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on Econometric Time Series |
| By: | Daniel J. Nordman (Department of Statistics, Iowa State University); Helle Bunzel (Department of Economics, Iowa State University & CREATES); Soumendra N. Lahiri (Department of Statistics, Texas A&M University) |
| Abstract: | Standard blockwise empirical likelihood (BEL) for stationary, weakly dependent time series requires specifying a fixed block length as a tuning parameter for setting confidence regions. This aspect can be difficult and impacts coverage accuracy. As an alternative, this paper proposes a new version of BEL based on a simple, though non-standard, data-blocking rule which uses a data block of every possible length. Consequently, the method involves no block selection and is also anticipated to exhibit better coverage performance. Its non-standard blocking scheme, however, induces non-standard asymptotics and requires a significantly different development compared to standard BEL. We establish the large-sample distribution of log-ratio statistics from the new BEL method for calibrating confidence regions for mean or smooth function parameters of time series. This limit law is not the usual chi-square one, but is distribution-free and can be reproduced through straightforward simulations. Numerical studies indicate that the proposed method generally exhibits better coverage accuracy than standard BEL. |
| Keywords: | Brownian motion, Confidence Regions, Stationarity, Weak Dependence |
| JEL: | C22 |
| Date: | 2012–12–03 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-55&r=ets |
| By: | Moawia Alghalith |
| Abstract: | We present a new simple method of estimating stochastic volatility and its volatility. This method is applicable to both cross-sectional and time-series data. Moreover, this method does not require volatility data series. |
| Date: | 2012–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1212.0380&r=ets |
| By: | Anton Skrobotov (Gaidar Institute for Economic Policy) |
| Abstract: | In this paper we extend the stationarity test proposed by Kurozumi and Tanaka (2010) for reducing size distortion with one structural break. We find the bias up to the order of 1/T for four types of models containing structural breaks. The simulations on finite samples show a reduction of size distortions in comparison with other tests, thus receiving higher power. |
| Keywords: | Stationarity tests, KPSS test, bias correction, size distortion, structural break. |
| JEL: | C12 C22 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:gai:wpaper:0043&r=ets |
| By: | P. O\'swi\k{e}cimka; S. Dro\.zd\.z; J. Kwapie\'n; A. Z. G\'orski |
| Abstract: | Different variants of MFDFA technique are applied in order to investigate various (artificial and real-world) time series. Our analysis shows that the calculated singularity spectra are very sensitive to the order of the detrending polynomial used within the MFDFA method. The relation between the width of the multifractal spectrum (as well as the Hurst exponent) and the order of the polynomial used in calculation is evident. Furthermore, type of this relation itself depends on the kind of analyzed signal. Therefore, such an analysis can give us some extra information about the correlative structure of the time series being studied. |
| Date: | 2012–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1212.0354&r=ets |
| By: | Roxana Halbleib (Department of Economics, University of Konstanz, Germany); Valeri Voev (School of Economics and Management, Aarhus University, Denmark) |
| Abstract: | In this paper we introduce a new method of forecasting covariance matrices of large dimensions by exploiting the theoretical and empirical potential of using mixed-frequency sampled data. The idea is to use high-frequency (intraday) data to model and forecast daily realized volatilities combined with low frequency (daily) data as input to the correlation model. The main theoretical contribution of the paper is to derive statistical and economic conditions, which ensure that a mixed-frequency forecast has a smaller mean squared forecast error than a similar pure low-frequency or pure high-frequency specification. The conditions are very general and do not rely on distributional assumptions of the forecasting errors or on a particular model specification. Moreover, we provide empirical evidence that, besides overcoming the computational burden of pure high-frequency specifications, the mixed-frequency forecasts are particularly useful in turbulent financial periods, such as the previous financial crisis and always outperforms the pure low-frequency specifications. |
