What is the type of these signals?
Types of signals:


According to their range set (values): Real Valued, Complex valued ;
According to their dimensions: Scalar, Vector ;
According to their values: Continuous Amplitude, Quantized ;
According to their domain set (arguments): Continuous-time, Discrete-time :
According to their mappings: Deterministic, Stochastic (Random) ;
According to their character: Periodic, Even, Odd, Symmetric... ;


A Time-Series is another name given to a discrete-time random sequence which is an instance of some discrete time random process. As it's a random signal, the sequence samples do not have a mathematical formula which connects the points to each other along the series, hence it's viewed as a series of numbers which were generated according to some probabilistic law. 

Consider the following: You generate a continuous-time deterministic signal $x(t)$ by exciting an oscillator which produces a periodic sine wave of exactly known frequency, phase and amplitude. Then sample this signal to produce a discrete-time sequence $x[n]$. The point is that by just observing the sampled signal you cannot tell whether the sequence of samples actually belong to a deterministic signal with a mathematical formula that can be used to generate all of its samples, or they belong to a random process whose values happen to be fitting into the observed sine wave (which has a very small probability (improbable) but is not impossible otherwsie). Hence any such sequence can be considered as a random sequence of numbers denoted as a time-series.

After a certain amount of analysis you may conclude that the observed sequence of numbers probably belong to a deterministic sine wave of certain frequency,phase and amplitude. But this deduction is only an estimation. The truth cannot be known but precise predictions can be computed.