x_1,x_2,\dots,x_{n_x} \}$$ (with $$n_x=10$$) the set of kinematic variables acquired at each time step, and with $$\mathbf{y}=\{y_1,y_2,\dots,y_{5} \}$$ the outputs. Moreover, we denote with $$X_i,Y_i$$ the time series respectively associated to the variable $$x_i, y_i$$.

Thanks for your help.

• rate of change ? – Roddy MacPhee Apr 16 at 19:00
• I did not understand your comment – kalmanIsAGameChanger Apr 24 at 12:31

One should try not to write redundancies like $$x_{n_x}$$. If you want to avoid confusions between indexes and bounds (here we have $$x_i$$ with $$i \le n_x$$), you should tend to use upper cases letters without any index. So I would rather write : $$\mathbf{x}=\{x_1,x_2,\dots,x_{N}\}$$.
To write the $$j$$-th term of the time serie, you have plenty of choices $$X_i(j), X_{ij}, X_i^{(j)}$$. If the treatment of those times series involves matrix operations, $$X_{ij}$$ seems like a very good choice.