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on Econometric Time Series |
| By: | Hendrik Kaufmann (Leibniz University Hannover); Robinson Kruse (Leibniz University Hannover and CREATES); Philipp Sibbertsen (Leibniz University Hannover and CREATES) |
| Abstract: | Linearity testing against smooth transition autoregressive (STAR) models when deterministic trends are potentially present in the data is considered in this paper. As opposed to recently reported results in Zhang (2012), we show that linearity tests against STAR models lead to useful results in this setting. |
| Keywords: | Nonlinearity, Smooth transition, Deterministic trend |
| JEL: | C12 C22 |
| Date: | 2012–05–08 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-20&r=ets |
| By: | R. Vilela Mendes; M. J. Oliveira; A. M. Rodrigues |
| Abstract: | Based on a criterion of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions of the model are obtained with different leverage behavior. Here, the no-arbitrage and completeness properties of the models are studied. |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1205.2866&r=ets |
| By: | Erdinc Akyildirim; Yan Dolinsky; H. Mete Soner |
| Abstract: | A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov process. The ?first two components are related to the stock and volatility processes and take values in a two dimensional Binomial tree. The other two components of the Markov process are the increments of random walks with simple values in {-1; +1}. The resulting effi?cient option pricing equations are numerically implemented for general American and European options including the standard put and calls, barrier, lookback and Asian type pay-o?ffs. The weak and extended weak convergence are also proved. |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1205.3555&r=ets |
| By: | Andrey Itkin |
| Abstract: | Classical solvable stochastic volatility models (SVM) use a CEV process for instantaneous variance where the CEV parameter $\gamma$ takes just few values: 0 - the Ornstein-Uhlenbeck process, 1/2 - the Heston (or square root) process, 1- GARCH, and 3/2 - the 3/2 model. Some other models were discovered in \cite{Labordere2009} by making connection between stochastic volatility and solvable diffusion processes in quantum mechanics. In particular, he used to build a bridge between solvable (super)potentials (the Natanzon (super)potentials, which allow reduction of a Schr\"{o}dinger equation to a Gauss confluent hypergeometric equation) and existing SVM. In this paper we discuss another approach to extend the class of solvable SVM in terms of hypergeometric functions. Thus obtained new models could be useful for pricing volatility derivatives (variance and volatility swaps, moment swaps). |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1205.3550&r=ets |
| By: | Guglielmo D'Amico; Filippo Petroni |
| Abstract: | In this paper we propose a new stochastic model based on a generalization of semi-Markov chains to study the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted indexed semi-Markov chain model. We show, through Monte Carlo simulations, that the model is able to reproduce important stylized facts of financial time series as the first passage time distributions and the persistence of volatility. The model is applied to data from Italian and German stock market from first of January 2007 until end of December 2010. |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1205.2551&r=ets |
| By: | Fan, Jianqing; Liao, Yuan; Mincheva, Martina |
| Abstract: | This paper deals with estimation of high-dimensional covariance with a conditional sparsity structure, which is the composition of a low-rank matrix plus a sparse matrix. By assuming sparse error covariance matrix in a multi-factor model, we allow the presence of the cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specic examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms, including the spectral norm. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also veried by extensive simulation studies. |
| Keywords: | High dimensionality; approximate factor model; unknown factors; principal components; sparse matrix; low-rank matrix; thresholding; cross-sectional correlation |
| JEL: | C13 C01 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:38697&r=ets |
| By: | Pitarakis, J |
| Abstract: | We develop a test of the joint null hypothesis of linearity and nonstationarity within a threshold autoregressive process of order one with deterministic components. We derive the limiting distribution of a Wald type test statistic and subsequently investigate its local power and nite sample properties. We view our test as a useful diagnostic tool since a non rejection of our null hypothesis would remove the need to explore nonlinearities any further and support a linear autoregression with a unit root. |
