A simple non-linear model with fractional integration for financial time series data

This paper provides several examples of simple non-linear time series models with fractionally integrated disturbances. Both types of models (non-linear and fractional integration) have been widely used in recent years when modeling financial data. We use a testing procedure that permits us to test the order of integration in raw time series in the context of non-linear models. The tests are applied to several financial time series, the results showing that when the non-linear sign structure is taken into account, the order of integration of the series is much higher than one, finding thus conclusive evidence against mean reversion in their behavior.     

Regional capital mobility in China: Economic reform with limited financial integration

This paper assesses the changes in the regional capital mobility in China during the period of economic reform in 1978–2008 by employing a panel time varying coefficient (TVP) model. This approach is much more suitable to model China's evolution in the regional capital mobility than a standard structural break model as China's reforms took place gradually and were often implemented over several stages. Using the TVP model, we find that (1) China's provincial capital mobility demonstrated a moderate improvement over the sample period, but worsened temporarily between 1994 and 1997. This is probably due to the government's effort to combat inflation which reduced the investment and transfers to regions; (2) regions with the most developed and least developed provinces experienced higher degree of capital mobility improvement than those in the middle.     

A multivariate distance nonlinear causality test based on partial distance correlation: a machine learning application to energy futures

This paper proposes a multivariate distance nonlinear causality test (MDNC) using the partial distance correlation in a time series framework. Partial distance correlation as an extension of the Brownian distance correlation calculates the distance correlation between random vectors X and Y controlling for a random vector Z. Our test can detect nonlinear lagged relationships between time series, and when integrated with machine learning methods it can improve the forecasting power. We apply our method as a feature selection procedure and combine it with the support vector machine and random forests algorithms to study the forecast of the main energy financial time series (oil, coal, and natural gas futures). It shows substantial improvement in forecasting the fuel energy time series in comparison to the classical Granger causality method in time series.     

Forward-looking portfolio selection with multivariate non-Gaussian models

In this study, we suggest a portfolio selection framework based on time series of stock log-returns, option-implied information, and multivariate non-Gaussian processes. We empirically assess a multivariate extension of the normal tempered stable (NTS) model and of the generalized hyperbolic (GH) one by implementing an estimation method that simultaneously calibrates the multivariate time series of log-returns and, for each margin, the univariate observed one-month implied volatility smile. To extract option-implied information, the connection between the historical measure P and the risk-neutral measure Q, needed to price options, is provided by the multivariate Esscher transform. The method is applied to fit a 50-dimensional series of stock returns, to evaluate widely known portfolio risk measures and to perform a forward-looking portfolio selection analysis. The proposed models are able to produce asymmetries, heavy tails, both linear and non-linear dependence and, to calibrate them, there is no need for liquid multivariate derivative quotes.     

Asymmetric information and imperfect competition in a continuous time multivariate security model

This paper deals with the problem of price formation in a market with asymmetric information and several risky assets. We then extend the multivariate security model of Caballé and Krishnan (1994) to a continuous time framework, and general utility function. Our model enables us to observe some results which are specific to multi security markets such as Giffen effect. An application of the main result will be the non trivial generalizations of the models of Back (1992) and Cho (1997).Mathematics Subject Classification (1991): 49L10, 60G44, 90A15JEL Classification: G11, G12The author would like to thank his supervisor H. Pham, K. Back and an anonymous referee for useful comments and discussions.     

Orthogonal GARCH and covariance matrix forecasting: The Nordic stock markets during the Asian financial crisis 1997–1998

In risk management, modelling large numbers of assets and their variances and covariances in a unified framework is often important. In such multivariate frameworks, it is difficult to incorporate GARCH models and thus a new member of the ARCH-family, Orthogonal GARCH, has been suggested as a remedy to inherent estimation problems in multivariate ARCH modelling. Orthogonal GARCH creates positive definite covariance matrices of any size but builds on assumptions that partly break down during stress scenarios. This article therefore assesses the stress performance of the model by looking at four Nordic stock indices and covariance matrix forecasts during the highly volatile years of 1997 and 1998. Overall, Orthogonal GARCH is found to perform significantly better than traditional historical variance and moving average methods. Out-of-sample evaluation measures include symmetric loss functions (RMSE), asymmetric loss functions, operational methods suggested by the Basle Committee on Banking Supervision, as well as a forecast evaluation methodology based on pricing of simulated ‘rainbow options’.     

