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on Econometric Time Series |
| By: | Eric M. Aldrich (Department of Economics, University of California Santa Cruz); Indra Heckenbach (Department of Physics, University of California Santa Cruz); Gregory Laughlin (Department of Astronomy and Astrophysics, University of California Santa Cruz) |
| Abstract: | WThis paper builds a model of high-frequency equity returns in clock time by separately modeling the dynamics of trade-time returns and trade arrivals. Our main contributions are threefold. First, we characterize the distributional behavior of high-frequency asset returns both in clock time and trade time and show that when controlling for pre-scheduled market news events, trade-time returns are well characterized by a Gaussian distribution at very fine time scales. Second, we develop a structured and parsimonious model of clock-time returns by subordinating a trade-time Gaussian distribution with a trade arrival process that is associated with a modified Markov-Switching Multifractal Duration (MSMD) model of Chen et al. (2013). Our modification of the MSMD model provides a much better characterization of high-frequency inter-trade durations than the original model of Chen et al. (2013). Over-dispersion in this distribution of inter-trade durations leads to leptokurtosis and volatility clustering in clock-time returns, even when trade-time returns are Gaussian. Finally, we use our model to extrapolate the empirical relationship between trade rate and volatility in an effort to understand conditions of market failure. Our model finds that physical separation of financial markets maintains a natural ceiling on systemic volatility and promotes market stability. |
| Keywords: | High-frequency trading, US Equities, News arrival |
| JEL: | C22 C41 C58 G12 G14 G17 |
| Date: | 2014–08 |
| URL: | http://d.repec.org/n?u=RePEc:byu:byumcl:201405&r=ets |
| By: | Roberto Leon-Gonzalez (National Graduate Institute for Policy Studies (GRIPS) and The Rimini Centre for Economic Analysis (RCEA)) |
| Abstract: | This paper develops a novel and efficient algorithm for Bayesian inference in inverse Gamma Stochastic Volatility models. It is shown that by conditioning on auxiliary variables, it is possible to sample all the volatilities jointly directly from their posterior conditional density, using simple and easy to draw from distributions. Furthermore, this paper develops a generalized inverse Gamma process with more flexible tails in the distribution of volatilities, which still allows for simple and efficient calculations. Using several macroeconomic and financial datasets, it is shown that the inverse Gamma and Generalized inverse Gamma processes can greatly outperform the commonly used log normal volatility processes with student-t errors. |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:19_14&r=ets |
| By: | Aman Ullah (Department of Economics, University of California Riverside); Yong Bao (Purdue University); Yun Wang (University of International Business and Economics, China) |
| Abstract: | Econometricians have recently been interested in estimating and testing the mean reversion parameter (κ) in linear diffusion models. It has been documented that the maximum likelihood estimator (MLE) of κ tends to over estimate the true value. Its asymptotic distribution, on the other hand, depends on how the data are sampled (under expanding, infill, or mixed domain) as well as how we spell out the initial condition. This poses a tremendous challenge to practitioners in terms of estimation and inference. In this paper, we provide new and significant results regarding the exact distribution of the MLE of κ in the Ornstein-Uhlenbeck process under different scenarios: known or unknown drift term, fixed or random start-up value, and zero or positive κ. In particular, we employ numerical integration via analytical evaluation of a joint characteristic function. Our numerical calculations demonstrate the remarkably reliable performance of our exact approach. It is found that the true distribution of the MLE can be severely skewed in finite samples and that the asymptotic distributions in general may provide misleading results. Our exact approach indicates clearly the non-mean-reverting behavior of the real federal fund rate. |
| Keywords: | Distribution, Mean Reversion Estimator, Ornstein-Uhlenbeck Process. |
| JEL: | C22 C46 C58 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:ucr:wpaper:201413&r=ets |
| By: | Giannone, Domenico (LUISS and Centre for Economic Policy Research); Monti , Francesca (Bank of England); Reichlin , Lucrezia (London Business School and Centre for Economic Policy Research) |
| Abstract: | This paper shows how and when it is possible to obtain a mapping from a quarterly dynamic stochastic general equilibrium (DSGE) model to a monthly specification that maintains the same economic restrictions and has real coefficients. We use this technique to derive the monthly counterpart of the well-known DSGE model by Galí, Smets and Wouters (GSW) for the US economy. We then augment it with auxiliary macro indicators which, because of their timeliness, can be used to obtain a nowcast of the structural model. We show empirical results for the quarterly growth rate of GDP, the monthly unemployment rate and GSW’s welfare-relevant output gap. Results show that the augmented monthly model does best for nowcasting. |