| Keywords: | Threshold Autoregressive Models; Unit Roots; Near Unit Roots; Brownian Bridge; Augmented Dickey Fuller Test |
| JEL: | C50 C22 |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:38845&r=ets |
| By: | Pitarakis, J |
| Abstract: | We formally define a concept of functional cointegration linking the dynamics of two time series via a functional coefficient. This is achieved through the use of a concept of summability as an alternative to I(1)'ness which is no longer suitable under nonlinear dynamics. We subsequently introduce a nonparametric approach for estimating the unknown functional coefficients. Our method is based on a piecewise local least squares principle and is computationally simple to implement. We establish its consistency properties and evaluate its performance in finite samples. |
| Keywords: | Functional Coefficients; Unit Roots; Cointegration; Piecewise Local Linear Estimation |
| JEL: | C50 C22 |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:38846&r=ets |
| By: | Fei Chen (Huazhong University of Science and Technology); Francis X. Diebold (Department of Economics, University of Pennsylvania); Frank Schorfheide (Department of Economics, University of Pennsylvania) |
| Abstract: | We propose and illustrate a Markov-switching multi-fractal duration (MSMD) model for analysis of inter-trade durations in financial markets. We establish several of its key properties with emphasis on high persistence (indeed long memory). Empirical exploration suggests MSMD's superiority relative to leading competitors. |
| Keywords: | High-frequency trading data, point process, long memory, time deformation, scaling law, self-similarity, regime-switching model, market microstructure, liquidity |
| JEL: | C41 C22 G1 |
| Date: | 2012–05–07 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:12-020&r=ets |
| By: | Christian Francq (CREST); Jean-Michel Zakoïan (CREST) |
| Keywords: | alpha-stable distribution, composite likelihood, GEV distribution, GPD, pseudo-likelihood, quasi-marginal maximum likelihood, stock returns distributions |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpaper:2011-30&r=ets |
| By: | Patrick Gagliardini (University of Lugano); Christian Gouriéroux (CREST, University of Toronto) |
| Abstract: | There is a growing literature on the possibility to identify correlation and contagion in qualitative risk analysis. Our paper considers this question by means of a model describing the joint dynamics of a set of individual binary processes. The two admissible values correspond to bad and good risk states of an individual. The risk correlation and its time dependence are captured by introducing a dynamic frailty, whereas the contagion passes through the effect of the lagged number of individuals in the bad risk state. We study carefully the dynamic properties of the joint process. Then, we focus on the limiting case of large populations (portfolios) and reconcile the microscopic and macroscopic dynamic views of the risk. The difficulty to identify in finite sample risk correlation and contagion is illustrated by means of Monte-Carlo simulations |
| Keywords: | Risk Dependence, Frailty, Systematic Risk, Contagion, Count Process, INAR Model, Compound Autoregressive Process, Affine Model, Credit Risk, Granularity Adjustment, Stochastic Intensity. |
| JEL: | G12 C23 |
| Date: | 2012–03 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpaper:2012-07&r=ets |
| By: | McElroy, Tucker S.; Politis, Dimitris N. |
| Abstract: | We consider the problem of estimating the variance of the partial sums of a stationary time series that has either long memory, short memory, negative/intermediate memory, or is the first-difference of such a process. The rate of growth of this variance depends crucially on the type of memory, and we present results on the behavior of tapered sums of sample autocovariances in this context when the bandwidth vanishes asymptotically. We also present asymptotic results for the case that the bandwidth is a fixed proportion of sample size, extending known results to the case of flat-top tapers. We adopt the fixed proportion bandwidth perspective in our empirical section, presenting two methods for estimating the limiting critical values - both the subsampling method and a plug-in approach. Extensive simulation studies compare the size and power of both approaches as applied to hypothesis testing for the mean. Both methods perform well - although the subsampling method appears to be better sized - and provide a viable framework for conducting inference for the mean. In summary, we supply a unified asymptotic theory that covers all different types of memory under a single umbrella. |
| Keywords: | Econometrics and Quantitative Economics, Kernel, Lag-windows, Overdifferencing, Spectral estimation, Subsampling, Tapers, Unit-root problem |
| Date: | 2012–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:ucsdec:qt35c7r55c&r=ets |