Background#

What is Time Series Forecasting?#

Generally speaking, forecasting just means making predictions about events in the future. Trivially, in time series forecasting we want to predict the future values of a given time series.

For example, in electricity production it is very important that demand and supply are in balance. Thus, producers anticipate consumer demand for electricity and plan production capacity accordingly. In other words, producers rely on accurate time series forecasting of consumer demand for electricity to generate just enough supply.

In forecasting, there is the implicit assumption that observable behaviours of the past that impact time series values continue into the future. To stay with the electricity example: People will generally consume less energy in the night than during the day, will watch TV mostly during the evenings and use air conditioners when it’s hot during summer.

Ten weeks of data plotted over each other – electricity dataset.#

Naturally, it’s impossible to forecast the unpredictable. For instance, in 2019 it was virtually impossible to account for the possibility of travel restrictions due to the Covid-19 pandemic when trying to forecacst travel demand for 2020.

Thus, forecasting operates on the caveat that the underlying factors that generate the time series values don’t fundamentally change in the future. It is a tool to predict the ordinary and not the surprising.

To look at this another way: Models are actually trained to predict the past and it is only us who use models to forecast into the future.

Target And Features#

We call the time series that we want to predict the target time series. The past target values are the most important information a model can use to make accurate predictions.

In addition, models can make use of features, additional values that have an impact on the target value. We differentiate between “static” and “dynamic” features.

A dynamic feature can be different for every time point. For example, this could be the price of a product, but also more general information such as outside air temperature. Internally, we generate dynamic features for things like the age of the time series or what day of the week it is.

Important

Most models require dynamic features to be available in the future time range when making predictions.

In contrast, static features describe a time series independently of time. If we were to predict different products across different stores, we can use static features to label each time series to include store and product indentifiers.

We further differentiate between categorical and continuous (real) features. The idea is that in continuous features the number itself has meaning, for example when using the price as a feature. A categorical feature on the other hand doesn’t have the same property: Stores 0, 1, and 2 are distinct entities and there is no notion of having a “higher store”.

Probabilistic Forecasting#

One core idea in GluonTS is that we don’t produce simple values as forecasts, but actually predict distributions.

An intuitive way to look at this is to imagine predicting a time series 100 times, which returns 100 different time series samples, which form a distribution around them - except that we can directly emit these distributions and then draw samples from them.

Distributions provide the benefit that they provide a range of likely values. Imagine being a restaurant owner, wondering how many ingredients to buy; if we buy too few we won’t serve customer demand, but buying too many will produce waste. Thus, when we forecast demand, it is valuable if a model can tell us that there is probably a demand of say 50 dishes, but unlikely more than 60.

Predicting 24 hours, showing p50, p90, p95, p98 prediction intervals.#

Note

The predicted distributions are not authorative: A predicted 90th percentile doesn’t mean that only 10% of actual values will be of higher value, but that this is the guess of the model about where this line is.

Local and Global Models#

In GluonTS we use the concepts of local and global models.

A local model is fit for a single time series and used to make predictions for that time series, whilst a global model is trained across many time series and a single global model is used to make predictions for all time series of a dataset.

Training a global model can take a lot of time: up to hours, but sometimes even days. Thus, it is not feasible to train the model as part of the prediction request and it happens as a separate “offline” step. In contrast, fitting a local model is usually much faster and is done “online” as part of the prediction.

In GluonTS, local models are directly available as predictors, whilst global models are offered as estimators, which need to be trained first.