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on Econometric Time Series |
| By: | Mark Podolskij (Aarhus University, Department of Mathematics and CREATES); Christian Schmidt (Aarhus University, Department of Mathematics and CREATES); Mathias Vetter (Christian-Albrechts-Universität zu Kiel, Mathematisches Seminar) |
| Abstract: | In this paper we examine the asymptotic theory for U-statistics and V-statistics of discontinuous Itô semimartingales that are observed at high frequency. For different types of kernel functions we show laws of large numbers and associated stable central limit theorems. In most of the cases the limiting process will be conditionally centered Gaussian. The structure of the kernel function determines whether the jump and/or the continuous part of the semimartingale contribute to the limit. |
| Keywords: | central limit theorems,It^o semimartingales, stable convergence, U-statistics. |
| JEL: | C10 C13 C14 |
| Date: | 2015–11–20 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2015-53&r=ets |
| By: | Paulo Rocha; Frank Raischel; Jo\~ao P. Boto; Pedro G. Lind |
| Abstract: | We present a framework for describing the evolution of stochastic observables having a non-stationary distribution of values. The framework is applied to empirical volume-prices from assets traded at the New York stock exchange. Using Kullback-Leibler divergence we evaluate the best model out from four biparametric models standardly used in the context of financial data analysis. In our present data sets we conclude that the inverse $\Gamma$-distribution is a good model, particularly for the distribution tail of the largest volume-price fluctuations. Extracting the time-series of the corresponding parameter values we show that they evolve in time as stochastic variables themselves. For the particular case of the parameter controlling the volume-price distribution tail we are able to extract an Ornstein-Uhlenbeck equation which describes the fluctuations of the largest volume-prices observed in the data. Finally, we discuss how to bridge from the stochastic evolution of the distribution parameters to the stochastic evolution of the (non-stationary) observable and put our conclusions into perspective for other applications in geophysics and biology. |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1510.07280&r=ets |
| By: | Kapetanious, George (Bank of England); Price, Simon (Bank of England); Theodoridis, Konstantinos (Bank of England) |
| Abstract: | DSGE models are of interest because they offer structural interpretations, but are also increasingly used for forecasting. Estimation often proceeds by methods which involve building the likelihood by one-step ahead (h=1) prediction errors. However in principle this can be done using different horizons where h>1. Using the well-known model of Smets and Wouters (2007), for h=1 classical ML parameter estimates are similar to those originally reported. As h extends some estimated parameters change, but not to an economically significant degree. Forecast performance is often improved, in several cases significantly. |
| Keywords: | DSGE models; multi-step prediction errors; forecasting. |
| Date: | 2015–11–20 |
| URL: | http://d.repec.org/n?u=RePEc:boe:boeewp:0567&r=ets |
| By: | Giuseppe Cavaliere (Università di Bologna); Iliyan Georgiev (Universidade Nova de Lisboa); A.M. Robert Taylor (University of Essex) |
| Abstract: | We extend the available asymptotic theory for autoregressive sieve estimators to cover the case of stationary and invertible linear processes driven by independent identically distributed (i.i.d.) infinite variance (IV) innovations. We show that the ordinary least squares sieve estimates, together with estimates of the impulse responses derived from these, obtained from an autoregression whose order is an increasing function of the sample size, are consistent and exhibit asymptotic properties analogous to those which obtain for a finite-order autoregressive process driven by i.i.d. IV errors. As these limit distributions cannot be directly employed for inference because they either may not exist or, where they do, depend on unknown parameters, a second contribution of the paper is to investigate the usefulness of bootstrap methods in this setting. Focusing on three sieve bootstraps: the wild and permutation bootstraps, and a hybrid of the two, we show that, in contrast to the case of finite variance innovations, the wild bootstrap requires an infeasible correction to be consistent, whereas the other two bootstrap schemes are shown to be consistent (the hybrid for symmetrically distributed innovations) under general conditions. |
| Keywords: | Bootstrap, Sieve autoregression, Infinite variance, Time Series |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:bot:quadip:wpaper:129&r=ets |
