Time Series Prediction

Imagine you run a bike rental service and want to know how many bikes people will rent tomorrow. You have a record of every rental that has happened so far. The natural approach is to look at that record, notice what has been happening, and use it to estimate what will happen next. This is the core idea behind time series prediction: use the past to forecast the future.

The idea sounds simple, but it hides a constraint that shapes the whole task. A forecaster never knows the future. Any honest way of testing a forecasting model has to reproduce that situation, where the model only has access to what came before the moment it makes a prediction. Keeping that constraint in mind is the subject of this article.

Time series data is recorded in sequence, so the order of the observations carries meaning. A plot of bike rentals over several days makes a pattern visible almost immediately: the daytime hours and the nighttime hours of each 24-hour cycle look clearly different. Weekdays also seem to follow a different rhythm than weekends.

These regularities are exactly what makes forecasting possible. They suggest that what happened before carries information about what will happen next. If the observations were shuffled into a random order, the daily and weekly rhythms would be scrambled, and the record would no longer tell a story about how the system moves through time.

To test a forecasting model honestly, you divide the dated record into two portions using a cutoff date. The training set consists of all data up to the chosen date, and the test set consists of all data after that date. The model learns only from the training portion and is judged only on the test portion.

The reason for this rule follows directly from the goal of prediction. If the test set contained moments that happened earlier than some training moments, the model would be evaluated on a situation it could never face in practice, because a real forecaster does not know the future. A date-based cutoff keeps the test period entirely in the future relative to everything the model learned from. The cutoff is a deliberate choice that marks where the past ends and the prediction period begins.

The source applies this rule to its bike rental data. It uses the first 184 data points, which correspond to the first 23 days, as the training set. The remaining 64 data points, which correspond to the remaining 8 days, form the test set. The cutoff falls between the 23rd day and the 24th day, so the model learns from the opening stretch of the record and is judged on the stretch that follows.

A forecasting task needs a precise statement of what goes in and what comes out. In the bike rental example, the only input feature is the date and time at which a given number of rentals occurred. The source gives the example timestamp 2015-08-01 00:00:00 as the input. Nothing else about the rentals, such as weather or station details, is used in this particular setup.

The output is the number of rentals in the following three hours. Each prediction is therefore about a window of time that starts at the input timestamp, not a single instant. The source notes that this three-hour window is set according to the DataFrame used in its analysis.

An evaluation becomes unrealistic when the model gains access to information it would not have at prediction time. The clearest case is a test set that contains moments earlier than some training moments. Because the model has already seen later data, its test score no longer reflects how it would perform on genuinely future days.

Time series prediction asks what will happen next, using what has already happened. The order of observations carries information, which is why an honest evaluation must respect the direction of time. You choose a cutoff date, train on everything before it, and test on everything after it. In the bike rental setup, the input is a date and time and the output is the number of rentals in the following three hours.