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on Econometric Time Series |
| By: | Oh, Dong Hwan (Board of Governors of the Federal Reserve System (U.S.)); Patton, Andrew J. (Duke University) |
| Abstract: | This paper proposes a new model for high-dimensional distributions of asset returns that utilizes mixed frequency data and copulas. The dependence between returns is decomposed into linear and nonlinear components, enabling the use of high frequency data to accurately forecast linear dependence, and a new class of copulas designed to capture nonlinear dependence among the resulting uncorrelated, low frequency, residuals. Estimation of the new class of copulas is conducted using composite likelihood, facilitating applications involving hundreds of variables. In- and out-of-sample tests confirm the superiority of the proposed models applied to daily returns on constituents of the S&P 100 index. |
| Keywords: | Composite likelihood; forecasting; high frequency data; nonlinear dependence |
| JEL: | C32 C51 C58 |
| Date: | 2015–05–19 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2015-50&r=ets |
| By: | Oh, Dong Hwan (Board of Governors of the Federal Reserve System (U.S.)); Patton, Andrew J. (Duke University) |
| Abstract: | his paper presents flexible new models for the dependence structure, or copula, of economic variables based on a latent factor structure. The proposed models are particularly attractive for relatively high dimensional applications, involving fifty or more variables, and can be combined with semiparametric marginal distributions to obtain flexible multivariate distributions. Factor copulas generally lack a closed-form density, but we obtain analytical results for the implied tail dependence using extreme value theory, and we verify that simulation-based estimation using rank statistics is reliable even in high dimensions. We consider "scree" plots to aid the choice of the number of factors in the model. The model is applied to daily returns on all 100 constituents of the S&P 100 index, and we find significant evidence of tail dependence, heterogeneous dependence, and asymmetric dependence, with dependence being stronger in crashes than in booms. We also show that factor copula models provide superior estimates of some measures of systemic risk. |
| Keywords: | Copulas; correlation; dependence; systemic risk; tail dependence |
| JEL: | C31 C32 C51 |
| Date: | 2015–05–18 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2015-51&r=ets |
| By: | Francisco Blasques (VU University Amsterdam, the Netherlands); Siem Jan Koopman (VU University Amsterdam, the Netherlands); Katarzyna Łasak (VU University Amsterdam, the Netherlands); André Lucas (VU University Amsterdam, the Netherlands) |
| Abstract: | We study the performance of alternative methods for calculating in-sample confidence and out of-sample forecast bands for time-varying parameters. The in-sample bands reflect parameter uncertainty only. The out-of-sample bands reflect both parameter uncertainty and innovation uncertainty. The bands are applicable to a large class of observation driven models and a wide range of estimation procedures. A Monte Carlo study is conducted for time-varying parameter models such as generalized autoregressive conditional heteroskedasticity and autoregressive conditional duration models. Our results show clear differences between the actual coverage provided by the different methods. We illustrate our findings in a volatility analysis for monthly Standard & Poor’s 500 index returns. |
| Keywords: | autoregressive conditional duration; delta-method; generalized autoregressive |
| JEL: | C52 C53 |
| Date: | 2015–07–09 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150083&r=ets |
| By: | Conrad, Christian; Schienle, Melanie |
| Abstract: | We develop a misspecification test for the multiplicative two-component GARCH-MIDAS model suggested in Engle et al. (2013). In the GARCH-MIDAS model a short-term unit variance GARCH component fluctuates around a smoothly time-varying long-term component which is driven by the dynamics of an explanatory variable. We suggest a Lagrange Multiplier statistic for testing the null hypothesis that the variable has no explanatory power. Hence, under the null hypothesis the long-term component is constant and the GARCH-MIDAS reduces to the simple GARCH model. We derive the asymptotic theory for our test statistic and investigate its finite sample properties by Monte-Carlo simulation. The usefulness of our procedure is illustrated by an empirical application to S&P 500 return data. |
| Keywords: | Volatility Component Models; LM test; Long-term Volatility. |
| Date: | 2015–07–09 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0597&r=ets |
| By: | David Harvey; Stephen Leybourne |
