*A time series consists of observations on a single variable at discrete points in time, usually at equal intervals. Typical time series may involve:

*Elements of the national income and product accounts at yearly, quarterly, or monthly intervals (Gross domestic product, government spending, consumer price index, unemployment rate, etc.)

* Measures appropriate to individual business operations (monthly sales machine efficiencies, defect rate, etc.)

* Financial market statistics (daily closing price of I13M stock)

* Meteorological data (daily high temperatures in Boston, monthly amount of precipitation in Chicago)

* Population data (U.S. population, or births, or deaths by year)

The order of the observations is an essential characteristic of each of thew series. We have already seen that some time series may exhibit trends and seasonal. For example, monthly retail sales in the United States are characterized by an upward trend and a pronounced seasonal, with a sharp peak in December and a trough in January and February. The upward trend may be explained, in part, by other time series: population growth, per-capita income growth, or inflation, for example. Fluctuations from the trend and seasonal effects may be explained, in part, as the effects of weather, consumer confidence, availability of credit, etc. Thus, it is quite natural to "explain" the behavior of a particular time series in terms of trend, seasonal, and the effects of other variables that me themselves time series. Unfortunately, those other variables, while potentially useful in explaining past values, may not be useful in predicting future values of the time series in which we am interested. For example, while bad weather may have reduced retail sales last month, unless we have a reliable forecast of the weather for next month, weather is not a useful variable for predicting future sales.'
Because current values of explanatory variables are not always useful in predicting future values of a time series, forecasters are often restricted to looking at the information within the series itself, without relying on other explanatory variables. There is considerable information embedded in such series: we have seen that trends tend to continue and seasonal patterns tend to repeat. Thus it's a safe bet to predict that next January's retail sales will be substantially less than those of the preceding month, and it's probably reasonable to predict that they will exceed the preceding January's sales.

What if we have a time series with no discernible trend or seasonal IS there any information in the time series itself that will help us to predict its value in future periods? The answer is "Yes," but it takes some analysis to extract this information. We can think of the observations that constitute the time series as a sample from a process that generates data according to some (probabilistic) rule. We seek ways of using the sample data to identify the rule that governs the data-generating process. If we know what the rule is, we can then make (probabilistic) forecasts of future values of the time series.

The number of rules that could give rise to time series observed in the real world-even those with no trend or seasonal-is huge, and any attempt to cover the subject of time-series analysis in all of its richness requires a book, not a chapter. The purpose of this chapter is to introduce you to the concept of time-series analysis and to introduce two very simple rules for generating data that describe the way some important time series behave in the real world. At the end of this chapter, we'll give an indication of where and how this subject unfolds, but for now we shall introduce the two rules, then show how time-series data generated by one or the other of these rules can be identified and analyzed, and how appropriate forecasts can be made.