Multivariate extremes for models with constant conditional correlations

Models with constant conditional correlations are versatile tools for describing the behavior of multivariate time series of financial returns. Mathematically speaking, they are solutions of a special class of stochastic recurrence equations (SRE). The extremal behavior of general solutions of SRE has been studied in detail by Kesten [Kesten, H., 1973. Random difference equations and renewal theory for products of random matrices. Acta Mathematica 131, 207–248] and Perfekt [Perfekt, R., 1997. Extreme value theory for a class of Markov chains with values in ^d. Advances in Applied Probability 29, 138–164]. The central concept to understanding the joint extremal behavior of such multivariate time series is the multivariate regular variation spectral measure. In this paper, we propose an estimator for the spectral measure associated with solutions of SRE and prove its consistency. Our estimator is the tail empirical measure of the multivariate time series. Successful use of the estimator depends on a good choice of k, the number of upper order statistics contributing to the empirical measure. We introduce a new criteria for the choice of k based on a scaling property of the spectral measure. We investigate the performance of our estimation technique on exchange rate time series from HFDF96 data set. The estimated spectral measure is used to calculate probabilities of joint extreme returns and probabilities of large movements in an exchange rate conditional on the occurrence of extreme returns in another exchange rate. We find a high level of dependence between the extreme movements of most of the currencies in the EU. We also investigate the changes in the level of dependence between the extreme returns of pairs of currencies as the sampling frequency decreases. When at least one return is extreme, a strong dependence between the components is present already at the 4-hour level for most of the European currencies.     

Cross‐sectional Tests of Conditional Asset Pricing Models: Evidence from the German Stock Market

We study the performance of conditional asset pricing models and multifactor models in explaining the German cross‐section of stock returns. We focus on several variables, which (according to previous research) are associated with market expectations on future market excess returns or business cycle conditions. Our results suggest that the empirical performance of the Capital Asset Pricing Model (CAPM) can be improved when allowing for time‐varying parameters of the stochastic discount factor. A conditional CAPM using the term spread explains the returns on our size and book‐to‐market sorted portfolios about as well as the Fama‐French three‐factor model and performs best in terms of the Hansen‐Jagannathan distance. Structural break tests do not necessarily indicate parameter instability of conditional model specifications. Another major finding of the paper is that the Fama‐French model – despite its generally good cross‐sectional performance – is subject to model instability. Unconditional models, however, do a better job than conditional ones at capturing time‐series predictability of the test portfolio returns.     

Multivariate GARCH Modeling of Exchange Rate Volatility Transmission in the European Monetary System

We construct a series of 3‐, 4‐ and 5‐variable multivariate GARCH models of exchange rate volatility transmission across the important European Monetary System (EMS) currencies including the French franc, the German mark, the Italian lira, and the European Currency Unit. The models are estimated without imposing the common restriction of constant correlation on both daily and weekly data from April 1979–March 1997. Our results indicate the importance of checking for specification robustness in multivariate Generalized Autoregressive Conditional Heleroskedasticity (GARCH) modeling, we find that increased temporal aggregation reduces observed volatility transmission, and that the mark plays a dominant position in terms of volatility transmission.     

U.S. Common stock prices, 1871–1970: playing with dummies

The received wisdom that the levels of many economic time series are generated by processes with a unit autoregressive root has been called into question by recent work of Perron. When break points, or interventions, in the time series are allowed it emerges that the unit roots hypothesis can often be rejected at quite low significance levels. Taking for illustration a single time series, U.S. common stock prices, we demonstrate that Perron's conclusions are very sensitive to the choice of break point, and that the data contain little support for the particular choice imposed by Perron.