| Keywords: | Forecasting; temporal aggregation; mixed frequency data; large data sets |
| JEL: | C33 C53 E30 |
| Date: | 2014–09–12 |
| URL: | http://d.repec.org/n?u=RePEc:boe:boeewp:0509&r=ets |
| By: | Leschinski, Christian; Sibbertsen, Philipp |
| Abstract: | We propose an automatic model order selection procedure for k-factor GARMA processes. The procedure is based on sequential tests of the maximum of the periodogram and semiparametric estimators of the model parameters. As a byproduct, we introduce a generalized version of Walker's large sample g-test that allows to test for persistent periodicity in stationary ARMA processes. Our simulation studies show that the procedure performs well in identifying the correct model order under various circumstances. An application to Californian electricity load data illustrates its value in empirical analyses and allows new insights into the periodicity of this process that has been subject of several forecasting exercises. |
| Keywords: | seasonal long memory, k-factor GARMA, model selection, electricity loads |
| JEL: | C22 C52 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:han:dpaper:dp-535&r=ets |
| By: | Arnaud Dufays (École Nationale de la Statistique et de l'Administration Économique, CREST) |
| Abstract: | Sequential Monte Carlo (SMC) methods are widely used for filtering purposes of non-linear economic or financial models. Nevertheless the SMC scope encompasses wider applications such as estimating static model parameters so much that it is becoming a serious alternative to Markov- Chain Monte-Carlo (MCMC) methods. Not only SMC algorithms draw posterior distributions of static or dynamic parameters but additionally provide an estimate of the normalizing constant. The tempered and time (TNT) algorithm, developed in the paper, combines (off-line) tempered SMC inference with on-line SMC inference for estimating many slightly different distributions. The method encompasses the Iterated Batch Importance Sampling (IBIS) algorithm and more generally the Resample Move (RM) algorithm. Besides the number of particles, the TNT algorithm self-adjusts its calibrated parameters and relies on a new MCMC kernel that allows for particle interactions. The algorithm is well suited for efficiently back-testing models. We conclude by comparing in-sample and out-of-sample performances of complex volatility models. |
| Keywords: | Bayesian inference, Sequential Monte Carlo, Annealed Importance sampling, Differential Evolution, Volatility models, Multifractal model, Markov-switching model |
| JEL: | C11 C15 C22 C58 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:nbb:reswpp:201409-263&r=ets |
| By: | Badi Baltagi (Center for Policy Research, Maxwell School, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244); Chihwa Kao (Center for Policy Research, Syracuse University); Long Liu (University of Texas at San Antonio) |
| Abstract: | This paper studies test of hypotheses for the slope parameter in a linear time trend panel data model with serially correlated error component disturbances. We propose a test statistic that uses a bias corrected estimator of the serial correlation parameter. The proposed test statistic which is based on the corresponding fixed effects feasible generalized least squares (FE-FGLS) estimator of the slope parameter has the standard normal limiting distribution which is valid whether the remainder error is I(0) or I(1). This performs well in Monte Carlo experiments and is recommended. |
| Keywords: | Panel Data, Generalized Least Squares, Time Trend Model, Fixed Effects, First Difference, and Nonstationarity |
| JEL: | C23 C33 |
| Date: | 2014–07 |
| URL: | http://d.repec.org/n?u=RePEc:max:cprwps:170&r=ets |
| By: | Atsushi Inoue; Lu Jin; Barbara Rossi |
| Abstract: | While forecasting is a common practice in academia, government and business alike, practitioners are often left wondering how to choose the sample for estimating forecasting models. When we forecast in ation in 2014, for example, should we use the last 30 years of data or the last 10 years of data? There is strong evidence of structural changes in economic time series, and the forecasting performance is often quite sensitive to the choice of such window size". In this paper, we develop a novel method for selecting the estimation window size for forecasting. Specically, we propose to choose the optimal window size that minimizes the forecaster's quadratic loss function, and we prove the asymptotic validity of our approach. Our Monte Carlo experiments show that our method performs quite well under various types of structural changes. When applied to forecasting US real output growth and in ation, the proposed method tends to improve upon conventional methods. |
| Keywords: | Macroeconomic forecasting; parameter instability; nonparametric estimation; band-width selection. |
| Date: | 2014–06 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1435&r=ets |