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Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

B2 - Forecasting high-dimensional time series

A forecast exercise for high dimensional time series is undoubtedly troubled by dimensionality.  Concentration on relevant information requires regularization by penalizing sparseness.  The majority of scientific research for this kind of forecast exercise has focussed on either static or mean predictive penalization techniques involving Lasso or SCAD.  Recent research has shown though that regularization in a moving window context contains predictive power of e.g. the Lagrange multiplier.  In a variety of time varying tail event studies researchers have found predictive tail moment information on top of almost constant mean variation.  This motivates to use time series of principal components that are calculated from an asymmetric norm, covering thus quantile and expectile tail risk measures.  In combination with the connectedness framework of Diebold and Yilmaz (2014) of high dimensional VAR systems we aim to research on a network based view allowing the modelling of high dimensional (non mean) dependencies.

 

Coordination

Haiqiang Chen: His main interests are Financial Econometrics, Time Series Econometrics and Financial Economics. His current research includes the estimation and inference for nonlinear nonstionary time series models, quantitative prediction models and high frequency data.

Ying Fang: His main interests are Econometrics, Applied Econometrics, Economy of China. His research includes work in nonparametric and semi-parametric method, panel data analysis, and instrumental variable selection.

Yingxing Li: Her research interests are about mathematical statistics. In particular, she concentrates on research topics including  non and semiparametric regression, longitudinal and functional data analysis, dimension reduction, and model specification tests.

Wolfgang Karl Härdle: His main interests are non- and semiparametrics statistics and econometrics. His research includes work in nonparametric modelling, local adaptive models, reduction techniques, stationary models, quantile regression.

Weining Wang: Her research interest are on financial econometrics and statistics. In particular, her research includes topics like non and semiparametric statistics, network models, high dimensional time series analysis, spatial temporal copula models, etc.

Lars Winkelmann: His main research interest is applied econometrics. His recent research concentrates on jumps in asset prices and volatility and the economic content behind such extreme events.

Wei Zhong: His research interests include high dimensional data analysis: large p small n problems including independence screening, variable selection, interaction detection, classification, hypothesis test etc., test of independence, data mining techniques and applications of statistics.

Michael Burda: His research interests lie at the many interfaces between macroeconomics and labour economics. He has also studied the economics of regional integration and in particular the German unification episode.

 

Exemplary PhD-Theses

1.    A Financial Risk Meter based on Time Varying Lasso

Reducing the dimension and predicting interdependencies and evolution of derived factors is eminent when one is focused on controlling risk.  Both can be achieved via the Lasso regression which has been largely used and extended into both quantile regression and time series analysis.  This is of particular interest when measuring systemic risk.  The Lasso penalization parameter is driven by tail characteristics, size of active set and singularity of design.  It has therefore a neat connection to risk control and its dynamics can therefore be interpreted in an economic context: FinancialRiskMeter (http://frm.wiwi.hu-berlin.de).  Finding a suitable model that captures  dependencies between underlying time series and the Lasso parameter itself can shed more light onto problems related to systemic risk and dealing with high dimensionality.  The prediction itself that is being constructed using only the dynamics of the Lasso parameter may thus overcome the complexity of forecasting in a high dimensional setting.

 

2.    Multivariate diffusion Copulae

We propose a semi parametric modelling approach for nonGaussian Multivariate diffusions, where the observed multivariate processes are nonlinear transformations of the underlying multivariate parametric diffusion processes.  This approach gives us another perspective in studying the non-Gaussian dependency structures with tractable underlying processes.  The model is applied to forecasting multivariate exchange rates and the performance is compared with existing models. 

