##### An introduction to time series forecasting

Industries from energy and retail to transportation and finance today rely on time series forecasting for projecting product demand, resource allocation, financial performance, predictive maintenance, and countless other applications. Despite the potential of time series forecasting to transform business models and improve bottom lines, many companies have yet to adopt its technologies and reap the benefits. Let’s start with a definition, and follow with a brief overview of applications and methods.

Time series forecasting is a technique for predicting future events by analyzing past trends, based on the assumption that future trends will hold similar to historical trends. Forecasting involves using models fit on historical data to predict future values. Prediction problems that involve a time component require time series forecasting, which provides a data-driven approach to effective and efficient planning.

## Time series forecasting applications

The applications of time series models are many and wide-ranging, from sales forecasting to weather forecasting. In decisions that involve a factor of uncertainty about the future, time series models have been found to be among the most effective methods of forecasting.

Time series forecasts inform all kinds of business decisions. Some examples:

- Forecasting power demand to decide whether to build another power generation plant in the next five years
- Forecasting call volumes to schedule staff in a call center next week
- Forecasting inventory requirements to stock inventory to meet demand
- Forecasting supply and demand to optimize fleet management and other aspects of the supply chain
- Predicting equipment failures and maintenance requirements to minimize downtime and uphold safety standards
- Forecasting infection rates to optimize disease control and outbreak programs
- Predicting customer ratings through to forecasting product sales

Depending on the circumstances and on what is being forecast, forecasts can involve different time horizons.

## How time series forecasts are developed

Time series forecasts are developed based on time series analysis, which comprises methods for analyzing time series data to extract meaningful statistics and other characteristics of the data. The goal of time series forecasting is to predict a future value or classification at a particular point in time.

Time series forecasting starts with a historical time series. Analysts examine the historical data and check for patterns of time decomposition, such as trends, seasonal patterns, cyclical patterns, and regularity. These patterns help inform data analysts and data scientists about which forecasting algorithms they should use for predictive modeling.

The historical time series used for data analytics in preparation for forecasting is often referred to as sample data. Sample data is a subset of the data that is representative of the entire set of data. Every machine learning or classical forecasting method incorporates some statistical assumptions. Data scientists examine the sample data to understand its statistical attributes. This allows them to determine which models they can choose from and what data preprocessing needs to be applied to avoid violating any assumptions of their model selection.

For example, many time series forecasting algorithms assume that the time series doesn’t exhibit a trend. So before using a forecasting algorithm, the data scientist must apply a variety of statistical tests on their sample data to determine whether or not their data exhibits a trend. If a trend is found, they can elect to either pick a different model or remove the trend from their data through differencing. Differencing is a statistical technique whereby a non-stationary time series, or a time series with trend, is transformed into a stationary time series.

Many types of machine learning forecasting models require training. Data scientists train time series forecasting models on the sample data. Once the model has been trained, the data scientists test out their predictive modeling or forecasting algorithms on additional sample data to determine the accuracy of their model selection and to tweak the parameters of the model to optimize it further.

To read about real-world time series forecasting use cases, see the Veritas storage forecasting and Playtech machine learning case studies.

## Time series decomposition

Time series data can exhibit a variety of patterns, so it is often helpful to split a time series into components, each representing an underlying pattern category. This is what decompositional models do.

The decomposition of time series is a statistical task that deconstructs a time series into several components, each representing one of the underlying categories of patterns. When we decompose a time series into components, we think of a time series as comprising three components: a trend component, a seasonal component, and residuals or “noise” (anything outside the trend or seasonality in the time series).

Moving average smoothing is often a first step in time series analysis and decomposition. The moving average removes some of the stochastic nature of the data and allows you to more easily identify whether or not your data exhibits any trend.

