Choosing model to predict next value in a sequence

Question

Background: I am currently starting to work on a Machine Learning project that might be of use in car racing.

The goal of it is to give engineers suggestions about strategies.

First thing I am trying to do is given some initial amount of test laps(for example specific driver has driven 20 warmup laps and we recorded the times taken for each of them) predict/show the distribution of probabilities for the next lap time.

The laps' times have a relatively small deviation(so far we are not taking into account pitstops).

I have read several articles, blog entries and answers on StackExchange for predicting next value in a sequence. Answers vary and (possibly due to me being rather a layman in ML and Stats) suggest different things with some of them suggesting to build an RNN or try various things and check which works best. However, implementing RNN or other ML algorithms is not an easy task, so I would prefer to have a sense of direction of where I should research.

Question(Part 1):

Given a sequence of real numbers $t_1,t_2,t_3,...,t_n$ with a relatively small standart deviation, how to predict the next value $t_{n+1}$(or the probability $P$ next value $t_{n+1}$ will be in some interval $(x,y)$ where $x\in \mathbb{R}$,$y\in \mathbb{R}$ (real numbers))?

Question(Part 2):

If there is no simple answer to the previous part, which areas of ML should I research to find the best model?

End of question.

I would be grateful if the answer was in rather simple terms, as I am a layman in Machine learning and Statistics.

Thank you.

Answer 1

You have a time series problem requiring a time series solution. The preferred method is an optimized weighted average of the past ... this method is called ARIMA or univariate Box-Jenkins. Concern has to be given to identifying and adjusting for unusual observations/plses AND allowing for future pulses/anomalies to arise in the future i.e. enabling confidence limits on the forecast to be robustified. Care need also be given to detecting level shifts and/orr time trends suggesting permanent activity

Answer 2

ARIMA methods are so 1960. Use an LSTM or RNN, or really any ML model. Ideally, give the model more features than just the historical values. You can engineer dozens of features just from a single timestamp, but you may have other external signals (including other concurrent time series) that are in some way predictive. There have been several Kaggle contests for predicting time series that you can look at for inspiration. For example, this LSTM won one competition.

(ok, I’m dismissive of old-school (S)ARIMA and ARCH methods. They’re still used some places, and in fact you can use one or more as inputs to an ML model. If you have no other predictive inputs of any kind, and don’t know how to encode time features, these methods can outperform ML.)