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Economic data sets come in variety of types. So there are different econometric methods to cope with many different kinds of data sets. The most important data structures in applied work are as follows: cross-sectional data, time-series data, pooled cross sections and panel data. The micro-econometric is characterized by its analysis of cross section and panel data, and the macro-econometric is involved in the analysis of time-series data.
The time-series data consist of the stationary and non-stationary time series. To find appropriate models for time series is a nontrivial task. There are four main steps in the process, each of which may be used several times:
1. Model specification or identification
After data diagnostics(time plot, ACF and so on), if we find that the time series is stationary, whether we should choice AR model, MA model or ARMA model depends on the behaviors of ACF and PACF. If the time series is non-stationary, we should transform it into a stationary time series by the difference method.
models | AR(p) | MA(q) | ARMA(p,q) |
ACF | Tails off | Cuts off after lag q | Tails off |
PACF | Cuts off after lag p | Tails off | Tails off |
The sample ACF and PACF provide effective tools for identifying pure AR(p) or MA(q) models. However, for a mixed ARMA model, we should take the EACF method to identify the model. And a number of other approaches to model specification have been proposed, for example, AIC and BIC. We should select the model through the minimum of AIC and BIC.
2. Model Estimation
After the model have been specified, it is necessary to estimate its parameters. There are three main approaches: the method-of-moments, the least squares and the maximum likelihood method. However, there are some restrictions on these methods respectively. For example, the method-of-moments seems to have better estimated accuracy for moderately large sample sizes. If the distribution is given, the properties of maximum likelihood method will be better than the others. However, if the distribution is unknown, it is wisdom to choose the least squares method.
3. Model Diagnostics or Criticism
Model diagnostics is concerned with testing the goodness of fit of a model and, if the fit is poor, suggesting appropriate modifications. Generally, we have two complementary approaches: analysis of residuals and testing of parameters. If the residual is a white noise process, the fitted model should be adequate.
4. The use of Model
After the above three steps, an adequate time series model have been established, and an import use of the fitted model is forecasting.
In brief, the univariate time series is involved in the above analysis. However, in many applications, the relationships among some time series are of major interest. Multivariate time series analysis considers simultaneously multiple time series. It is, in general, much more complicated than the univariate time series analysis, especially when the number of series considered is large.
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