| Abstract: | We propose methods for constructing confidence sets for the timing of a break in level and/or trend that have asymptotically correct coverage for both I(0) and I(1) processes. These are based on inverting a sequence of tests for the break location, evaluated across all possible break dates. We separately derive locally best invariant tests for the I(0) and I(1) cases; under their respective assumptions, the resulting confidence sets provide correct asymptotic coverage regardless of the magnitude of the break. We suggest use of a pre-test procedure to select between the I(0)- and I(1)- based confidence sets, and Monte Carlo evidence demonstrates that our recommended procedure achieves good finite sample properties in terms of coverage and length across both I(0) and I(1) environments. An application using US macroeconomic data is provided which further evinces the value of these procedures. |
| Keywords: | Level break; Trend break; Stationary; Unit root; Locally best invariant test; Con?- dence sets. JEL classification: C22, |
| URL: | http://d.repec.org/n?u=RePEc:not:notgts:14/04&r=ets |
| By: | Fengler, Matthias R.; Herwartz, Helmut |
| Abstract: | In highly integrated markets, news spreads at a fast pace and bedevils risk monitoring and optimal asset allocation. We therefore propose global and disaggregated measures of variance transmission that allow one to assess spillovers locally in time. Key to our approach is the vector ARMA representation of the second-order dynamics of the popular BEKK model. In an empirical application to a four-dimensional system of US asset classes - equity, fixed income, foreign exchange and commodities - we illustrate the second-order transmissions at various levels of (dis)aggregation. Moreover, we demonstrate that the proposed spillover indices are informative on the value-at-risk violations of portfolios composed of the considered asset classes. |
| Keywords: | Multivariate GARCH, spillover index, value-at-risk, variance spillovers, variance decomposition |
| JEL: | C32 C58 F3 G1 |
| Date: | 2015–07 |
| URL: | http://d.repec.org/n?u=RePEc:usg:econwp:2015:17&r=ets |
| By: | Nicolas Langren\'e; Geoffrey Lee; Zili Zhu |
| Abstract: | This paper introduces the Inverse Gamma (IGa) stochastic volatility model with time-dependent parameters, defined by the volatility dynamics $dV_{t}=\kappa_{t}\left(\theta_{t}-V_{t}\right)dt+\lambda_{t}V_{t}dB_{t}$. This non-affine model is much more realistic than classical affine models like the Heston stochastic volatility model, even though both are as parsimonious (only four stochastic parameters). Indeed, it provides more realistic volatility distribution and volatility paths, which translate in practice into more robust calibration and better hedging accuracy, explaining its popularity among practitioners. In order to price vanilla options with IGa volatility, we propose a closed-form volatility-of-volatility expansion. Specifically, the price of a European put option with IGa volatility is approximated by a Black-Scholes price plus a weighted combination of Black-Scholes greeks, where the weights depend only on the four time-dependent parameters of the model. This closed-form pricing method allows for very fast pricing and calibration to market data. The overall quality of the approximation is very good, as shown by several calibration tests on real-world market data where expansion prices are compared favorably with Monte Carlo simulation results. This paper shows that the IGa model is as simple, more realistic, easier to implement and faster to calibrate than classical transform-based affine models. We therefore hope that the present work will foster further research on non-affine models like the Inverse Gamma stochastic volatility model, all the more so as this robust model is of great interest to the industry. |
| Date: | 2015–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1507.02847&r=ets |
| By: | JIN SEO CHO (Yonsei University); TAE-HWAN KIM (Yonsei University); YONGCHEOL SHIN (University of York) |
| Abstract: | Xiao (2009) develops a novel estimation technique for quantile cointegrated time series by extending Phillips and Hansen¡¯s (1990) semiparametric approach and Saikkonen¡¯s (1991) parametrically augmented approach. This paper extends Pesaran and Shin¡¯s (1998) autoregressive distributed-lag approach into quantile regression by jointly analysing short-run dynamics and long-run cointegrating relationships across a range of quantiles. We derive the asymptotic theory and provide a general package in which the model can be estimated and tested within and across quantiles. We further affirm our theoretical results by Monte Carlo simulations. The main utilities of this analysis are demonstrated through the empirical application to the dividend policy in the U.S. |
| Keywords: | QARDL, Quantile Regression, Long-run Cointegrating Relationship, Dividend Smoothing, Time-varying Rolling Estimation. |
| JEL: | C22 G35 |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:yon:wpaper:2015rwp-80&r=ets |