In “What is Time Series Analysis?” I presented some basic concepts and uses for time series models, but I did not write much about time series data. Here we will explore characteristics or components of time series data. All of the components have a bit of complexity surrounding them and I will only cover the basics in this article.
Many phenomena that produce time series data exhibit seasonality.Seasonality is a component of a time series in which the data experiences regular and predictable changes that recur in regular calendar intervals such as months or fiscal year. For instance, summer clothing is sold more in the spring than other seasons and vacation packages sell more in the summer when school is not in session. Similarly, in habitats with cold winters may consume far more heating oil, natural gas, etc. In the insurance industry, times series data comes into play in places susceptible to tropical storms, wildfires, and hail producing storms. The stock market is affected by many of these factors and it too exhibits seasonality. Another example of a time series that can probably be described using an additive model with a trend and seasonality is the time series of the US Birth data we have already used (discussed in one of my bicorner.com articles: “What is Time Series Analysis?“)
Cycle has often been described as a non-fixed pattern usually of at least 2 years in duration. The length of the cycle is described as theperiod. An example of time series data exhibiting cyclic behavior is the harvesting of game or fish. For instance, harvesting Georges Bank haddock. The cycle may have a period of length 4 to5 years. However, the haddock population is dependent of herring roe (and external influence) for its survival, in addition to the harvesting rate. Another example is pork retailer prices in Germany from April 1995 to April 2012, as shown below.
Trend is the long-term movement in a time series without time or irregular effects and is a reflection of the underlying level. The trend can be increasing or decreasing as well as linear or nonlinear. You might hear terms like nonseasonal trend, additive trend, andmultiplicative trend, combined with linear, damped, polynomial, orexponential trend. As an example, For example, suppose we want to forecast the number of households that purchase an LED television on a monthly basis. Every year, the number of households that purchase an LED TV will increase; however, this trend will be damped (e.g., the upward trend will slowly disappear) over time as the market becomes saturated. This would be described as dampened nonseasonal trend, assuming that the sales are not seasonal. An example of a time series that can probably be described using an additive model with a trend and no seasonality is the time series of US Treasury bill contracts on the Chicago market for 100 consecutive trading days in 1981.
The irregular component is unpredictable. It is the residual time series after the trend-cycle and the seasonal components have been removed. It results from short-term fluctuations in a series which are not systematic and in some instances not predictable. The figure below shows all the components of time series data. The irregular component is labeled random.
Understanding the components of time series data helps a modeler choose the appropriate methods of accounting for the error variance produced by them.
Jeffrey Strickland, Ph.D.
Jeffrey Strickland, Ph.D., is the Author of Predictive Analytics Using R and a Senior Analytics Scientist with Clarity Solution Group. He has performed predictive modeling, simulation and analysis for the Department of Defense, NASA, the Missile Defense Agency, and the Financial and Insurance Industries for over 20 years. Jeff is a Certified Modeling and Simulation professional (CMSP) and an Associate Systems Engineering Professional (ASEP). He has published nearly 200 blogs on LinkedIn, is also a frequently invited guest speaker and the author of 20 books including:
- Operations Research using Open-Source Tools
- Discrete Event simulation using ExtendSim
- Crime Analysis and Mapping
- Missile Flight Simulation
- Mathematical Modeling of Warfare and Combat Phenomenon
- Predictive Modeling and Analytics
- Using Math to Defeat the Enemy
- Verification and Validation for Modeling and Simulation
- Simulation Conceptual Modeling
- System Engineering Process and Practices