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on Econometrics |
| 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=ecm |
| By: | Govert Bijwaard (Netherlands Interdisciplinary Demographic Institute (NIDI)); Geert Ridder (University of Southern California); Tiemen Woutersen (Johns Hopkins University) |
| Abstract: | Ridder and Woutersen (2003) have shown that under a weak condition on the baseline hazard, there exist root-N consistent estimators of the parameters in a semiparametric Mixed Proportional Hazard model with a parametric baseline hazard and unspecified distribution of the unobserved heterogeneity. We extend the Linear Rank Estimator (LRE) of Tsiatis (1990) and Robins and Tsiatis (1991) to this class of models. The optimal LRE is a two-step estimator. We propose a simple one-step estimator that is close to optimal if there is no unobserved heterogeneity. The efficiency gain associated with the optimal LRE increases with the degree of unobserved heterogeneity. |
| Keywords: | mixed proportional hazard, linear rank estimation, counting process. |
| JEL: | C41 C14 |
| Date: | 2012–11 |
| URL: | http://d.repec.org/n?u=RePEc:nor:wpaper:2012035&r=ecm |
| 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=ecm |
| By: | Jonathan James |
| Abstract: | The mixed logit is a framework for incorporating unobserved heterogeneity in discrete choice models in a general way. These models are difficult to estimate because they result in a complicated incomplete data likelihood. This paper proposes a new approach for estimating mixed logit models. The estimator is easily implemented as iteratively re-weighted least squares: the well known solution for complete data likelihood logits. The main benefit of this approach is that it requires drastically fewer evaluations of the simulated likelihood function, making it significantly faster than conventional methods that rely on numerically approximating the gradient. The method is rooted in a generalized expectation and maximization (GEM) algorithm, so it is asymptotically consistent, efficient, and globally convergent. |
| Keywords: | Econometrics ; Econometric models |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedcwp:1219&r=ecm |
| By: | Denis Chetverikov |
| Abstract: | Monotonicity is a key qualitative prediction of a wide array of economic models derived via robust comparative statics. It is therefore important to design effective and practical econometric methods for testing this prediction in empirical analysis. This paper develops a general nonparametric framework for testing monotonicity of a regression function. Using this framework, a broad class of new tests is introduced, which gives an empirical researcher a lot of flexibility to incorporate ex ante information she might have. The paper also develops new methods for simulating critical values, which are based on the combination of a bootstrap procedure and new selection algorithms. These methods yield tests that have correct asymptotic size and are asymptotically nonconservative. It is also shown how to obtain an adaptive rate optimal test that has the best attainable rate of uniform consistency against models whose regression function has Lipschitz-continuous first-order derivatives and that automatically adapts to the unknown smoothness of the regression function. Simulations show that the power of the new tests in many cases significantly exceeds that of some prior tests, e.g. that of Ghosal, Sen, and Van der Vaart (2000). An application of the developed procedures to the dataset of Ellison and Ellison (2011) shows that there is some evidence of strategic entry deterrence in pharmaceutical industry where incumbents may use strategic investment to prevent generic entries when their patents expire. |
| Date: | 2012–11 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:35/12&r=ecm |
| By: | Denis Chetverikov |
| Abstract: | In this paper, the author constructs a new test of conditional moment inequalities based on studentised kernel estimates of moment functions. The test automatically adapts to the unknown smoothness of the moment functions, has uniformly correct asymptotic size, and is rate optimal against certain classes of alternatives. Some existing tests have nontrivial n-½- local alternatives of the certain type whereas my method only allows ( n / log n )-½ - local alternatives of this type. There exist, however, large classes of sequences of well-bahaved alternatives against which the test developed in this paper is consistent and those tests are not. |
| Keywords: | Conditional moment inequalities, minimax rate optimality |
| Date: | 2012–11 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:36/12&r=ecm |
| 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=ecm |
| 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=ecm |
| By: | J. L. van Velsen |
| Abstract: | A method is developed to estimate the parameters of a Levy copula of a discretely observed bivariate compound Poisson process without knowledge of common shocks. The method is tested in a small sample simulation study. Also, the method is applied to a real data set and a goodness of fit test is developed. With the methodology of this work, the Levy copula becomes a realistic tool of the advanced measurement approach of operational risk. |
| Date: | 2012–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1212.0092&r=ecm |
| 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=ecm |
| By: | Hern\'an Larralde |
| Abstract: | The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased" choice corresponds to the distribution of maximum entropy. The calculation of the maximum entropy distribution requires the solution of rather complicated nonlinear coupled integral equations, exact solutions to which are obtained for the case of Gaussian marginals; otherwise, the solution can be expressed as a perturbation around the product of the marginals if the marginal moments exist. |
| Date: | 2012–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1212.0440&r=ecm |
| By: | Matthew T. Holt (University of Alabama, Department of Economics, Finance & Legal Studies); Timo Teräsvirta (Aarhus University, Department of Economics and Management and CREATES) |
| Abstract: | This paper examines trends in annual temperature data for the northern and southern hemisphere (1850-2010) by using variants of the shifting-mean autoregressive (SM-AR) model of González and Teräsvirta (2008). Univariate models are first fitted to each series by using the so called QuickShift methodology. Full information maximum likelihood (FIML) estimates of a bivariate system of temperature equations are then obtained. The system is then used to perform formal tests of co-system in the hemispheric series. The results show there is evidence of co-shifting in the temperature data, most notably since the early 1980s. |
| Keywords: | Co-breaking, Co-shifting, Hemispheric surface temperatures, Vector nonlinear model, Structural change, Shifting-mean vector autoregression |
| JEL: | C22 C32 C52 C53 Q54 |
| Date: | 2012–11–21 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-54&r=ecm |
| 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=ecm |
| 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=ecm |
| 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=ecm |
| By: | Andrade, P.; Ghysels, E.; Idier, J. |
| Abstract: | We introduce a new measure called Inflation-at-Risk (I@R) associated with (left and right) tail inflation risk. We estimate I@R using survey-based density forecasts. We show that it contains information not covered by usual inflation risk indicators which focus on inflation uncertainty and do not distinguish between the risks of low or high future inflation outcomes. Not only the extent but also the asymmetry of inflation risks evolve over time. Moreover, changes in this asymmetry have an impact on future inflation realizations as well as on the current interest rate central banks target. |
| Keywords: | inflation expectations, risk, uncertainty, survey data, inflation dynamics, monetary policy. |
| JEL: | E31 E37 E43 E52 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:bfr:banfra:407&r=ecm |