| By: | Luiz Hotta; Carlos Trucíos; Esther Ruiz |
| Abstract: | Bootstrap procedures are useful in GARCH models to obtain forecast densities for returns and volatilities.In this paper, we analyze the effect of outliers on the finite sample properties of these densities when they are based on standard maximum likelihood and robust procedures. We show that when the former procedure is implemented, the bootstrap densities are badly affected by the presence of outliers. However,the robust estimator based on variance targeting with an adequate modification of the volatility filter has the best performance when compared with alternative robust procedures. The results are illustrated withboth simulated and real data. |
| Keywords: | BM estimator , Outliers , Smooth bootstrap , Variance targeting , Winsorized bootstrap |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws1523&r=ets |
| By: | Jensen, Mark J. (Federal Reserve Bank of Atlanta) |
| Abstract: | Empirical volatility studies have discovered nonstationary, long-memory dynamics in the volatility of the stock market and foreign exchange rates. This highly persistent, infinite variance—but still mean reverting—behavior is commonly found with nonparametric estimates of the fractional differencing parameter d, for financial volatility. In this paper, a fully parametric Bayesian estimator, robust to nonstationarity, is designed for the fractionally integrated, autoregressive, stochastic volatility (SV-FIAR) model. Joint estimates of the autoregressive and fractional differencing parameters of volatility are found via a Bayesian, Markov chain Monte Carlo (MCMC) sampler. Like Jensen (2004), this MCMC algorithm relies on the wavelet representation of the log-squared return series. Unlike the Fourier transform, where a time series must be a stationary process to have a spectral density function, wavelets can represent both stationary and nonstationary processes. As long as the wavelet has a sufficient number of vanishing moments, this paper's MCMC sampler will be robust to nonstationary volatility and capable of generating the posterior distribution of the autoregressive and long-memory parameters of the SV-FIAR model regardless of the value of d. Using simulated and empirical stock market return data, we find our Bayesian estimator producing reliable point estimates of the autoregressive and fractional differencing parameters with reasonable Bayesian confidence intervals for either stationary or nonstationary SV-FIAR models. |
| Keywords: | Bayes; infinite variance; long-memory; Markov chain Monte Carlo; mean-reverting; wavelets |
| JEL: | C11 C14 C22 |
| Date: | 2015–11–01 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedawp:2015-12&r=ets |
| By: | Gary Koop; Dimitris Korobilis |
| Abstract: | In this paper, we develop econometric methods for estimating large Bayesian timevarying parameter panel vector autoregressions (TVP-PVARs) and use these methods to forecast inflation for euro area countries. Large TVP-PVARs contain huge numbers of parameters which can lead to over-parameterization and computational concerns. To overcome these concerns, we use hierarchical priors which reduce the dimension of the parameter vector and allow for dynamic model averaging or selection over TVP-PVARs of different dimension and different priors. We use forgetting factor methods which greatly reduce the computational burden. Our empirical application shows substantial forecast improvements over plausible alternatives. |
| Keywords: | Panel VAR, inflation forecasting, Bayesian, time-varying parameter model |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:gla:glaewp:2015_25&r=ets |
| By: | Deniz Dilan Karaman Örsal (Leuphana University Lueneburg, Germany); Antonia Arsova (Leuphana University Lueneburg, Germany) |
| Abstract: | This paper proposes two new panel cointegrating rank tests which are robust to cross-sectional dependency. The dependence in the data generating process is modeled using unobserved common factors. The new tests are based on a metaanalytic approach, in which the p-values of the individual likelihood-ratio (LR) type test statistics computed from defactored data are combined to develop the panel statistics. A simulation study shows that the tests have reasonable size and power properties in finite samples. |
| Keywords: | Panel cointegration; p-value; common factors; rank test; crosssectional dependence |
| JEL: | C12 C15 C33 |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:lue:wpaper:349&r=ets |
| By: | Marcin Faldziñski (Nicolaus Copernicus University, Poland); Michal Bernard Pietrzak (Nicolaus Copernicus University, Poland) |
