The impacts of multi-scale macroeconomic variables on market risks

The project aimed at new mathematical models to capture multi-scale effects for financial variables. The main directions of research have been maintained and progressed according to the plan. The main focus in the first phase, as originally planned, is on the investigation of suitability of the models with conditional heterscedasity to account for important features of economics data. In particular, we have developed non-linear time series models  for non-Gaussian error distribution. We have proposed and investigated several extensions to the asymmetric-power autoregressive conditionally heteroscedastic (APARCH) that served for years as an effective model for financial data.   Model fitting and prediction methods have been developed. We have demonstrated that the extensions allow for more accurate modeling the observed data.  Applications to new spatial econometrics models have been studied jointly in collaboration with Hossein Asgarian and Lu Liu, the Department of Economics. New results for models of high frequency data and their incorporation to the multi-scale modeling have been progressing very well. The results resulted in a number of published papers, see items  7, 11, 16, 17.  

The central article in this group `Tail behavior and dependence structure in the APARCH model', paper 7, presents some previously unknown properties of a fundamental financial model. The importance of this study lies in showing to what extent this popular model can account for the actual empirical features shown in the real life of data and thus showing limitation of the model. Currently, at least two articles are continuing this research by exploring modeling different temporal scales to predict financial market volatility and to study dependence between pairs of returns and how macroeconomic variables affect them. By using very convenient classes of distributions, the generalized asymmetric Laplace (GAL) and normal inverse Gaussian, our models have captured different time scales due to the infinite divisibility property.

The new models introduced have ability to account for the so-called leverage effect and dependence in the volatility modeling exploring beyond the traditionally Gaussian error models. This multi-scale modeling will integrate macroeconomic and financial variables into a consistent methodological setup. These are more parsimonious models and serve well as a summary of volatility for commodities. The resulting efficiency in the number of characteristics describing intra-market risk will facilitate meaningful comparisons between different markets. The remaining papers the above group are investigated different mathematical properties of GAL based models and thus providing with further understanding of the models. The consequences of these studies explain benefits of some fundamental models for economics and financial data both in the multivariate setup and in the temporal multi-scale framework. Analysis of the behavior of the non-gaussian process in the context of geometrical asymmetry observed in many empirical data including those in economics and finance was hardly addressed in the past research. Our results, see papers 3, 11, 17, significantly enhance our understanding of the behavior of the non-gaussian processes thus the third aim of our project, i.e. modeling heavy tails and asymmetry in the assets, economic variables and volatility, was thoroughly investigated and applicability of generalized Laplace distributions  as an alternative to the Gaussian counterpart confirmed. The effect heavy-tailed behavior in the data and possible asymmetry and flexibility in accounting for different time scales in the econometric models through the generalized Laplace distribution has been confirmed. In particular, paper 17 ties geometrical asymmetry features observed in the data with the non-gaussian assumptions of a model.
 
The second theme of the project aims at multivariate extensions in financial and macroeconomic models that will be utilized to assess market risks, which is the ultimate goal. Some of the new models, specifically, related to the so-called Wright process and matrix valued distributions has shown potential to be useful in multi-scale modeling of economics data. These new research directions are promising and constitute novel aspects that resulted from the above mentioned research and originally were less emphatically spelled out in the original project description. The published papers from this area are  3, 6, 12, 13.

Our studies of multivariate volatilities and correlations models disclosed that analysis of historical data may miss changes in risk unless the modelling and estimation methods are carefully designed to account for extreme events. Also the linkages between volatility and other (macroeconomic and financial) variables can be analyzed more efficiently if the observations are made only at random and not so frequent events. The most gain was seen if such events are determined by extreme behavior in the data. Several papers in the project focused on methodological research to investigate this aspect, see papers 1, 2, 9, 10, 14, 15. Here the most important paper 15 gives an elegant approach to study volatility models at extreme levels using a concept of functional Slepian model. For the continuous time models with non-gaussian distribution little is known about statistics properties that are observed at the instants described by observed data. A typical example of such would be an extreme behavior of the model such as a sudden drop in the value or behavior at the instants when the value of the price process is high. Slepian models for Gaussian models well describe statistical properties at such events but little is known for the non-gaussian models. The paper investigate the problem and provides both theoretical and computational tools to effectively investigate properties of a particular non-gaussian model – Laplace moving average. In the continuation of this research we currently verify its effectiveness in the empirical context of a given market by studying how extreme random events as defined by macroeconomic variables (such as unexpected inflation, term premium, per capital labor income growth, default premium, unemployment rate, short term interest rate, per capital consumption) influence financial variables (such as stock returns, value at risk) of a firm/market or portfolio.  

