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I would recommend Darts in Python [1]. It's easy to use (think fit()/predict()) and includes
* Statistical models (ETS, (V)ARIMA(X), etc)
* ML models (sklearn models, LGBM, etc)
* Many recent deep learning models (N-BEATS, TFT, etc)
* Seamlessly works on multi-dimensional series
* Models can be trained on multiple series
* Many models offer rich support for probabilistic forecasts
* Model evaluation is easy: Darts has many metrics, offers backtest etc
* Deep learning scales to large datasets, using GPUs, TPUs, etc
* There's even now an explainability module for some of the models - showing you what matters for computing the forecasts
* (coming soon): an anomaly detection module :)
* (also, it even include FB Prophet if you really want to use it)
Warning: I'm probably biased because I'm Darts creator.
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Prophet
Tool for producing high quality forecasts for time series data that has multiple seasonality with linear or non-linear growth.
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InfluxDB
Power Real-Time Data Analytics at Scale. Get real-time insights from all types of time series data with InfluxDB. Ingest, query, and analyze billions of data points in real-time with unbounded cardinality.
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As a few other people have mentioned, I find R to be the easiest tool for this job, specifically the forecast package [0]. I had to use this package for an applied econometrics course in college a few years ago, and I have been using it ever since. I find the syntax to be more straightforward than comparable libraries in Python. I also assume that this library (and other libraries in R) offer higher quality models and results than their counterparts in Python, but this is just an assumption.
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For feature extraction check out tsfel:
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