Classical decomposition is one of the most popular types of time series decomposition. There are two main types of classical decomposition: decomposition based on rates of change and decomposition based on predictability. Further, decomposition based on rates of change can be either additive or multiplicative decomposition:

- In an additive time series, the three components (trend, seasonality, and residuals) add together to make the time series. An additive model is used when the variations around the trend do not vary with the level of the time series.
- In a multiplicative time series, the three components multiply together to make the time series. A multiplicative model is appropriate if the trend is proportional to the level of the time series.

## Time series regression

Regression models are among the most common types of time series analysis and forecasting techniques. Regression models describe a mathematical relationship between the forecasted variable and a single predictor variable. The most well-known regression model is a linear model. However, nonlinear regression models are extremely popular. Multiple regression models describe a relationship between a forecasted variable and several predictor variables. Understanding regression models is the basis for understanding more sophisticated time series forecasting methods.

## Exponential smoothing

Exponential smoothing is the basis for some of the most powerful forecasting methods. Exponential smoothing produces forecasts based on weighted averages of past observations. In other words, these models produce forecasts where the forecast most closely resembles recent observations. Exponential smoothing techniques are extremely popular because they can be very effective predictors and can be applied to a wide variety of data and use cases.

Common types of exponential smoothing include single exponential smoothing (SES), double exponential smoothing (DES), and triple exponential smoothing (TES, also known as the Holt-Winters method). SES forecasts are weighted averages of the time series itself while DES forecasts are weighted averages of both the trend and the time series. Finally, Holt Winters or TES forecasts are weighted averages of the seasonality, trend, and time series.

The ETS model (referring to the explicit modeling of error, trend, and seasonality) is another type of exponential smoothing technique. ETS is similar to Holt-Winters but was developed after Holt-Winters. It uses a different optimization method for the model initialization and also overcomes some esoteric shortcomings of Holt-Winters that exist in relatively uncommon time series scenarios.

## ARIMA models

Autoregressive integrated moving average, or ARIMA, models are another time series forecasting method. They are among the most widely used time series forecasting techniques — as widely used as exponential smoothing methods. While exponential smoothing methods generate forecasts based on historical components of the data, ARIMA models take advantage of autocorrelation to produce forecasts. Autocorrelation is when a time series displays correlation between the time series and a lagged version of the time series.

There are two main types of ARIMA models, non-seasonal ARIMA models and seasonal ARIMA, or SARIMA, models. To define ARIMA and SARIMA, it’s helpful to first define autoregression. Autoregression is a time series model that uses observations from previous time steps as input to a regression equation to predict the value at the next time step. So, in an autoregressive model, the forecasts correspond to a linear combination of past values of the variable. And in a moving average model, the forecasts correspond to a linear combination of past forecast errors. The ARIMA models combine the two approaches.

One of the underlying assumptions of an ARIMA model is that the time series is stationary. Stationary time series is a time series whose components do not depend on when the time series is observed. In other words, the time series doesn’t exhibit trend or seasonality. Because ARIMA models require the time series to be stationary, differencing may be a necessary preprocessing step before using an ARIMA model for forecasting.

The SARIMA model extends ARIMA by adding a linear combination of seasonal past values and/or forecast errors.

## Neural networks

Neural networks are growing in popularity. Neural networks aim to solve problems that would be impossible or difficult to solve with statistical or classical methods. Two of the most popular time series forecasting neural networks are artificial neural networks (ANNs) and recurrent neural networks (RNNs). ANNs were inspired by the way the nervous system and brain processes information. RNNs were designed to be able to remember important information about recent inputs, which they can then use to generate accurate forecasts.

A long short term memory network (LSTM) is a type of RNN that is especially popular in the time series space. It has forget gates and feed forward mechanisms that allow the network to retain information, forget extraneous inputs, and update the forecasting procedure to model and forecast complex time series problems.

*Anais Dotis-Georgiou is a developer advocate for InfluxData with a passion for making data beautiful with the use of data analytics, AI, and machine learning. She takes the data that she collects and applies a mix of research, exploration, and engineering to translate the data into something of function, value, and beauty. When she is not behind a screen, you can find her outside drawing, stretching, boarding, or chasing after a soccer ball.*

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