In field of economics (I think) we have ARIMA and GARCH for regularly spaced time series and Poisson, Hawkes for modeling point processes, so how about attempts for modeling irregularly (unevenly) spaced time series – are there (at least) any common practices?
(If you have some knowledge in this topic you can also expand the corresponding wiki article.)
I see irregular time series simply as series of pairs (value, time_of_event), so we have to model not only value to value dependencies but also value and time_of_event and timestamps themselves.
Edition (about missing values and irregular spaced time series) :
Answer to @Lucas Reis comment. If gaps between measurements or realizations variable are spaced due to (for example) Poisson process there is no much room for this kind of regularization, but it exists simple procedure : t(i) is the i-th time index of variable x (i-th time of realization x), then define gaps between times of measurements as g(i)=t(i)-t(i-1), then we discretize g(i) using constant c, dg(i)=floor(g(i)/c and create new time series with number of blank values between old observations from original time series i and i+1 equal to dg(i), but the problem is that this procedure can easily produce time series with number of missing data much larger then number of observations, so the reasonable estimation of missing observations' values could be impossible and too large c delete "time structure/time dependence etc." of analysed problem (extreme case is given by taking c>=max(floor(g(i)/c)) which simply collapse irregularly spaced time series into regularly spaced
Edition2 (just for fun):
Image accounting for missing values in irregularly spaced time series or even case of point process.
Best Answer
If the observations of a stochastic process are irregularly spaced the most natural way to model the observations is as discrete time observations from a continuous time process.
What is generally needed of a model specification is the joint distribution of the observations $X_{1}, \ldots, X_n$ observed at times $t_1 < t_2 < \ldots < t_n$, and this can, for instance, be broken down into conditional distributions of $X_{i}$ given $X_{i-1}, \ldots, X_1$. If the process is a Markov process this conditional distribution depends on $X_{i-1}$ $-$ not on $X_{i-2}, \ldots, X_1$ $-$ and it depends on $t_i$ and $t_{i-1}$. If the process is time-homogeneous the dependence on the time points is only through their difference $t_i - t_{i-1}$.
We see from this that if we have equidistant observations (with $t_i - t_{i-1} = 1$, say) from a time-homogeneous Markov process we only need to specify a single conditional probability distribution, $P^1$, to specify a model. Otherwise we need to specify a whole collection $P^{t_{i}-t_{i-1}}$ of conditional probability distributions indexed by the time differences of the observations to specify a model. The latter is, in fact, most easily done by specifying a family $P^t$ of continuous time conditional probability distributions.
A common way to obtain a continuous time model specification is through a stochastic differential equation (SDE) $$dX_t = a(X_t) dt + b(X_t) dB_t.$$ A good place to get started with doing statistics for SDE models is Simulation and Inference for Stochastic Differential Equations by Stefano Iacus. It might be that many methods and results are described for equidistant observations, but this is typically just convenient for the presentation and not essential for the application. One main obstacle is that the SDE-specification rarely allows for an explicit likelihood when you have discrete observations, but there are well developed estimation equation alternatives.
If you want to get beyond Markov processes the stochastic volatility models are like (G)ARCH models attempts to model a heterogeneous variance (volatility). One can also consider delay equations like $$dX_t = \int_0^t a(s)(X_t-X_s) ds + \sigma dB_t$$ that are continuous time analogs of AR$(p)$-processes.
I think it is fair to say that the common practice when dealing with observations at irregular time points is to build a continuous time stochastic model.