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Project Number20-78-10113

Project titleNew methods of robust inference for developing markets: Financial bubbles, time-varying volatility, structural breaks and beyond

Project LeadSkrobotov Anton

AffiliationFederal State Budgetary Educational Institution of Higher Education "Saint-Petersburg State University",

Implementation period 07.2020 - 06.2023 

Research area 08 - HUMANITIES AND SOCIAL SCIENCES, 08-154 - Finance, credit, money circulation, market infrastructure

KeywordsFinancial and economic markets; insurance markets; robust statistical and econometric inference; dependent and heterogeneous data; heavy-tailed distributions; copula dependence models; econometric and mathematical modeling in finance, economics and actuarial science; multivariate statistical methods for economic analysis; financial bubbles; structural breaks; time-varying volatility



The project is aimed at the development of new statistical methodology suitable for the analysis of developing financial markets, including markets in Russia. The methods will be adapted to the complex financial and actuarial price setting mechanisms, which are subject to a large number of interrelated random shocks, where the shocks can affect the markets at a very large scale and can take extreme values. The adaptive and robust nature of the proposed methods will ensure that they can accommodate several important stylized facts about real data and remain valid under a much wider set of assumptions as compared to the existing methodology. Thus, the new methods will allow substantially relaxing the unrealistic assumptions that are currently often employed in the analysis of developing markets. In particular, this is important for the analysis of financial bubbles (e.g., detection and timing of them), for the study of monetary and fiscal policies, for the study of the effects of time-varying volatility (dispersion) and heavy tails in distributions of economic and financial indicators considered on conclusions of key models employed in the study of modern transition economies. The proposed research lies at he intersection of at least four fields: (1) economics, (2) finance and actuarial study, (3) statistics, (4) applied mathematics and computer science. As an outcome of the project, it is expected to provide a toolbox of new powerful econometric inference methods and machine learning algorithms with software prototypes for the analysis of developing financial markets. An important concurrent outcome of the project will also consist in creation and the development of a world-class research laboratory in theoretical and applied econometrics at St Petersburg State University with the majority of its researchers being under 39. One of the most significant contributions of the project is expected in the field of econometric modelling, that is, in the intersection of statistics and economics, where the proposed research is expected to produce a new type of robust methods and models well suited for the use in the analysis of massive datasets on complex real-world financial and actuarial markets. The research on the project in the laboratory will be conducted by an international team of leading young researchers in econometrics with a well-established record and the potential for high impact publications in leading journals in econometrics, statistics, economics, finance and related fields. Among other expected outcomes, the project will contribute to the Russian Science Foundation's goal of promoting the efficiency of international research collaboration, attracting talented young researchers to Russian universities and strengthening national research capability.

Expected results
One of the key expected outcomes of the project will consist in a series of publications on its results in leading scholarly journals indexed in the Web of Science and Scopus, mainly in publication outlets with the 5-year impact factor of 2 and higher, such as the Journal of Econometrics, the Journal of Business and Economic Statistics, Emerging Markets Review, and others. The project's outcomes will also include presentation of the results at prestigious international conferences by the project participants as well as the development of a network of international research collaborations. An important aspect of the project's value for the Russian economy is its applicability to real world problems, permitting a deeper understanding and analysis of the structure and the dynamics of Russian markets. This is particularly important for ensuring a well-coordinated work of the financial sector and for achieving higher efficiency of the Russian economy as well as that of the Central Bank and government entities. Extreme fluctuations and downfalls in nominal indicators of financial, credit and insurance markets have significant negative effects on the real sector. Typically, a high level of uncertainty leads to a decrease in economic growth and productivity. The proposed methods of economic and econometric analysis are expected to lead to more precise economic forecasts and better economic decisions by market participants. This will allow them to reduce the impact of negative external shocks on productivity and economic development. In this direction, the work on the project will provide applications of the proposed methods for robust analysis in the development of economic policy recommendations and long-term forecasts for the Russian economy. The robust analysis and inference methodology proposed in the project is expected to lead to changes in the practice of statistical analysis of economic activity and development. The methodology will provide robust and reliable alternatives to currently employed approaches. One of the key expected outcomes of the project consists in the development of new econometric and statistical models and methods for the most adequate description and accounting for real-world dynamics of markets, captured by important economic and financial indicators. It is expected that the developed models and methods will be widely used by researchers and practitioners of economic and financial analysis and by market participants as a whole. In the long-run perspective, the project will contribute to many fields of knowledge, which cover applications of high-dimensional models and robust methods of their analysis. This, in turn, will lead to stronger interconnections between existing fields of scholarly endeavor. An important contribution of the project is to develop undergraduate and post-graduate courses covering the proposed robust models and methods that will be taught by the project participants at Saint Petersburg State University and other institutions of higher education. In addition, the project's team is expected to include several master and doctoral students; it is planned that several problems in the area of the project will be suggested as possible thesis topics for them. It is expected that the work on the project will lead to the development of a long-term collaboration network consisting of active early and middle career researchers in the areas of the project and beyond. As a whole, the project will significantly contribute to the development of international research collaboration and to involvement of young scientists in world-class research.



