084. Time Series and Their Components

Developing a forecast often starts with the collection of past data over several time periods. The resulting data set is called a Time series because it contains observations over time. The time periods can vary in length. They can be early, quarterly, or even daily. Time periods of only one hour may be used for highly volatile variables such as the price of heavily traded stock on one of the organized stock exchanges. Table 8.1 shows time-series data for the U. S. gross national product. It registers data for some variable (GNP) over time.

Table 8.1 – GNP Time-Series (in billions of dollars)

Year	GNP
1985	4,014.9
1986	4,240.3
1987	4,662.8
1988	4,939.2
1989	5,403.7

Sometimes time-series data are used to forecast future values from past observations. One approach to this effort is to simply estimate the value in the next time period to be equal to that of the last time period. That is,

= ,

Where is the estimate of the value of the time series in the next time period, and is the actual value in the current time period.

Referred to as the Naive method of forecasting, this approach might be used when the data exhibit a Random walk.

Random walk movements demonstrate no trend upward or downward and typically shift direction suddenly. They can be expressed as

= + ,

Where is some random amount, positive or negative, by which Y changes in time period t. because it totally random, it is virtually unpredictable. The best way is to simply use the most recent observation as the prediction for the next value.

That is, the Naive method of forecasting uses the most recent observation for the forecast of the next observation.

All time series contain at least one of the following four components:

1. Trend.

2. Seasonal variation.

3. Cyclical variation.

4. Irregular or random variation.

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