Finally to perform  methodological research on the data for new models we needed a better understanding of statistical inference and mathematical properties of newly derived models. Thus a number of publications explore methodologies both from theoretical perspective and from an inference point of view. These are  papers 2, 8, 10 and while not addressing the main goals of the project they solve certain statistical and methodological problems that arised when the main topics were investigated in other work.

The participants in the project have taken part in a number of research meetings and seminars, partially sponsored by the project funding, that allowed us to, firstly, present the results of the research, secondly, to learn about the most recent developments in the field. Here is the list of attended meetings:

1. The 10th International Conference on Computational and Methodological Statistics, University of London, UK, December 2017.
2. Statistische Woche 2017 (German Statistical Week), Rostock, Germany, September 2017.
3. Mathematical Statistical Seminar at the Department of Economics and Statistics, Linnaeus University, Växjö, Sweden, May 2017.
4. Mathematical Statistics Seminar at the Department of Mathematics, Stockholm University, Sweden, April 2017.
5. Mathematical Statistics Seminar at the Centre for Mathematical Sciences, Lund University, Sweden, April 2017.
6. Seminar of the Department of Mathematics, Wrocław University of Science and Technology, Poland, March 2017.
7. Winter Conference in Statistics 2017, Åre, Sweden, March 2017.
8. The 9th International Conference on Computational and Methodological Statistics, University of Seville, Spain, December 2016.
9. Statistische Woche 2016 (German Statistical Week), Augsburg, Germany, September 2016.
10. Workshop on Migration Algorithms–Swedish Migration Agency, Malmö, Sweden, September 2016.
11. Smögen Workshop on Spatial and Spatio-temporal Models, Hierarchical Modeling and Model Selection, Smögen, Sweden, August 2016.
12. International Conference on Event-based Control, Communication, and Signal Processing (EBCCSP), Kraków, Poland, June 2016.
13. Workshop on Spatio-Temporal Statistics, Imperial College London, April 2016.
14. Statistical Seminar, Chalmers University, March 2016.
15.    ConferenceGDR GeoSto, Poitiers, August 2015
16.    The Århus Conference on Probability Statistics and Their Applications, Århus, Denmark, June 15-19, 2015
17.    The DynStoch meeting, the Center of Mathematical Science, Lund University, Lund, Sweden, May 2015
18.    Arne Ryde Workshop in Financial Economics, Lund, Sweden, May 2015
19.    The XIII International Conference on Economics and Econometrics, L.A., U.S.A, April 3-4, 2015
20.    The ASA Statistical Meeting, Flint, Michigan, U.S.A, June 24-28, 2014.
21.    New challenges in spatial and spatio-temporal modeling a Smögen workshop August 2014

The international collaboration has been facilitated through visits of researchers that cooperate with us on our project and thus we have hosted the following visitors:

Anastassia Baxevani, the University of Cyprus, Cyprus, Tom J. Kozubowski, University of Nevada, Reno, USA, Taras Bodnar, Humboldt University of Berlin, Germany, Nicola Loperfido, University of Urbino, Italy, Igor Rychlik, Chalmers University, Sweden, Nestor Parolya, Leibniz University of Hannover, Germany, Jaroslaw Harezlak, Indiana University-Bloomington, USA, Marie Kratz, ESSEC, France, Anna Panorska, the University of Nevada, Reno, USA