Annotation of the results obtained in 2022
During the reporting period, the project participants conducted research in the areas planned for 2022-2023. In particular, research has been conducted in the following areas and directions and the following results have been obtained: 1. New methods have been developed for dating financial bubbles under time-varying volatility, based on two-step procedures and weighted least squares methods. 2. New methods have been developed for testing predictability in regression in the presence of time-varying and potentially non-stationary volatility of a general form. 3. Improved methods for predicting technological inefficiency based on machine learning algorithms such as local random forest, LASSO, double and robust LASSO have been proposed. 4. The previously developed algorithm for the problem of mixed integer optimization has been improved to identify the number of structural breaks using information criterion optimization. 5. Research has been carried out on the analysis of predictability of crypto-currency returns and prices using time-varying crypto-currency networks 6. A software package in the R programming environment with the implementation of the developed inference and forecasting methods available in public domain has been developed 7. Research on the analysis of the the spread of fiscal consolidation shocks through production networks and their impact on output has been carried out 8. The analysis of the impact of HFT traders making trading decisions based on reinforcement learning (reinforcement learning) on the development of financial market dynamics using multi-agent modeling has been conducted 9. A Python software package for multi-agent simulation of exchange trading has been developed. Under tentative grant extension, research on the project will continue and develop and results will be obtained in the following areas and directions: 1. Development of asymptotic properties of estimates of the number of structural breaks and model parameters in applications of mixed integer optimization in problems of identification and dating of structural breaks and bubbles 2. Development of new generalized robust inference methods for the analysis of market (non-)efficiency in the presence of heavy tails of returns distributions using modified Ljung-Box statistics and methods based on randomization 3. Development of new robust t-statistic approaches for the analysis and inference of predictive regressions in economic and financial markets and the analysis of their asymptotic and finite sample statistical properties 4. The analysis of interdependence between bubbles in several time series and in various financial markets



1. Eiji Kurozumi, Anton Skrobotov On the asymptotic behavior of bubble date estimators Journal of Time Series Analysis, принято, без номера, но система требует всё равно что-то заполнить (year - 2022)

2. Mikhail Mamonov , Christopher Parmeter, Artem Prokhorov Dependence modeling in stochastic frontier analysis Dependence Modeling, Volume 10, Issue 1, 123–144 (year - 2022)

3. R. Ibragimov, J. Kim, A. Skrobotov NEW ROBUST INFERENCE FOR PREDICTIVE REGRESSIONS Econometric Theory, in press (year - 2023)

4. Robert James, Artem Prokhorov, Christine Amsler, Peter Schmidt Improving Predictions of Technical Inefficiency Advances in Econometrics, - (year - 2023)

