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The advent of low cost computation has made many previously intractable econometric models empirically feasible and computational methods are now realized as an integral part of the theory.
This book provides graduate students and researchers not only with a sound theoretical introduction to the topic, but allows the reader through an internet based interactive computing method to learn from theory to practice the different techniques discussed in the book. Among the theoretical issues presented are linear regression analysis, univariate time series modelling with some interesting extensions such as ARCH models and dimensionality reduction techniques.
The electronic version of the book including all computational possibilites can be viewed at



1. Univariate Linear Regression Model

In this section we concentrate our attention in the univariate linear regression model. In economics, we can find innumerable discussions of relationships between variables in pairs: consumption and real disposable income, labor supply and real wages and many more. However, the main interest in the study of this model is not its real applicability but the fact that the mathematical and the statistical tools developed for the two variable model are foundations of other more complicated models.
Ignacio Moral, Juan M. Rodriguez-Poo

2. Multivariate Linear Regression Model

A Multivariate linear regression model (MLRM) is a generalization of the univariate linear regression model which has been dealt with in Chapter 2. In this chapter we consider an endogenous or response variable denoted by y, which depends on a set of k variables x j (j = 1,…, k), called “regressors”, “independent variables” or “explanatory variables”, and an unobservable random term called “disturbance” or “error” term. The latter includes other factors (some of them non-observable, or even unknown) associated with the endogenous variable, together with possible measurement errors.
Teresa Aparicio, Inmaculada Villanua

3. Dimension Reduction and Its Applications

This chapter is motivated by our attempt to answer pertinent questions concerning a number of real data sets, some of which are listed below.
Pavel Čížek, Yingcun Xia

4. Univariate Time Series Modelling

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 y at moment t 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 y is correlated with itself, that is, it is autocorrelated.
Paz Moral, Pilar González

5. Multiplicative SARIMA models

In the history of economics, the analysis of economic fluctuations can reclaim a prominent part. Undoubtedly, the analysis of business cycle movements plays the dominant role in this field, but there are also different perspectives to look at the ups and downs of economic time series. Economic fluctuations are usually characterized with regard to their periodic recurrence. Variations that last several years and occur in more or less regular time intervals are called business cycles, whereas seasonality (originally) indicates regularly recurring fluctuations within a year, that appear due to the season. Such seasonal patterns can be observed for many macroeconomic time series like gross domestic product, unemployment, industrial production or construction.
Rong Chen, Rainer Schulz, Sabine Stephan

6. AutoRegressive Conditional Heteroscedastic Models

The linear models presented so far in cross-section data and in time series assume a constant variance and covariance function, that is to say, the homoscedasticity is assumed.
Pilar Olave, José T. Alcalá

7. Numerical Optimization Methods in Econometrics

Techniques of numerical mathematics are often used in statistics, e.g., r oot finding and optimization (minimization or maximization) in maximum likelihood, where analytical methods usually cannot be used because closed form solutions do not exist. This chapter explains the principles of some important numerical methods and their
Lenka Čížková


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