Time Series: Understanding the Past to Predict the Future

Have you ever stopped to think about how we manage to understand and predict events related to the passage of time? The data used for these tasks are called time series! But what exactly is that?

Time series are sets of data organized in a regular and known chronological order. In other words, they are information that we record to analyze how they change over time. Time series can be found everywhere! Here are some everyday examples:

• Health: Heart rate monitored by smartwatches;

• Economics: A country's monthly inflation rate;

• Sports: A team's performance throughout a championship;

• Technology: The number of visits to a website per hour.

Why are they so important? Because they allow us to identify patterns, understand trends, and even make predictions! Imagine predicting a city's energy consumption or the production of the next harvest of a product of interest. The applications are countless!

Components of Time Series

A time series can have one or more components, and these components can reveal important details about the behavior of the data. These components include:

1. Trend : Increasing or decreasing behavior of values over time;

2. Seasonality : A pattern of repetition observed within a certain periodicity (such as increased sales at Christmas);

3. Cycle : Cyclical patterns that occur as fluctuations around a trend due to economic, environmental, or other factors. Cycles do not have a fixed duration and can vary in length, thus differing from seasonality.

4. Noise or error : Random part of the time series.

The figure below shows the decomposition of a time series into its different components. At the top (1) we have the original series. Below, we see its trend (2), seasonality (3) and noise or random part (4).

Additive and Multiplicative Models

The decomposition of a time series can occur according to two models:

• Additive model: Where the original time series is equal to the sum of its components;

• Multiplicative model: Where the time series is equivalent to the multiplication of its components.

The multiplicative model is appropriate when the variation of the seasonal component around the trend component is proportional to the magnitude of the data, while the additive model is more suitable when such a relationship is not proportional.

Conclusion

Time series can provide valuable insights into data and its behavior over time. Furthermore, they are the input data for predictive models such as Autoregressive Models . By applying such models to time series, we can use what we've learned from the past to predict the future! But that's a topic for the next post!

References :

• Hyndman, RJ and Athanasopoulos, G. Forecasting: principles and practice. OTexts, 2018.

• Barros, AC, Ferreira, Pedro Guilherme Costa and Mattos, DM d., Oliveira, IC d., and Duca, VE ld A. Time Series Analysis in R: An Introductory Course. FGV IBRE, 2018.