The classical approaches to time series regression are:
auto-regressive models (there are whole literatures about them)
Fourier decomposition or similar to extract the periodic components of the signal (i.e., hidden oscillations in the data)
Other less common approaches that I know about are
Neural Network (NN) approaches, either using recurrent NNs (i.e., built to process time signals) or classical feed-forward NNs that receive as input part of the past data and try to predict a point in the future; the advantage of the latter is that recurrent NNs are known to have a problem with taking into account the distant past
In my opinion for financial data analysis it is important to obtain not only a best-guess extrapolation of the time series, but also a reliable confidence interval, as the resulting investment strategy could be very different depending on that. Probabilistic methods, like Gaussian Processes, give you that "for free", as they return a probability distribution over possible future values. With classical statistical methods you'll have to rely on bootstrapping techniques.
There are many Python libraries that offer statistical and Machine Learning tools, here are the ones I'm most familiar with: