There are ARCH and GARCH style models. These models predict volatility and variation across time.

There are continuous time modeling methods (e.g., differential equations). These models treat time as a continuous variable and model the state of a system. With a good enough continuous time model, you could predict any number of steps ahead.

There are also state space and Markov process models which do something similar.

Finally, you may want to look into recurrence neural networks. These are a type of artificial neural network (ANN) used to predict time series.

It depends on the nature of the time series. The Arch and garch models apply to volatile time series ( i. e. heteroscedastic series). Long-memory series are modelled with Arfima models which are generalizations of the arima models. Long-term forecasts may be obtained using these models also.

If seasonality is evident you can think of using SARIMA models (either additive or multiplicative depending on the nature of data. Neural network models usually performs better (great in-sample and out-of-sample model fitness) if your sample is relatively smaller.

I don't agree with " I know about exponential smoothing however it only can forecast for one period ahead". There are many exponential smoothing methods and they are able to produce several periods ahead forecasts. See for example the forecast R package. Moreover many of them have ARIMA representations, possibly after transformation. I had a paper on that with Mrs Laurence Broze in 1990. The only problem is with forecast intervals for some non-additive methods like the multiplicative Winters method.

I agree to the explanations provided by Dr. Ette Etuk and Dr. Guy Melard.

In your question, it is not clear your problem with ARIMA models, however ANN can be a good alternative especially for nonlinear time series modeling.

Dear Jacob

please have a look at below address, I thought maybe it could be helpful for you:

https://www.researchgate.net/post/How_I_can_forecast_future_inflows_of_a_reservoir_using_historical_data_serie?_sg=3EjWYRvvQKuyVPRFrpXCOmoXJ6gYN1Q7fzmANDRS8gQfXrQVV6lMMaTxiLcvCjQ6qpHvPoTj31ybMw.uJD3-hiDWt4sv9zo6vV5ACLzfvaElGWXjGkqSGlXlV4ibQvV24PcqOuFfDwYKyKmnFXELFZ9kh6V0kVcMeeE1Al7ys8nFG7MLSkOSA

For macro stuff (forecasting for instance), if data there are data issue you can consider VAR or BVAR framework. But in general, you should be more specific what you mean by alternative for ARIMA.

Structural model within the state space framework may also be helpful.

I would recommend LSTM!