## Financial & Economic Time Series

In order to meet the ever-changing needs of the marketplace, industry, and other factors affecting the organization, managers need to estimate or predict future trends. This practice often involves the analysis of time series data — data gathered on a specific characteristic over a period of time. The goal of time series data analysis is to build a model that will allow managers or other decision makers to forecast future needs so that they can develop an appropriate strategy. There are a number of techniques available to forecast stationary time series data, but their application is part art and part science. Even in the simplest situations, one must determine which variables to include in the model and which variables to exclude. Several approaches are available for building time series models. These include moving average models, autoregressive techniques, and integrated techniques that incorporate both approaches in the manipulation and analysis of time series data.

Keywords Autoregression; Business Cycle; Moving Average; Seasonal Fluctuation; Stationarity; Stochastic; Time Series Data; Trend

### Statistics: Financial

### Overview

American philosopher George Santayana said that those who cannot learn from history are doomed to repeat it. Although time and time again this truism is proven in political arenas, it has applicability in other areas, too. Certainly, businesses can learn from the past. Understanding the effects of trends, business cycles, seasonal fluctuations, and irregular or random events on the needs of the marketplace or the trajectory of the industry can help businesses better position themselves to leverage this knowledge into a better market position and enable themselves to predict coming needs and remain competitive in the marketplace. This process is called forecasting: the science of estimating or predicting future trends. Forecasts are used to support managers in making decisions about many aspects of the business including buying, selling, production, and hiring. Although there are purely judgmental approaches to forecasting available that depend on the expertise and experience of the manager, statistical techniques that build data-driven models and help forecast trends, seasonality, and patterns can help quantify the variables causing such fluctuations. Most of these techniques require the use of time series data.

### Time Series Data

Time series data are data gathered on a specific characteristic over a period of time. 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. Time series methods include naïve methods, averaging, smoothing, regression analysis, and decomposition. These techniques are used in the forecasting of future trends or needs in decision making about many aspects of the business including buying, selling, production, and hiring.

Time series data are data gathered on a specific characteristic over a period of time. To be useful for forecasting, time series data must be collected at intervals of regular length. In time series analysis, the sequence of observations is assumed to be a set of jointly distributed random variables. Unlike the ad hoc approach to forecasting where it is impossible to tell whether or not the formula chosen is the most appropriate for the situation, in time series analysis 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.

The primary reason for the analysis of times series data is to be able to understand and predict patterns. Time series analysis typically involves observing and analyzing the patterns of historical data in order to extrapolate past trends into future forecasts. To do this, most statistical analysis of time series data involves model building, which is the development of a concise mathematical description of past events. These models, in turn, are used to forecast how the pattern will continue into the future.

### Deterministic

There are two types of variables involved in time series data and analysis: deterministic and stochastic. Deterministic variables are those for which there are specific causes or determiners. These include 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. Most trends are linear rather than cyclic, and grow or shrink steadily over a period of years. An example of a trend would be the increasing tendency to outsource and offshore technical support and customer service within many high tech companies. Not all trends are linear, however. 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. A second type of deterministic factor is business cycles. These are continually recurring variations in total economic activity. Business cycles tend to occur across most sectors of the economy at the same time. For example, several years of a boom economy with expansion of economic activity (e.g., more jobs, higher sales) are often followed by slower growth or even contraction of economic activity. Business cycles may occur not only across one industry or business sector, but also across the economy in general. A third type of deterministic factor is seasonal fluctuations. These are changes in economic activity that occur in a fairly regular annual pattern and are related to seasons of the year, the calendar, or holidays. For example, office supply stores experience an upsurge in business in August as children receive their school supply lists for the coming year. Similarly, the demand for heating oil is greater during the cool months than it is in the warm months.

Stochastic variables, on the other hand, are those that are caused by randomness or include an element of chance or probability. Stochastic variables include both irregular and random fluctuations in the economy that occur due to unpredictable factors. Examples of irregular variables include natural disasters such as earthquakes or floods, political disturbances such as war or change in the political party in charge, strikes, and other external factors. Other unpredictable or random factors that can affect a business's profitability include situations such as high absenteeism due to an epidemic.

A simple example of a stochastic time series is the random walk process. This is based on an investment theory that claims that market prices follow a random path up and down and are not influenced by past price movements. This theory concludes that it is impossible to predict the direction of the market with any degree of accuracy, particularly in the short term. In the random walk process, each successive change is independently drawn form a probability distribution with a mean of zero. The simplest example of a times series is one that is completely random (i.e., has no recognizable pattern).

Forecasting in the real world typically involves many variables. Although in theory a purely deterministic model is possible, the complexity of real world problems usually results in situations involving both deterministic and stochastic variables. Business and economic problems usually involve unknown variables or uncontrollable factors. As a result, most time series in the business world are stochastic in nature.

### Stationarity

Another characteristic of time series is stationarity. This condition exists when the probability distribution of a time series does not change over time. Stationarity is of interest to analysts because when one can assume that the underlying stochastic process is invariant with respect to time (i.e., stationary), then one can 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, that probability of a given...

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