## Info

Notes: GDP (Gross Domestic Product), billions of 1987 dollars, p. A-96. PDI (Personal disposable income), billions of 1987 dollars, p. A-112. PCE (Personal consumption expenditure), billions of 1987 dollars, p. A-96. Profits (corporate profits after tax), billions of dollars, p. A-110. Dividends (net corporate dividend payments), billions of dollars, p. A-110.

Source: U.S. Department of Commerce, Bureau of Economic Analysis, Business Statistics, 1963-1991, June 1992.

CHAPTER TWENTY-ONE: TIME SERIES ECONOMETRICS: SOME BASIC CONCEPTS 795

Figure 21.1 is a plot of the data for GDP, PDI, and PCE, and Figure 21.2 presents the other two time series. A visual plot of the data is usually the first step in the analysis of any time series. The first impression that we get from these graphs is that all the time series shown in Figures 21.1 and 21.2 seem to be "trending" upward, albeit with fluctuations. Suppose we wanted to speculate on the shape of these curves over the quarterly period, say, from Year

FIGURE 21.1 GDP, PDI, and PCE, United States, 1970-1991 (quarterly).

Year

FIGURE 21.1 GDP, PDI, and PCE, United States, 1970-1991 (quarterly). Year

FIGURE 21.2 Profits and dividends, United States, 1970-1991 (quarterly).

Year

FIGURE 21.2 Profits and dividends, United States, 1970-1991 (quarterly).

Models

Econometrics: Some Basic Concepts

796 PART FOUR: SIMULTANEOUS-EQUATION MODELS

1992-I to 1996-IV.2 Can we simply mentally extend the curves shown in the above figures? Perhaps we can if we know the statistical, or stochastic, mechanism, or the data generating process (DGP), that generated these curves? But what is that mechanism? To answer this and related questions, we need to study some "new" vocabulary that has been developed by time series analysts, to which we now turn.

What is this vocabulary? It consists of concepts such as these:

1. Stochastic processes

2. Stationarity processes

3. Purely random processes

4. Nonstationary processes

5. Integrated variables

6. Random walk models

7. Cointegration

8. Deterministic and stochastic trends

### 9. Unit root tests

In what follows we will discuss each of these concepts. Our discussion will often be heuristic. Wherever possible and helpful, we will provide appropriate examples.

A random or stochastic process is a collection of random variables ordered in time.4 If we let Y denote a random variable, and if it is continuous, we denote it as Y(t), but if it is discrete, we denoted it as Yt. An example of the former is an electrocardiogram, and an example of the latter is GDP, PDI, etc. Since most economic data are collected at discrete points in time, for our purpose we will use the notation Yt rather than Y(t). If we let Y represent GDP, for our data we have Y1, Y2, Y3,..., Y86, Y87, Y88, where the subscript 1 denotes the first observation (i.e., GDP for the first quarter of 1970) and the subscript 88 denotes the last observation (i.e., GDP for the fourth quarter of 1991). Keep in mind that each of these Ys is a random variable.

In what sense can we regard GDP as a stochastic process? Consider for instance the GDP of \$2872.8 billion for 1970-I. In theory, the GDP figure for

2Of course, we have the actual data for this period now and could compare it with the data that is "predicted" on the basis of the earlier period.

3The following discussion is based on Maddala et al., op. cit., and Charemza et al., op. cit.

4The term "stochastic" comes from the Greek word "stokhos," which means a target or bull's-eye. If you have ever thrown darts on a dart board with the aim of hitting the bull's-eye, how often did you hit the bull's-eye? Out of a hundred darts you may be lucky to hit the bull's-eye only a few times; at other times the darts will be spread randomly around the bull's-eye.

21.2 KEY CONCEPTS3 