Seeking advice on using time series estimation, for a specific type of data

I am new to time series modeling and am trying to come up with a solution for a problem. My problem is about estimation of next value in a time series, which is made of four components. One is picked randomly from 3 different gamma distributions. One follows a uniform distribution and the other follows a Weibull distribution.

My simple query is, that if there is hope for such a data to use time series modeling and forecasting of future data. I am asking just a guidance on whether I should go through this path or find some other alternative solution to my problem, by not using prediction at all.

Is it worth investing time in learning topics like ARMA/ARIMA/GARCH etc. in this scenario?

Edit: Adding one more important piece of information which I missed. I will explain this with an example. Imagine that I have a series of cups coming toward me, and I fill them with variable amount of water. The amount of water is filled like this:

1. Pick one value randomly from one of the 4 gamma distributions with different $\alpha$ and $\beta$ parameters.
2. Some of the cups need special attention. Those cups are selected using a Weibull distribution which is fixed. If a particular cup is marked as special, then more water is filled, and this quantity is picked from an exponential distribution.
3. The above step is considered again simultaneously with same distributions but with different parameters.

So I have to predict how much water will fall into a new cup which comes to me. The cups are coming toward me and the water is filled in each from these 3 sources. Can I use time series modeling here?

EDIT: If time series modeling is not good here, please give suggestions about other feasible methods!

• If the distributions are constant over time, time series models would be irrelevant. If, however, the distributions change with time and knowing the last distribution (or a few recent ones) gives you extra information about the newest distribution (the outcome of which you want to predict), then time series models may be relevant. Could you write down a model for one or all of your series? – Richard Hardy Nov 12 '16 at 11:44
• @RichardHardy Apologies for my ignorance. When you ask about writing down the model, do you mean the distribution parameters? – kosmos Nov 12 '16 at 12:10
• Yes, especially to elicit any time dependence or lack thereof. Something like: $X_t|I_{t-1}\sim N(0,1)$ (no time dependence) or $X_t|I_{t-1}\sim N(x_{t-1},1)$ (time dependence); here $I_{t-1}$ is the information available when making the prediction of $X_t$, and $x_{t-1}$ is the observed realization of $X_{t-1}$. – Richard Hardy Nov 12 '16 at 12:40
• After your edit, I still do not see an explicit temporal relationship, so I do not see how time series models could be useful here. But maybe I am failing to understand your setup. – Richard Hardy Nov 12 '16 at 14:23
• @RichardHardy The only time dependent relationship is that if one cup is considered as special now then the probability of next immediate cup to be special is low. So I will see spikes which are spread out. Moreover, what other method can I use to predict ? – kosmos Nov 12 '16 at 23:39