Annotation of the results obtained in 2020
In the reporting period, the project participants have conducted research in the main directions planned for 2020-2021. In particular, they have conducted research in the following directions: 1. Development of new methods for detecting financial bubbles under time-varying volatility that does not require computationally expensive resampling methods. 2. Estimation of fiscal multipliers based on the identification of structural vector autoregressions using the generalized method of moments (GMM) based on non-normality of errors. 3. Development of new robust inference methods for testing on trends in data with uncertainty over the order of integration of errors (stationary or non-stationary) based on t-statistics inference using group estimators of parameters of interest. 4. Development of new approaches to constructing conservative risk assessments based on buffered probabilities of exceedance. 5. Development of new robust approaches for the study of hypotheses of (non-) efficiency, nonlinear dependence and volatility clustering in economic and financial markets, the analysis of predictive regressions with potential nonstationarity of predictors, nonstationary volatility, outliers and heavy tails in the distribution of the data used. 6. Development of new methods for estimating the joint tail distribution, in which the marginal tail probabilities are estimated on the basis of the generalized exreme value distributions, and the structure of the dependence between the components is modeled by a stable tail dependence function. Currently, the project participants are working in the following areas: 1. Application of mixed integer optimization to the problems of identifying the number of structural breaks and dating of bubbles. 2. Investigation of the asymptotic properties of the dates of bubble estimators (dates of exuberation and collapse) in the case of moderately explosive processes for bubbles and moderately stationary processes of collapse, the latter passing into the usual regime with a unit root. 3. Research on time-varying cryptocurrency networks to predict cryptocurrency returns. 4. Development of bootstrap algorithms for constructing confidence intervals for multivariate tail statistics and investigating their effectiveness in practice. 5. Research on the application of multi-agent approaches to study anomalies in financial markets and the influence of self-learning agents on them. 6. Collecting a large number of features and designing an optimal neural network architecture capable of achieving good quality in predicting the behavior of cryptocurrencies. 7. Collection of signs and study of the mechanism of influence of predictors on the predictive ability of a neural network for stock indices. 8. Integration of the developed methods and models into statistical and econometric software.



1. Pertaiaa G., Prokhorov A., Uryasev S. A New Approach to Credit Ratings Journal of Banking & Finance, - (year - 2021)

Annotation of the results obtained in 2021
In the reporting period, the project participants have conducted research in the main directions planned for 2021-2022. In particular, they have conducted research in the following directions: 1. A new time-transformed method for detecting financial bubbles with time-varying volatility has been developed, that does not require computationally expensive resampling methods. 2. The statistical properties of estimates of cointegrating vectors in the presence of multicointegration are investigated. 3. The problem of analysis, modeling and application of dependencies between asset quotations in various capital markets is considered. 4. The influence of HFT traders, who make trading decisions based on reinforcement learning, on the development of financial market dynamics using multi-agent modeling was studied. 5. The validity of the bootstrap algorithm for constructing confidence intervals for multivariate tail statistics is proved. 6. The asymptotic properties of the bubble date estimates based on the two-step split-sample method are obtained. 7. An algorithm for the problem of mixed integer optimization has been developed to identify the number of structural breaks, using information criterion as objective function. Currently, the project participants are working in the following areas: 1. Application of mixed integer optimization to problems of identification and dating of bubbles. 2. Investigation of the asymptotic properties of estimates for the dates of the emergence and collapse of a bubble under a moderately explosive bubble process and a moderately stationary collapse process under nonstationary volatility. 3. Research on time-varying crypto-currency networks to predict crypto-currency returns. 4. Study of the principles of inertia-free dynamics of the evolution of the state of electronic capital markets. 5. Development of a methodology for extracting knowledge from poorly structured information necessary for making management decisions. 6. Research on assessing the quality of forecasting non-stationary processes in terms of the efficiency of the control system.



1. Alexander Musaev, Dmitry Grigoriev Analyzing, Modeling, and Utilizing Observation Series Correlation in Capital Markets Computation, 9 (year - 2021)

2. Eiji Kurozumi, Anton Skrobotov, Alexey Tsarev Time-Transformed Test for Bubbles under Non-stationary Volatility Journal of Financial Econometrics, - (year - 2022)

3. Igor L.Kheifets, Peter C.B.Phillips Fully modified least squares cointegrating parameter estimation in multicointegrated systems Journal of Econometrics, - (year - 2021)