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Econometrics
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Publisher: Editura Universitară
Author: George Cristian Gruia
Edition: I
Pages: 214
Publisher year: 2025
ISBN: 978-606-28-2020-6
DOI: 10.5682/9786062820206
Product Code:
9786062820206
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TABLE OF CONTENTS
PREFERENCE/9
1. INTRODUCTION TO ECONOMETRICS/11
1.1. What is an econometric model?/13
1.2. Statistical data/15
1.2.1. Time series/16
1.2.2. Cross-sectional data/17
1.2.3. Panel data/18
1.3. Data correction/19
1.3. Graphical illustration of data/20
1.3.1. Line graph/21
1.3.2. Histogram/22
1.3.3. Scatter plot/25
2. DESCRIPTIVE STATISTICS AND CORRELATIONS/28
2.1. Expected value and variance/31
2.2. Correlation/34
2.3. Why are quantities correlated?/40
2.3.1. Correlation and the puncta diagram/42
2.3.2. Correlation between several variables/43
2.3.3. Population correlation and covariance/44
3. ECONOMETRIC MODEL/47
3.1. Regression model of an explanatory variable/51
3.1.1. Regression as a linear function – practical description /51
3.1.2. Interpreting the results of OLS estimations/57
3.1.3. Measuring the goodness of fit of the regression model/59
3.1.4. Basic statistical concepts in regression modeling/61
3.1.5. Hypothesis Testing Involving R2: F Statistics/66
3.1.6. Regression Model of Multiple Explanatory Variables/69
3.1.7. Statistical Aspects of Multiple Regression/71
3.1.8. Interpreting OLS Estimates in a Multiple Regression Model/72
3.1.9. Which Explanatory Variable to Choose?/75
3.1.10. Multicollinearity/79
3.1.11. Multiple Regression with Dummy Variables/80
4. LINEAR REGRESSION MODEL WITH A SINGLE EXPLANATORY VARIABLE/87
4.1. Probability basics in the context of a regression model/88
4.2. Classical assumptions of the regression model/92
4.3. Properties of the OLS estimator for the parameter β/95
4.4. Deriving a confidence interval for the parameter β/105
4.5. Testing the hypotheses of the parameter β/107
4.6. Modification with the unknown error variance σ2/108
5. LINEAR REGRESSION MODEL WITH MULTIPLE EXPLANATORY VARIABLES/112
5.1. Choosing the explanatory variables/117
5.2. Multicollinearity/122
5.3. Testing the hypotheses in a multiple regression model/123
5.3.1. F-test/124
5.3.2. Likelihood ratio tests/126
5.4. Choosing the functional form of the multiple regression model/ 132
5.4.1. Nonlinearity in regression/132
5.4.2. How to decide on the form of a nonlinear dependence?/135
5.5. Heteroskedasticity/138
5.5.1. Theoretical results with known error variance σ2ωi2/139
5.5.2. Estimation for the case of unknown variances of random errors/144
5.5.3. Testing for heteroskedasticity/148
5.5.4. Recommendations for empirical practice/153
5.6. Regression model with autocorrelation of random errors/157
5.6.1. Properties of autocorrelated random errors/158
5.6.2. GLS Estimator for a Model with Autocorrelation of Random Components/161
5.6.3. Testing for Autocorrelation of Random Errors/164
5.6.4. Recommendations for Empirical Practice/168
6. ONE-DIMENSIONAL TIME SERIES ANALYSIS/171
6.1. Notation within time series/173
6.2. Trends in time series/176
6.3. Autocorrelation function/179
6.4. Autoregressive model/181
6.4.1. AR(1) model /181
6.4.2. Extension of AR(1) model/185
6.4.3. Testing the AR(p) model with deterministic trend/190
6.5. Stationarity of time series/198
ANNEX I/200
ANNEX II/203
ANNEX III/208
BIBLIOGRAPHY/212
PREFERENCE/9
1. INTRODUCTION TO ECONOMETRICS/11
1.1. What is an econometric model?/13
1.2. Statistical data/15
1.2.1. Time series/16
1.2.2. Cross-sectional data/17
1.2.3. Panel data/18
1.3. Data correction/19
1.3. Graphical illustration of data/20
1.3.1. Line graph/21
1.3.2. Histogram/22
1.3.3. Scatter plot/25
2. DESCRIPTIVE STATISTICS AND CORRELATIONS/28
2.1. Expected value and variance/31
2.2. Correlation/34
2.3. Why are quantities correlated?/40
2.3.1. Correlation and the puncta diagram/42
2.3.2. Correlation between several variables/43
2.3.3. Population correlation and covariance/44
3. ECONOMETRIC MODEL/47
3.1. Regression model of an explanatory variable/51
3.1.1. Regression as a linear function – practical description /51
3.1.2. Interpreting the results of OLS estimations/57
3.1.3. Measuring the goodness of fit of the regression model/59
3.1.4. Basic statistical concepts in regression modeling/61
3.1.5. Hypothesis Testing Involving R2: F Statistics/66
3.1.6. Regression Model of Multiple Explanatory Variables/69
3.1.7. Statistical Aspects of Multiple Regression/71
3.1.8. Interpreting OLS Estimates in a Multiple Regression Model/72
3.1.9. Which Explanatory Variable to Choose?/75
3.1.10. Multicollinearity/79
3.1.11. Multiple Regression with Dummy Variables/80
4. LINEAR REGRESSION MODEL WITH A SINGLE EXPLANATORY VARIABLE/87
4.1. Probability basics in the context of a regression model/88
4.2. Classical assumptions of the regression model/92
4.3. Properties of the OLS estimator for the parameter β/95
4.4. Deriving a confidence interval for the parameter β/105
4.5. Testing the hypotheses of the parameter β/107
4.6. Modification with the unknown error variance σ2/108
5. LINEAR REGRESSION MODEL WITH MULTIPLE EXPLANATORY VARIABLES/112
5.1. Choosing the explanatory variables/117
