This article outlines the basic principles of times series analysis  for non-analysts. A more detailed technical treatment is provided at the end.

 What is Time Series Data?

In order to approach time series analysis and forecasting, we must first answer the question regarding what constitutes time series data. A time series is a sequence of data points, typically consisting of successive measurements made over a time interval. Examples of time series are solar activity, ocean tides, stock market behavior, and the spread of disease. Time series are often plotted using line charts. Time series data are found in any domain of applied science and engineering which involves time-based measurements.

Definition. Time series data are a collection of ordered observations recorded at a specific time, for instance, hours, months, or years.

The plot above represents sun post data from 1720 to 1980.

Most often, the observations are made at regular time intervals. Time series analysis accounts for the fact that data points taken over time may have an internal structure, such as autocorrelation, trend or seasonal variation.

What is Time Series Analysis?

Time series analysis comprises methods for analyzing time series data to extract meaningful statistics and other characteristics of time series data.  It focuses on comparing values of a single time series or multiple dependent time series at different points in time.

What is Time Series Forecasting?

Time series forecasting is the use of a time series model to predict future values based on previously observed values in the series.

The green line in the plot above is the forecast and the gray surrounding it is the confidence interval.

Where do we use Time Series Analysis?

We use Time Series Analysis and Forecasting for many applications where pertinent time series data can be collected, such as:

• Budget Analysis
• Financial Market Analysis
• Census Analysis
• Inventory Management
• Economic Forecasting
• Marketing and Sales Forecasting
• Yield Projections
• Seismological Predictions
• Workload Projections
• Military Planning

What are the Goals of Time Series Analysis?

There are two main goals of time series analysis. First, we identify the nature of the phenomenon represented by the sequence of observations in the data. Second, we use the data to forecast or predict future values of the time series variable. Both of these goals require that we identify the pattern of observed time series data and more or less formally describe it. Once the we establish the pattern, we can interpret and integrate it with other data (i.e., use it in our theory of the investigated phenomenon, e.g., seasonal commodity prices). Regardless of the depth of our understanding and the validity of our interpretation of the phenomenon, we can extrapolate the identified pattern to predict future events with this caveat: the further out in time we try to predict, the less accurate is the forecast.

What Techniques are used in Time Series Analysis?

The fitting of time series models can be an ambitious yet ruthless undertaking. It requires much more data preparation than the usual statistical models applied to “ordinary” data—such as response models, uplift models, and so on—where trends and seasonal effects may not be present. For example, unlike data used for standard linear regression, time series data are not necessarily independent and not necessarily identically distributed.  One defining characteristic of time series is that this is a list of observations where the ordering matters.  Ordering is very important because there is a dependency and changing the order could change the meaning of the data.

There are a number of different methods for modeling time series data including the following:

• Box-Jenkins ARIMA models
• Box-Jenkins Multivariate Models
• Holt-Winters Exponential Smoothing (single, double, triple)
• Unobserved Components Model

The user’s application and preference will often decide the selection of the appropriate technique. It is beyond the scope of this article to cover all these methods.

What are Smoothing Techniques?

Inherent in the collection of data taken over time is some form of random variation. There are methods for reducing or canceling the effect due to random variation. “Smoothing” data removes random variation and shows the underlying trends and cyclic components and is an often-used technique in industry.

Smoothing is often referred to as filtering.  There are two distinct groups of smoothing methods:

• Averaging Methods
• Exponential Smoothing Methods

Conclusion

The basic objective of Time Series Analysis usually is to determine a model that describes the pattern of the time series.  We use these models to describe the important features of the time series pattern and to forecast future values of the series. For a more technical treatment of time series analysis, see

See also: Time Series Analysis using iPython

Authored by:
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

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