## Time Series

Time series data are used in business forecasting to examine patterns, trends, and cycles from the past in order to predict patterns, trends, and cycles in the future. In general, there are three objectives for the use of time series data: Understand the mechanism underlying the observed data, extrapolate the data in order to predict their effect on future behavior or data values, and control a process or system so that its outcome is more favorable to the business. Time series data can take several distinctive forms and can be influenced both by deterministic and stochastic variables. Although there are several approaches to modeling time series data, they often yield different results. Model building and fore casting using time series data is a complicated process that is part art and part science. Human beings will always have to determine which variables to include, where the line of best fit lays, what time periods to consider, and how to interpret the results. This can be both strength and a weakness.

Managers and other business decision makers frequently need to determine the best course of action and develop strategic plans to help the organization reach its goals and objectives. To optimize the worth of such decisions, good business strategy needs to be based on the rigorous analysis of empirical data. Sometimes the data are readily obtainable through activities, such as an analysis of the organization's resources and abilities. Sometimes the data require research and analysis, such as data concerning competitor capabilities and offerings. Sometimes the data require creative guesswork, such as determining market needs and trends in the future. Fortunately, there are a wide range of descriptive and inferential statistical tools available for analyzing and interpreting the data that managers rely on to make decisions. One of the tools that is particularly helpful for the latter category of analysis, in which one needs to forecast trends as the basis for decision making, is time series analysis.

### Uses of Time Series Data

Time series data are data gathered on one or more specific characteristics of interest over a period of time at intervals of regular length. These data series are used in business forecasting to examine patterns, trends, and cycles from the past in order to predict patterns, trends, and cycles in the future. Time series analysis typically involves observing and analyzing the patterns in historical data. These patterns are extrapolated to forecast future behavior. Most statistical analysis of time series data involves model building, the development of a concise mathematical description of past events. These mathematical models are used to forecast how the pattern will continue into the future. Time series are analyzed through several techniques including naïve methods, averaging, smoothing, regression analysis, and decomposition. These analysis techniques assume that the sequence of observations is a set of jointly distributed random variables. Through the analysis of time series data, one can study the structure of the correlation (i.e., the degree to which two events or variables are consistently related) over time to determine the appropriateness of the model.

### Objectives of Time Series Data

In general, there are several objectives for the use of time series data.

- First, time series data are often analyzed in order to understand the mechanism underlying the observed data and to build a model that describes the mechanism and its influence on the variables of interest.
- Second, while understanding the mechanisms that influence events and trends is of interest, time series data are frequently analyzed not only to understand these mechanisms, but more importantly to extrapolate them in order to predict their affect on future behavior or data values.
- Third, although sometimes knowing this information is sufficient for making decisions and developing strategies, there are also situations in which the results of the analysis of time series data can also give organizations information that will enable them to control a process or system so that its outcome is more favorable to the business. For example, one might find that changes in industry technology are progressively making a current widget design obsolete and that sales are dropping off. If acquired in time, this information can point out areas in which the organization needs to change (e.g., a new widget design that incorporates more technology might be appropriate) in order to change the trend in the future.

### Forms of Time Series Data

As shown in Figure 1, real world time series data can take several distinctive forms.

### Stationarity

Figure 1a shows the viscosity data on a chemical product over time. These data remain fairly constant over time and are said to be constant about the mean (an arithmetically derived measure of central tendency in which the sum of the values of all the data points is divided by the number of data points). This characteristic of the data is referred to as stationarity. Stationarity exists when the probability distribution of a time series does not change over time. Stationarity is of interest to analysts because it allows one to mathematically model the process with an equation with fixed coefficients that estimate future values from past history. If the process is assumed to be stationary, the probability of a given fluctuation in the process is assumed to be the same at any given point in time. The time series data in Figure 1b, however, do not exhibit the same degree of constancy or stationarity. It is difficult to mathematically model a non-stationary process using a simple algebraic equation. However, it can be possible to use a simple mathematical procedure to transform non-stationary processes into ones that are approximately stationary for purposes of analysis. This allows the development of models to help the analyst or decision maker better understand the underlying mechanisms in the data series.

### Deterministic Variables

A third general form that can be taken by time series data is illustrated in Figure 1c. Time series data that can be influenced by various deterministic variables are those for which there are specific causes or determiners. This type of variable includes trends, business cycles, and seasonal fluctuations.

- Trends are persistent, underlying directions in which a factor or characteristic is moving in either the short, intermediate, or long term. Trends tend to be linear rather than cyclic and grow or shrink steadily over a period of years. For example, a trend might be an increasing tendency for business to outsource and offshore technical support and customer service in many high tech companies. Trends are not necessarily linear, however. For example, trends in new industries tend to be curvilinear as the demand for the new product or service grows after its introduction then declines after the product or service becomes integrated into the economy.
- Another type of deterministic factor is business cycles. These factors are continually recurring variation in total economic activity. Business cycles tend to occur across most sectors of the economy at the same time. For example, several...

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