5.2. Multicollinearity/122
5.3. Testing the hypotheses in a multiple regression model/123
5.3.1. F-test/124
5.3.2. Likelihood ratio tests/126
5.4. Choosing the functional form of the multiple regression model/ 132
5.4.1. Nonlinearity in regression/132
5.4.2. How to decide on the form of a nonlinear dependence?/135
5.5. Heteroskedasticity/138
5.5.1. Theoretical results with known error variance σ2ωi2/139
5.5.2. Estimation for the case of unknown variances of random errors/144
5.5.3. Testing for heteroskedasticity/148
5.5.4. Recommendations for empirical practice/153
5.6. Regression model with autocorrelation of random errors/157
5.6.1. Properties of autocorrelated random errors/158
5.6.2. GLS Estimator for a Model with Autocorrelation of Random Components/161
5.6.3. Testing for Autocorrelation of Random Errors/164
5.6.4. Recommendations for Empirical Practice/168
6. ONE-DIMENSIONAL TIME SERIES ANALYSIS/171
6.1. Notation within time series/173
6.2. Trends in time series/176
6.3. Autocorrelation function/179
6.4. Autoregressive model/181
6.4.1. AR(1) model /181
6.4.2. Extension of AR(1) model/185
6.4.3. Testing the AR(p) model with deterministic trend/190
6.5. Stationarity of time series/198
ANNEX I/200
ANNEX II/203
ANNEX III/208
BIBLIOGRAPHY/212
As the author of this work, it is a great honor for me to present to you "Econometrics" - a textbook designed with the increasingly acute need for rigorous tools in the analysis and interpretation of economic data in mind. In a world marked by globalization and accelerated economic and financial changes, I believe that econometrics remains the key through which we can transform raw data into useful knowledge, both for the academic environment, for public decision-makers and for market professionals.
I have structured the book in a gradual way, starting with the fundamentals – the typology and characteristics of time series, cross-sectional and panel data – to the development of advanced dynamic models. I want each chapter to provide not only solid theoretical notions, but also practical examples that illustrate the real-world applicability of econometric methodology. You will find step-by-step demonstrations of the least squares method, along with hypothesis testing and techniques for remediating common problems, such as heteroskedasticity, autocorrelation or multicollinearity.
We have included the analysis of AR(p) models and stationarity testing procedures, essential in any empirical study of economic evolution. Whether you are tracking the impact of monetary policies on the exchange rate or evaluating the effects of marketing campaigns on sales figures, I hope that this manual will provide you with the methodological framework and analytical tools you need.
The graphic illustrations – line graphs, histograms, scatter plots – have been chosen to facilitate intuitive understanding of the relationships between variables and to support your learning process. We have paid special attention to the balance between academic rigor and accessibility of explanations, with the conviction that this will make econometrics not only a discipline of study, but also a reliable partner in research and consultancy.
I recommend this volume to undergraduate and graduate students, doctoral students, and all those involved in empirical projects, convinced that the theory combined with practice presented here will guide you to valuable and relevant results for the real world.
I have structured the book in a gradual way, starting with the fundamentals – the typology and characteristics of time series, cross-sectional and panel data – to the development of advanced dynamic models. I want each chapter to provide not only solid theoretical notions, but also practical examples that illustrate the real-world applicability of econometric methodology. You will find step-by-step demonstrations of the least squares method, along with hypothesis testing and techniques for remediating common problems, such as heteroskedasticity, autocorrelation or multicollinearity.
We have included the analysis of AR(p) models and stationarity testing procedures, essential in any empirical study of economic evolution. Whether you are tracking the impact of monetary policies on the exchange rate or evaluating the effects of marketing campaigns on sales figures, I hope that this manual will provide you with the methodological framework and analytical tools you need.
The graphic illustrations – line graphs, histograms, scatter plots – have been chosen to facilitate intuitive understanding of the relationships between variables and to support your learning process. We have paid special attention to the balance between academic rigor and accessibility of explanations, with the conviction that this will make econometrics not only a discipline of study, but also a reliable partner in research and consultancy.
I recommend this volume to undergraduate and graduate students, doctoral students, and all those involved in empirical projects, convinced that the theory combined with practice presented here will guide you to valuable and relevant results for the real world.
George Cristian Gruia
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