| Abstract: | The article seeks to investigate the issue of interdependence that during crisis periods in the capital markets is of particular importance due to the likelihood of causing a crisis in the real economy. The research objective of the article is to identify this interdependence in volatility. Therefore, first we propose our own modification of the DCC-GARCH model which is so designed as to test for interdependence in conditional variance. Then, the DCC-GARCH-In model was used to study interdependence in volatility of selected stock market indices. The results of the research confirmed the presence of interdependence among the selected markets.Creation-Date: 2015-11 |
| Keywords: | DCC-GARCH model, interdependence, conditional variance |
| JEL: | C32 |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:pes:wpaper:2015:no164&r=ets |
| By: | Naoto Kunitomo (Faculty of Economics, The University of Tokyo); Daisuke Kurisu (Graduate School of Economics, The University of Tokyo) |
| Abstract: | Several new statistical procedures for high frequency financial data analysis have been developed for estimating risk quantities and testing the presence of jump in the underlying continuous-time financial processes. Although the role of micro-market noise is important in high frequency financial data, there are some basic questions on the effects of presence of noise and jump in the underlying stochastic processes. When there can be jump and (micro-market) noise at the same time, it is not obvious whether the existing statistical methods are reliable or not for the applications in actual data analysis. We investigate the misspecification effects of jump and noise on some basic statistics and the testing procedures for jumps proposed by Ait-Sahalia and Jacod (2009, Annals of Statistics) as an illustration. We have found that their firrst test is asymptotically robust in the small-noise asymptotic sense against possible misspecification while their second test is quite sensitive to the presence of noise. |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2015cf996&r=ets |
| By: | Götz T.B.; Hecq A.W.; Smeekes S. (GSBE) |
| Abstract: | We analyze Granger causality testing in a mixed-frequency VAR, where the difference in sampling frequencies of the variables is large. Given a realistic sample size, the number of high-frequency observations per low-frequency period leads to parameter proliferation problems in case we attempt to estimate the model unrestrictedly. We propose several tests based on reduced rank restrictions, and implement bootstrap versions to account for the uncertainty when estimating factors and to improve the finite sample properties of these tests. We also consider a Bayesian VAR that we carefully extend to the presence of mixed frequencies. We compare these methods to an aggregated model, the max-test approach introduced by Ghysels et al. 2015a as well as to the unrestricted VAR using Monte Carlo simulations. The techniques are illustrated in an empirical application involving daily realized volatility and monthly business cycle fluctuations. |
| Keywords: | Bayesian Analysis: General; Hypothesis Testing: General; Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; |
| JEL: | C11 C12 C32 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2015036&r=ets |
| By: | Majid M. Al-Sadoon |
| Abstract: | The methodology of multivariate Granger non-causality testing at various horizons is extended to allow for inference on its directionality. This paper presents empirical manifestations of these subspaces and provides useful interpretations for them. It then proposes methods for estimating these subspaces and finding their dimensions utilizing simple vector autoregressions modelling that is easy to implement. The methodology is illustrated by an application to empirical monetary policy. |
| Keywords: | Granger causality, VAR model, rank testing, Okun's law, policy trade-offs. |
| JEL: | C12 C13 C15 C32 C53 E3 E4 E52 |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1495&r=ets |
| By: | Jungwoo kim (Yonsei University); Joocheol kim (Yonsei University) |
| Abstract: | I adopt a regime shift model to investigate a shift of distribution of each regime during a time series data. Unlike previous studies, I applied three types of distribution to use a regime shift model, i.e., normal, GEV and stable distribution, which allows me to consider a heavy tail regime in the model. From some theoretical basis and empirical results, I find that the regime shift model in stable distribution is best appropriate. I also find that tail index of the innovation and dependence measure move together, implying dependence among a consecutive data may lead extreme event and vice versa. |
| Keywords: | regime shift model, tail index, dependence measure, extreme event |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:yon:wpaper:2015rwp-86&r=ets |