# An Introduction to Time Series Analysis

Time is a factor that affects every aspect of human life and constantly influences how we live. As a result, it is critical to understand how the events in our lives have shaped us over **time**. This is possible thanks to time series analysis. It allows us to look into the past and understand what happened and, more importantly, when it happened, allowing us to connect the dots on why it happened given the circumstances at the time.

Time series become more useful when combined with machine learning and artificial intelligence because we can not only look into the past but also predict the future. For example, we can predict the behavior of a company’s stock, the weather for a specific day in the future, and the future sales of supermarkets, among other things.

Before we go any further, let’s go over the fundamentals: What exactly is a Time Series?

# What is Time Series And Time Series Analysis?

A time series is a collection of time data points that are typically recorded at regular intervals such as daily, weekly, or yearly. This data allows for the study of events over time, the identification of patterns or trends, and the prediction of future events.

Time series analysis, on the other hand, is the process of analyzing and studying time series data in order to extract meaningful insights. To identify these patterns and make predictions or forecasts. This process typically employs mathematical and statistical approaches.

Time series analysis is useful in fields such as engineering, environmental sciences, and social sciences where occurrences are best studied over time, such as tracking changes in air or water sciences for environmental sciences, studying economic and demographic changes for social sciences, or monitoring a system’s performance in an engineering scenario. It is also widely used in the financial services industry.

Following that, we’ll look at the components of time series analysis.

# Components of Time Series Analysis

Time series analysis components are underlying factors that aid in understanding observed patterns in data. Simply put, these components allow you to determine “what’s going on” when you examine time-series data. Time series analysis has four main components: Trend, Seasonality, Cyclical, and Irregulatory (or Random).

Deeper dive:

1. Trend: A trend depicts the behavior of a time series over an extended period of time. It usually dictates the series’ long-term movement or direction. A series’ trend can be either upward (move up), downward (move down), or flat (horizontal).

2. Seasonality: The seasonality component of time series aids in the discovery of events or patterns that occur from time to time at the same time. A good example is the Christmas Rush, when shoppers flock to stores during the holiday season to buy gifts for friends and family. During such times, e-commerce sites like Amazon’s website traffic is consistently at an all-time high. In summary, the seasonality component exhibits a recurring pattern over a fixed time period.

3. Cyclical: The cyclical component is similar to the seasonal component, with the difference that the seasonal component occurs regularly over a short period of time, say a month or two, whereas the cyclical component of time series analysis occurs irregularly over a long period of time.

This is common in economic and business cycles. Consider the Great Depression, which lasted from 1929 to 1939. During this time, the majority of the world’s economies suffered a severe setback. The 2008 financial crisis, also known as the Great Recession, saw most of the world’s economies suffer similar setbacks to the Great Depression, though not to the same extent.

The time difference between the Great Depression and the Great Recession was about 69 years, with the former lasting about 10 years and the latter about a year and a half, but it cannot be said that it will happen in the next 69 years because these events are unpredictable.

4. Irregular (Random): This time series analysis component, also known as noise or residual variation, typically displays unpredictable, short-term events that do not represent or show any associated pattern or trend. This pattern is typically caused by measurement errors, sampling errors, and unmeasured factors that affect the data under consideration.

# When and Where Not To Apply Time Series Analysis

Not all data that comes with a timestamp is eligible for use in time series analysis. You tend not to use time series analysis when dealing with:

- Static Data: Time series analysis is commonly used to discover patterns that change over time. When the data being studied does not change over time, time series analysis is not appropriate or necessary. A good example is attempting to study the changes in height of adults in a specific geographic location over time. Adults rarely experience growth after the ages of 18–21, so no realistic change in height is expected.
- Small Sample Size: If the sample size being studied is small, using time series analysis may not be profitable because it requires a large amount of data to detect patterns and trends. Other statistical methods may be more appropriate in situations like this.
- Nonlinear Relationships: If the relationship in the data set is nonlinear or complex, it is best to avoid using times series because it is difficult to capture underlying patterns in the data. In such cases, regression analysis or machine learning algorithms would be preferable.

Time series analysis, on the other hand, can be used to forecast or predict future trends based on historical data. If you want to forecast sales for a specific product, for example, you can use time series analysis to identify seasonal and cyclical patterns in sales data and make predictions about future sales based on these patterns.

When analyzing trends, you can also use time series. Time series analysis can help you identify long-term trends in specific phenomena, such as population growth, economic growth, or climate change, and their underlying causes.

The following section defines stationarity; a key concept in time series analysis.

# Stationarity In Time Series

Stationarity is a fundamental concept in time series analysis. It refers to the property of a time series where its statistical properties do not change over time. Specifically, a stationary time series has a constant mean, variance, and autocovariance structure, regardless of when it is observed.

The significance of stationarity lies in the fact that many times series analysis techniques require that the time series be stationary. Stationarity permits predictions about the future behavior of the time series, as its statistical properties remain consistent over time.

There are two types of stationarity: weak stationarity and strong stationarity. Weak stationarity necessitates that the mean, variance, and autocovariance of the time series are constant over time, while strong stationarity necessitates that the probability distribution of the time series is constant over time.

One important implication of stationarity is that it enables the use of certain statistical techniques such as the autocorrelation function (ACF) and the partial autocorrelation function (PACF) to analyze the time series. These techniques provide crucial information about the underlying structure of the time series, such as the presence of trends, seasonality, and cycles.

Another important implication of stationarity is that it enables accurate forecasting of future values of the time series. This is because stationary time series have stable statistical properties that permit reasonable assumptions about the future behavior of the time series.

However, not all time series are stationary. Many time series exhibit non-stationarity due to trends, seasonality, or other factors. In such cases, techniques such as differencing, which involves subtracting each observation from the previous observation, may be used to transform the time series into a stationary one.

# Conclusion

This article provides a brief overview of the concept of time series analysis. Both time series and time series analysis were defined and explained in depth. In addition, you were introduced to the four components of time series analysis: trend, seasonality, cyclic variation, and irregularity or randomness. To conclude, you learned when and where not to use time series analysis, which was followed by the concept of stationarity.

We hope you enjoyed this article. Please follow the page to be notified when the next article is published. Content is released weekly. Thank you for reading, and we’ll see you next time.