Data in economics are frequently collected in form of time series. A time
series is a set of observations ordered in time and dependent of each
other. We may find time series data in a wide variety of fields:
macroeconomics, finance, demographics, etc. The intrinsic nature of a time
series is that its observations are ordered in time and the modelling
strategies of time series must take into account this property. This does
not occur with cross-section data where the sequence of data points does
not matter. Due to this order in time, it is likely that the value of a
variable at moment
reflects the past history of the series, that
is, the observations of a time series are likely to be correlated. Since
the observations are measurements of the same variable, it is usually said
that
is correlated with itself, that is, it is autocorrelated.
Time Series Analysis is the set of statistical methodologies that analyze this kind of data. The main tool in Time Series Analysis is a model that should reproduce the past behavior of the series, exploiting its autocorrelation structure. The objectives of Time Series Analysis are basically two: to describe the regularity patterns present in the data and to forecast future observations. Since a pure time series model does not include explanatory variables, these forecasts of future observations are simply extrapolations of the observed series at the end of the sample. If we consider a single variable in our study, we shall construct what is called a univariate time series model. But if two of more variables are available, the possibility of dynamic interactions among them may be important. We can think, for instance, in economic variables such as consumption, investment and income that influence each other. In this case, multivariate time series models can be constructed to take into account these relations among variables (Lütkepohl; 1991).
This chapter will focus on which is called Univariate Time Series
Analysis, that is, building a model and forecasting one variable
in terms of its past observations. It is centered in time series
models based on the theory of linear stochastic processes. A good
survey on nonlinear formulations of time series models may be
found in Granger and Teräsvirta (1993) among others. The chapter starts
with a brief introduction of some basic ideas about the main
characteristics of a time series that have to be considered when
building a time series model (section 4.1).
Section 4.2 presents the general class of nonseasonal
linear models, denoted by models that can be shown to be
able to approximate most stationary processes. Since few time
series in economics and business are stationary,
section 4.3 presents models capable of reproducing
nonstationary behavior. Focus is set on
models, obtained
by assuming that a series can be represented by an
stationary model after differencing. In section 4.4,
the theory to obtain Minimum Mean Squared Error forecasts is
presented. Model building and selection strategy for
models is explained in section 4.5 along with an
economic application analyzing the European Union G.D.P. series.
Finally, in section 4.6 the issue of regression models
with time series data is brought up briefly.