Can you use linear regression for time series data?

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Are you wondering whether you can use linear regression models for time series data? Or maybe you want to hear more about how to use linear regression for time series data? Well either way, you are in the right place! In this article, we tell you everything you need to know about linear regression for time series data.

First, we discuss what time series data is and how it is different from other data. Then we discuss what time series analysis is and what the main objectives of time series analysis are. After that, we talk about whether linear regression models can be used on time series data. Next, we discuss how to use linear regression for time series data. Finally, we provide examples of other models that are specifically designed for time series data.

What is time series data?

What is time series data? Time series data is data that contains multiple measurements on the same outcome variable that were taken at different time points. Most of the time, these measurements are taken at regular intervals and are repeated over an extended period of time. While time series datasets sometimes contain measurements on features that are associated with the outcome variable, they often only contain measurements on the outcome variable.

There are multiple characteristics that make time series data different from the data that is typically used for linear regression. The first difference is that data that is used for time series modeling does not necessarily need to include features that are associated with the outcome variable. Another difference is that time series data contains multiple measurements that are taken on the same subject whereas datasets that are typically used for linear regression only contain one observation per subject.

What are the goals of time series analysis?

What are the main goals of time series analysis? In this section, we will talk about the main goals of time series analysis. First, we will discuss retrospective time series analyses that seek to understand historical patterns in data. Next, we will discuss prospective time series analyses that aim to predict future values patterns.

Decompose historical time series values

The first type of time series analysis is a retrospective time series analysis where the main goal is to analyze historical time series data. In this situation, the main goal of a time series analysis is to decompose the values observed into different components to determine how much each component contributed to the final value.

Here are some examples of different components that a time series can be decomposed into.

  • Trend. The first component of a time series decomposition is trend. The trend in the data represents how fast the time series is increasing or decreasing over time. The concept of trend is present in most time series models.
  • Seasonality. The next component of a time series decomposition is seasonality. The seasonality in the data represents the impact of recurring seasonal patterns that repeat at regular intervals. The concept of seasonality is present in most advanced time series models, but may not be present in simple time series models.
  • Random error. The next component in a time series decomposition is random error. This represents random fluctuations in the data that are not explained by other components in the decomposition. The concept of random error is present in most time series models.

Forecast future time series values

The second type of time series analysis is a prospective time series analysis where the main goal is to predict future values of a time series. In this situation, the main goal of a time series analysis is to predict what values the time series will take on in the future. This is done by analyzing previous values of the time series and projecting the trends observed in the past out into the future.

Can you use linear regression for time series data?

Can you use linear regression for time series data? In this section, we will discuss whether linear regression can be used for time series data. Specifically, we will discuss whether linear regression can be used to perform the types of tasks that are traditionally performed in time series modeling, such as forecasting future values of a time series.

The short answer to whether it is possible to use linear regression for time series data is yes, it is technically possible to use linear regression for time series data. That being said, there are other models that are specifically designed for time series data. These models that are designed specifically with time series data in mind typically perform better on time series data, so while it is possible to use linear regression on time series data, it is often better to use a dedicated time series model.

How to use linear regression for time series data

How do you use a linear regression model to conduct a time series analysis? In this section we will provide examples of steps that you can take to leverage linear regression for time series analysis. Most of these steps involve introducing features into your model that represent components that would traditionally be included in time series models.

  • Add trend terms. The first thing you can do to conduct a time series analysis using a linear regression model is to incorporate terms into your model that represent how fast your trend is increasing or decreasing over time. One simple way to do this is to add autoregressive terms to your model that allow you to predict the current value of your time series based on previous values. As a simple example, you might include a term that represents the previous value of the time series. The coefficient associated with that variable will give you an indication of how much the value is increasing or decreasing with each additional data point that is added.
  • Add seasonality terms. The next thing that you should do to conduct a time series analysis is introduce terms that represent seasonality into your linear regression model. There are multiple ways that you can do this. If your cycles are relatively short, you can include an indicator variable for each increment in the cycle. For example, if you want to measure weekly seasonal patterns, then you can include a binary indicator for each day of the week that takes on a value of 1 if a data point corresponds to that day of the week. If your cycles are longer, then it might make sense to use fourier terms or related concepts to reduce the number of variables that are required to represent seasonality.
  • Add holidays or events. If there are large holidays or other recurring events that affect the value of your time series, it might also make sense to add indicators for these holidays. For example, if your time series represents online sales, then it might make sense to include indicators that take on a value of 1 if that day is Black Friday and a value of 0 otherwise.

What models are designed for time series data?

And what if you want to use a dedicated time series model for your time series data? Here are some examples of models that are designed to be used for time series data. For each model we list, we provide details that will help you to decide whether that model is the best model for you.

  • Exponential smoothing. Exponential smoothing models are common and well known models that are used for non-stationary time series data.
  • ARIMA. ARIMA models are common and well known models that are used for stationary time series data. ARIMA models can be modified to include features, so they are a common choice if you have features that you want to include in your model.
  • TBATS. TBATS models are models that are designed for situations where you have multiple different seasonal patterns in your data. For example, these models can be used when you have data that is recorded in hourly intervals that includes both daily seasonal patterns and weekly seasonal patterns.
  • Facebook Prophet. Facebook Prophet is a beginner friendly model that was designed to be used by people without much knowledge of traditional time series modeling. It can also account for situations where there are large disruptions or mean shifts in your time series.

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