In this paper – “DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks”, the authors discuss a method for learning a global model from several individual time series.

Let’s break down some aspects of the approach and design.

“In probabilistic forecasting one is interested in the full predictive distribution, not just a single best realization, to be used in downstream decision making systems.”

The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term).

Recurrent Neural Network is used to refer to NNs with an infinite impulse response, and are used for speech recognition, handwriting recognition and such tasks involving sequences. https://en.wikipedia.org/wiki/Recurrent_neural_network

An LSTM or The Long Short-Term Memory (LSTM) is a type of RNN, that came about to solve a problem of vanishing gradients in previous RNN designs. An LSTM cell can process data sequentially and keep its hidden state through time.

A covariate is an independant random variable, with which the target random variable is assumed to have some covariance.

The approach has distinct features described in this snippet

“In addition to providing better forecast accuracy than previous methods, our approach has a number key advantages compared to classical approaches and other global methods: (i) As the model learns seasonal behavior and dependencies on given covariates across time series, minimal manual feature engineering is needed to capture complex, group-dependent behavior; (ii) DeepAR makes probabilistic forecasts in the form of Monte Carlo samples that can be used to compute consistent quantile estimates for all sub-ranges in the prediction horizon; (iii) By learning from similar items, our method is able to provide forecasts for items with little or no history at all, a case where traditional single-item forecasting methods fail; (vi) Our approach does not assume Gaussian noise, but can incorporate a wide range of likelihood functions, allowing the user to choose one that is appropriate for the statistical properties of the data.
Points (i) and (iii) are what set DeepAR apart from classical forecasting approaches, while (ii) and (iv) pertain to producing accurate, calibrated forecast distributions learned from the historical behavior of all of the time series jointly, which is not addressed by other global methods (see Sec. 2). Such probabilistic forecasts are of crucial importance in many applications, as they—in contrast to point forecasts—enable optimal decision making under uncertainty by minimizing risk functions, i.e. expectations of some loss function under the forecast distribution.”

Facebook Prophet is an open-source library for forecasting – https://facebook.github.io/prophet/

ARMA – AutoRegressive Moving Average Estimator

ARIMA estimator – AutoRegressive Integrated Moving Average is a generalization of ARMA and can better handle non-stationarity in a time series.