| Keywords: | Multivariate volatility, Volatility forecasting, High-frequency data, Realized variance, Realized covariance |
| JEL: | C32 C53 |
| Date: | 2012–10–12 |
| URL: | http://d.repec.org/n?u=RePEc:knz:dpteco:1230&r=ets |
| By: | Giorgio Calzolari (Dipartimento di Statistica "G. Parenti", Università di Firenze, Italy); Roxana Halbleib (Department of Economics, University of Konstanz, Germany); Alessandro Parrini (Vrije Universiteit Amsterdam, The Netherlands) |
| Abstract: | It is a well-known fact that financial returns exhibit conditional heteroscedasticity and fat tails. While the GARCH-type models are very popular in depicting the conditional heteroscedasticity, the α-stable distribution is a natural candidate for the conditional distribution of financial returns. The α-stable distribution is a generalization of the normal distribution and is described by four parameters, two of which deal with tail-thickness and asymmetry. However, practical implementation of α-stable distribution in finance applications has been limited by its estimation difficulties. In this paper, we propose an indirect approach of estimating GARCH models with α-stable innovations by using as auxiliary models GARCH-type models with Student's t distributed innovations. We provide comprehensive empirical evidence on the performance of the method within a series of Monte Carlo simulation studies and an empirical application to financial returns. |
| Keywords: | Indirect Inference, α-stable Distribution, GARCH Models, Student's t Distribution |
| Date: | 2012–11–23 |
| URL: | http://d.repec.org/n?u=RePEc:knz:dpteco:1231&r=ets |
| By: | Audrino, Francesco; Knaus, Simon |
| Abstract: | Realized volatility computed from high-frequency data is an important measure for many applications in finance. However, its dynamics are not well understood to date. Recent notable advances that perform well include the heterogeneous autoregressive (HAR) model which is economically interpretable and but still easy to estimate. It also features good out-of-sample performance and has been extremely well received by the research community. We present a data driven approach based on the absolute shrinkage and selection operator (lasso) which should identify the aforementioned model. We prove that the lasso indeed recovers the HAR model asymptotically if it is the true model, and we present Monte Carlo evidence in finite sample. The HAR model is not recovered by the lasso on real data. This, together with an empirical out-of-sample analysis that shows equal performance of the HAR model and the lasso approach, leads to the conclusion that the HAR model may not be the true model but it captures a linear footprint of the true volatility dynamics. |
| Keywords: | Realized Volatility, Heterogeneous Autoregressive Model, Lasso, Model Selection |
| JEL: | C58 C63 C49 |
| Date: | 2012–11 |
| URL: | http://d.repec.org/n?u=RePEc:usg:econwp:2012:24&r=ets |
| By: | Linda Ponta; Enrico Scalas; Marco Raberto; Silvano Cincotti |
| Abstract: | We study tick-by-tick financial returns belonging to the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We find that non-stationarities detected in other markets in the past are still there. Moreover, scaling properties reported in the previous literature for other high-frequency financial data are approximately valid as well. Finally, we propose a simple method for describing non-stationary returns, based on a non-homogeneous normal compound Poisson process and we test this model against the empirical findings. It turns out that the model can reproduce several stylized facts of high-frequency financial time series. |
| Date: | 2012–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1212.0479&r=ets |
| By: | Kociecki, Andrzej |
| Abstract: | We propose the unified approach to construct the non–informative prior for time–series econometric models that are invariant under some group of transformations. We show that this invariance property characterizes some of the most popular models hence the applicability of the proposed framework is quite general. The suggested prior enjoys many desirable properties both from the Bayesian and non–Bayesian perspective. We provide detailed derivations of our prior in many standard time–series models including, AutoRegressions (AR), Vector AutoRegressions (VAR), Structural VAR and Error Correction Models (ECM). |
| Keywords: | Bayesian; Model invariance; Groups; Free group action; Orbit; Right Haar measure; Orbital decomposition; Maximal invariant; Cross section; Intersubjective prior; Vector AutoRegression (VAR); Structural VAR; Error Correction Model (ECM) |
| JEL: | C10 C32 C11 |
| Date: | 2012–11–23 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:42804&r=ets |