 

3.    Crypto currencies: detecting and predicting events

Crypto currencies have become more and more versatile over the years with big companies adopting and investing in the technology.  However, the systems are decentralized, unregulated and highly volatile, making their situation at any given moment difficult to assess.  On the other hand, an almost bottomless source of information can be found in the form of unstructured text written by crypto currency users on the internet.  In attempting to take advantage of this and analysing and assigning quantitative meaning to such resources one may detect events, new trends, fraudulent schemes or legal and economic issues. Utilizing techniques from text mining and machine learning, one pulls data from a popular crypto currency forum and collects user information and text associated with time stamps and apply unsupervised dynamic topic modelling (DTM), studying how opinions and the evolution of topics are connected with big events in the crypto currency universe. Furthermore, the predictive power of these techniques are investigated and the possibilities of herding will be discussed.

 

4.    Centrality-based risk quantification, management and capital allocation

By the means of a network framework, the complex interactions within the financial system can function as a mechanism for the propagation and amplification of shocks. The research interests are identifying central SIFIs, quantifying their risk spill over and determining their capital requirements as a final goal. Some key challenges are which interdependences should be prioritized and emphasized (e.g. default probability, tail risk, variance risk), the dynamics of connectedness, and the dynamics of centrality. We refine the graph theory with more focus on statistics and economics. For instance, although the eigenvector centrality, based on the eigenvector of adjacency matrix corresponding to the largest eigenvalue, measures the connective importance of financial institutions, the nodal risk or nodal characteristics beyond connections may also affect the number of central nodes and nature of its connections. We therefore propose the novel edge-node combined central measures.  The DYTEC technique can be applied here in order to establish a framework of dynamic systemic risk and dynamic capital requirements.

 

5.    Model stochastic sentiment score distilled from textual information

Using mixed text sources from professional platforms, blog fora and stock message boards, we distil, via different lexica, sentiment variables along with improved accuracy from the machine learning based methods. The sentiment score quantified by the SVM is driven by stochastic or irregular article posting; it essentially follows a Geometric Brownian motion-like stochastic process with some nice properties embedded. As we know that sentiment is impossible to go infinite (unbounded optimism or pessimism), sentiment in nature will covert to the neutral mood in the long run. We propose the local-momentum autoregression (LM-AR) model developed by Duan (2016) to capture a global mean-reverting to “neutral” but locally driven by momentum (herding effect). The parameters in this model indicate the degree of “herding” in the momentum component and the speed of converting to the neutral mood. Having the parameters estimated, we then simulate the sentiment process and perform the h-period ahead forecast.

 

6.    Bayesian estimation of macroeconomic models with underlying nonstationarity with higher dimensional data

Macroeconomic variables are hardly distinguishable from nonstationary in a statistical sense, given the low power of available tests and the limited time series data at our disposal. At the same time, detecting nonstationarity in data is an important issue for policymakers and econometricians alike. To overcome low power of conventional analyses, additional information from other datasets may be useful. The presence of latent factors driving fluctuations of a large number of macroeconomic and financial variables suggest that wide, unconventional macro micro datasets could be used fruitfully in conducting inference about economic phenomena, especially structural change. Apparent shifts in the behaviour of households, firms and governments after the Great Recession raise questions about whether structural change has occurred and about the nature and possible long lasting  - if not permanent - effects of structural change. Therefore, dynamic models with latent factors and possible breaks or other forms of nonstationarity are a natural class of model that might address questions surrounding the evolution of economic behaviour during the Great Recession.

 

 

 

References

  • Cheng X, Liao Z, Schorfheide F (2016) Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities. Review of Economic Studies, 83(4), 1511-1543, DOI: https://doi.org/10.1093/restud/rdw005
  • Duan J C (2016) Local-momentum autoregression and the modeling of interest rate term structure. Journal of Econometrics, 194 (2), 349-359, DOI: http://dx.doi.org/10.1016/j.jeconom.2016.05.012.
  • Diebold F X, Yilmaz K (2014) On the Network Topology of Variance Decompositions: Measuring the Connectedness of Financial Firms. Journal of Econometrics, 182(1), 119-134, DOI:        http://dx.doi.org/10.1016/j.jeconom.2014.04.012.