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on Econometric Time Series |
| By: | Petr Jizba; Jan Korbel |
| Abstract: | Multifractal analysis is one of the important approaches that enables us to measure the complexity of various data via the scaling properties. We compare the most common techniques used for multifractal exponents estimation from both theoretical and practical point of view. Particularly, we discuss the methods based on estimation of R\'enyi entropy, which provide a powerful tool especially in presence of heavy-tailed data. To put some flesh on bare bones, all methods are compared on various real financial datasets, including daily and high-frequency data. |
| Date: | 2016–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1610.07028&r=ets |
| By: | Jaroslaw Kwapien; Pawel Oswiecimka; Marcin Forczek; Stanislaw Drozdz |
| Abstract: | Based on a recently proposed $q$-dependent detrended cross-correlation coefficient $\rho_q$ (J.~Kwapie\'n, P.~O\'swi\k{e}cimka, S.~Dro\.zd\.z, Phys. Rev.~E 92, 052815 (2015)), we introduce a family of $q$-dependent minimum spanning trees ($q$MST) that are selective to cross-correlations between different fluctuation amplitudes and different time scales of multivariate data. They inherit this ability directly from the coefficients $\rho_q$ that are processed here to construct a distance matrix being the input to the MST-constructing Kruskal's algorithm. In order to illustrate their performance, we apply the $q$MSTs to sample empirical data from the American stock market and discuss the results. We show that the $q$MST graphs can complement $\rho_q$ in detection of "hidden" correlations that cannot be observed by the MST graphs based on $\rho_{\rm DCCA}$ and, therefore, they can be useful in many areas where the multivariate cross-correlations are of interest (e.g., in portfolio analysis). |
| Date: | 2016–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1610.08416&r=ets |
| By: | Badi H. Baltagi (Syracuse University); Chihwa Kao (University of Connecticut); Bin Peng (Huazhong University of Science and Technology) |
| Abstract: | This paper considers the problem of testing cross-sectional correlation in large panel data models with serially correlated errors. It finds that existing tests for cross-sectional correlation encounter size distortions with serial correlation in the errors. To control the size, this paper proposes a modification of Pesaran’s CD test to account for serial correlation of an unknown form in the error term. We derive the limiting distribution of this test as (N, T) → ∞. The test is distribution free and allows for unknown forms of serial correlation in the errors. Monte Carlo simulations show that the test has good size and power for large panels when serial correlation in the errors is present. JEL Classification: C13; C33 Key words: Cross-sectional Correlation Test; Serial Correlation; Large Panel Data Model |
| Date: | 2016–10 |
| URL: | http://d.repec.org/n?u=RePEc:uct:uconnp:2016-32&r=ets |
| By: | Chihwa Kao (University of Connecticut); Lorenzo Trapani (Cass Business School); Giovanni Urga (Cass Business School and Universitá di Bergamo) |
| Abstract: | We propose a test for the stability over time of the covariance matrix of multivariate time series. The analysis is extended to the eigensystem to ascertain changes due to instability in the eigenvalues and/or eigenvectors. Using strong Invariance Principles and Law of Large Numbers, we normalise the CUSUM-type statistics to calculate their supremum over the whole sample. The power properties of the test versus alternative hypotheses, including also the case of breaks close to the beginning/end of sample are investigated theoretically and via simulation. We extend our theory to test for the stability of the covariance matrix of a multivariate regression model. The testing procedures are illustrated by studying the stability of the principal components of the term structure of 18 US interest rates. JEL Classification: Key words: Covariance Matrix, Eigensystem, Changepoint, CUSUM Statistic. |
| Date: | 2016–08 |
| URL: | http://d.repec.org/n?u=RePEc:uct:uconnp:2016-33&r=ets |
| By: | Annika Schnücker |
| Abstract: | As panel vector autoregressive (PVAR) models can include several countries and variables in one system, they are well suited for global spillover analyses. However, PVARs require restrictions to ensure the feasibility of the estimation. The present paper uses a selection prior for a data-based restriction search. It introduces the stochastic search variable selection for PVAR models (SSVSP) as an alternative estimation procedure for PVARs. This extends Koop and Korobilis’s stochastic search specification selection (S4) to a restriction search on single elements. The SSVSP allows for incorporating dynamic and static interdependencies as well as cross-country heterogeneities. It uses a hierarchical prior to search for data-supported restrictions. The prior differentiates between domestic and foreign variables, thereby allowing a less restrictive panel structure. Absent a matrix structure for restrictions, a Monte Carlo simulation shows that SSVSP outperforms S4 in terms of deviation from the true values. Furthermore, the results of a forecast exercise for G7 countries demonstrate that forecast performance improves for the SSVSP specifications which focus on sparsity in form of no dynamic interdependencies. |
| Keywords: | model selection, stochastic search variable selection, PVAR |
| JEL: | C11 C33 C52 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:diw:diwwpp:dp1612&r=ets |
| By: | Martin Forde; Hongzhong Zhang |
| Abstract: | Using the large deviation principle (LDP) for a re-scaled fractional Brownian motion $B^H_t$ where the rate function is defined via the reproducing kernel Hilbert space, we compute small-time asymptotics for a correlated fractional stochastic volatility model of the form $dS_t=S_t\sigma(Y_t) (\bar{\rho} dW_t +\rho dB_t), \,dY_t=dB^H_t$ where $\sigma$ is $\alpha$-H\"{o}lder continuous for some $\alpha\in(0,1]$; in particular, we show that $t^{H-\frac{1}{2}} \log S_t $ satisfies the LDP as $t\to0$ and the model has a well-defined implied volatility smile as $t \to 0$, when the log-moneyness $k(t)=x t^{\frac{1}{2}-H}$. Thus the smile steepens to infinity or flattens to zero depending on whether $H\in(0,\frac{1}{2})$ or $H\in(\frac{1}{2},1)$. We also compute large-time asymptotics for a fractional local-stochastic volatility model of the form: $dS_t= S_t^{\beta} |Y_t|^p dW_t,dY_t=dB^H_t$, and we generalize two identities in Matsumoto&Yor05 to show that $\frac{1}{t^{2H}}\log \frac{1}{t}\int_0^t e^{2 B^H_s} ds$ and $\frac{1}{t^{2H}}(\log \int_0^t e^{2(\mu s+B^H_s)} ds-2 \mu t)$ converge in law to $ 2\mathrm{max}_{0 \le s \le 1} B^H_{s}$ and $2B_1$ respectively for $H \in (0,\frac{1}{2})$ and $\mu>0$ as $t \to \infty$. |
| Date: | 2016–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1610.08878&r=ets |