Econometrics, Finance, and Time Series Analysis.pdf
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This resource presents a modern perspective on time series and panel data methods in econometrics and finance. It introduces a very general divergence measure between spectral densities and develops associated inference procedures that are both efficient and robust, thereby opening new directions for methodological research. The volume also proposes a novel measure of systemic risk in energy markets that quantifies
the economic costs of energy asset distress during crisis periods, and examines the dynamic interaction between solvency and funding liquidity risk in the banking sector using panel vector autoregressive models. In addition, the resource develops a new integrated likelihood approach for estimating nonlinear panel data models. Unlike existing integrated ikelihood methods, the proposed approach yields a likelihood
that more closely approximates a genuine parametric ikelihood. The resource further explains how this improvement is driven by first-order information unbiasedness, and why this property plays a more central role for inference than for point estimation. Together, the contributions in this volume illustrate recent advances in econometric methodology and their relevance for empirical research in economics and finance.
The impetus for this resource arose from the 2023 interdisciplinary grant “TIMEDATA,” awarded by the Institute of Advanced Study (IAS) of the University of Luxembourg to Christophe Ley (Department of Mathematics), Diane Pierret (Department of Finance), and Gautam Tripathi (Department of Economics and Management). This grant supported the 2024 visit of Masanobu Taniguchi to the University of Luxembourg as a Distinguished Professor. The authors gratefully acknowledge
the generous support of the IAS and thank Professor Ley for his initiative in making Taniguchi’s visit possible.

1 Introduction . 1
2 Hellinger Distance Estimation for Non-regular Spectra  5
2.1 Introduction  5
2.2 Approximation of the Hellinger Distance Between
Non-regular Spectra . 7
2.3 Asymptotics of MLE in View of the Hellinger Distance . 10
2.4 Estimation Theory . 12
References . 17
3 Local Whittle Likelihood Approach for Generalized Divergence  19
3.1 Introduction  19
3.2 Preliminaries . 21
3.3 Estimation Theory . 23
3.4 Applications of the Local Whittle Estimator . 31
3.5 Numerical Results . 32
References . 34
4 Systemic Risk in Energy Markets: Measuring Co-movements
in Energy Asset Prices During Crises . 37
4.1 Introduction  37
4.2 Risk Measures and Estimation  38
4.2.1 Risk Measures Definition . 38
4.2.2 Econometric Methodology  39
4.3 Empirical Illustration  43
4.3.1 Data Description . 43
4.3.2 Results . 44
4.4 Conclusion . 46
References . 47
5 Modeling Solvency–Liquidity Interactions in Banking: A Panel
VAR Analysis  49
5.1 Introduction  49
5.2 Data and Variables . 50
5.3 Methodology: Panel VAR Model  51
5.4 Empirical Results . 52
5.4.1 Solvency–Liquidity Nexus  52
5.4.2 Interaction Between Solvency and Profitability . 52
5.4.3 Impulse Response Functions  53
5.5 Conclusion . 57
References . 58
6 Integrated Likelihood-Based Inference for Nonlinear Panel
Data Models . 59
6.1 Introduction  59
6.2 Panel Data . 60
6.3 Likelihood for Panel Data Models . 61
6.4 Problem with the Maximum Likelihood Estimator (MLE) . 62
6.4.1 Heterogeneous Means Model of Neyman and Scott . 63
6.4.2 Source of the Incidental Parameters Problem . 64
6.5 Addressing the Problem of the Fixed-Effects MLE . 65
6.6 The ZSE Transformation . 66
6.6.1 A Panel Model with Heterogeneous Variances . 69
6.7 The MILE  69
6.8 Approximating the ZSE Transformed IL  71
6.9 Desirable Properties of the ZSE Transformed IL . 72
6.9.1 Invariance  72
6.9.2 Irrelevance of the Weight-Function . 73
6.9.3 First-Order Score Unbiasedness  73
6.9.4 First-Order Information Unbiasedness  73
6.10 Asymptotic Properties of the MILE  74
6.11 Inference . 75
6.12 Examples: The ZSE Approach in Some Familiar Settings . 75
6.12.1 Static Neyman-Scott Model . 76
6.12.2 Panel Poisson . 77
6.12.3 Panel Logit . 78
6.12.4 Panel Probit . 79
6.12.5 Dynamic Neyman-Scott Model  80
References . 82
7 Reducing Score and Information Bias in Panel Data Likelihoods  85
7.1 Introduction  85
7.2 Pseudolikelihood  86
7.3 Notation and Assumptions  88
7.4 Score and Information Bias of a Panel Data Pseudolikelihood  89
7.4.1 Score Bias  89
7.4.2 Information Bias . 90
7.5 A Generic Panel Data Pseudolikelihood  91
7.6 Target Likelihood . 92
7.7 Conditional Likelihood . 92
7.8 Effect of First-Order Score and Information Unbiasedness
of the Pseudolikelihood on the Bias of the Likelihood Ratio . 93
7.8.1 Score and Information Bias in the Neyman-Scott
Model  93
7.9 Effect of First-Order Score and Information Unbiasedness
of the Pseudolikelihood on the Bias and Variance
of the Estimator . 96
7.10 Relevance for Applied Research . 100
References . 101
8 Shrinkage Estimators of BLUE for Time Series Regression
Models  103
8.1 Introduction  103
8.2 Elements of Time Series Regression Models  105
8.3 Asymptotic Theory for BLUE . 107
8.4 A Feasible Approximator of βˆ . 111
8.5 Example and Numerical Analysis  118
8.6 Conclusions  124
References . 124