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on Econometrics |
| By: | Qihua Wang; Tao Zhang; Wolfgang Karl Härdle; |
| Abstract: | An extended single-index model is considered when responses are missing at random. A three-step estimation procedure is developed to define an estimator for the single index parameter vector by a joint estimating equation. The proposed estimator is shown to be asymptotically normal. An iterative scheme for computing this estimator is proposed. This algorithm only involves one-dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Some simulation study is conducted to investigate the finite sample performances of the pro- posed estimators. |
| Keywords: | Missing data, Estimating equations, Single-index models, Asymptotic normality |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2014-003&r=ecm |
| By: | Patrick M. Kline |
| Abstract: | We derive the limiting distribution of the Oaxaca estimator of average treatment effects studied by Kline (2011). A consistent estimator of the asymptotic variance is proposed that makes use of standard regression routines. It is shown that ignoring uncertainty in group means will tend to lead to an overstatement of the asymptotic standard errors. Monte Carlo experiments examine the finite sample performance of competing approaches to inference. |
| JEL: | C01 J31 J7 |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:19784&r=ecm |
| By: | Lijie Gu; Li Wang; Wolfgang Karl Härdle; Lijian Yang |
| Abstract: | We consider a varying coefficient regression model for sparse functional data, with time varying response variable depending linearly on some time independent covariates with coefficients as functions of time dependent covariates. Based on spline smoothing, we propose data driven simultaneous confidence corridors for the coefficient functions with asymptotically correct confidence level. Such confidence corridors are useful benchmarks for statistical inference on the global shapes of coefficient functions under any hypotheses. Simulation experiments corroborate with the theoretical results. An example in CD4/HIV study is used to illustrate how inference is made with computable p-values on the effects of smoking, preinfection CD4 cell percentage and age on the CD4 cell percentage of HIV infected patients under treatment. |
| Keywords: | B spline, confidence corridor, Karhunen-Loève L^2 representation, knots, functional data, varying coefficient |
| JEL: | C14 C23 |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2014-002&r=ecm |
| By: | Shonosuke Sugasawa (Graduate School of Economics, The University of Tokyo); Tatsuya Kubokawa (Faculty of Economics, The University of Tokyo) |
| Abstract: | 　　 Consider the small area estimation when positive area-level data like income, revenue, harvests or production are available. Although a conventional method is the logtransformed Fay-Herriot model, the log-transformation is not necessarily appropriate. Another popular method is the Box-Cox transformation, but it has drawbacks that the maximum likelihood estimator (ML) of the transformation parameter is not consistent and that the transformed data are truncated. In this paper, we consider parametric transformed Fay-Herriot models, and clarify conditions on transformations under which the ML estimator of the transformation is consistent. It is shown that the dual power transformation satisfies the conditions. Based on asymptotic properties for estimators of parameters, we derive a second-order approximation of the prediction error of the empirical best linear unbiased predictors (EBLUP) and obtain a second-order unbiased estimator of the prediction error. Finally, performances of the proposed procedures are investigated through simulation and empirical studies. |
| Date: | 2013–12 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2013cf911&r=ecm |
| By: | Zhongxian Men (Department of Statistics and Actuarial Science, University of Waterloo, Canada); Tony S. Wirjanto (Department of Statistics and Actuarial Science, University of Waterloo, Canada); Adam W. Kolkiewicz (Department of Statistics and Actuarial Science, School of Accounting and Finance, University of Waterloo, Canada) |
| Abstract: | There is evidence to suggest that a single factor of duration running on single time scale is not adequate to capture the dynamics of the duration process of financial transaction data. This assertion is motivated by the observation that some existing one-factor stochastic duration models have had difficulty in successfully fitting the left tail of the marginal distribution of the observed durations. This empirical poor fit of the left tail of the duration distribution may be indicative of the possible existence of multiple stochastic duration factors running on different time scales. This paper proposes multiscale stochastic conditional duration (MSCD) models to describe the dynamics of financial transaction data. Novel algorithms of Markov Chain Monte Carlo (MCMC) are developed to fit the resulting MSCD models under three distributional assumptions about the innovation of the measurement equation. In addition, instead of subjecting the observation equation to a logarithmic transformation, we work on the MSCD model directly. Simulation studies suggest that our proposed models and corresponding estimation methodology work quite well. We also apply an auxiliary particle filter technique to construct one-step-ahead in-sample and out-of-sample duration forecasts based on the fitted models. Applications to two duration data sets of FIAT and IBM indicate the existence of at least two factors that determine the dynamics of the two stock transactions. |
| Keywords: | Stochastic conditional Duration; Markov Chain Monte Carlo; Multiscale; Auxiliary particle filter; Probability integral transform; Deviance information criterion. |
| Date: | 2013–12 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:63_13&r=ecm |
| By: | Kazumitsu Nawata; Michael McAleer (University of Canterbury) |
| Abstract: | Hausman (1978) developed a widely-used model specification test that has passed the test of time. The test is based on two estimators, one being consistent under the null hypothesis but inconsistent under the alternative, and the other being consistent under both the null and alternative hypotheses. In this paper, we show that the asymptotic variance of the difference of the two estimators can be a singular matrix. Moreover, in calculating the Hausman test there is a maximum number of parameters which is the number of different equations that are used to obtain the two estimators. Three illustrative examples are used, namely an exogeneity test for the linear regression model, a test for the Box-Cox transformation, and a test for sample selection bias. |
| Keywords: | Hausman test, specification test, number of parameters, instrumental variable (IV) model, Box-Cox model, Sample selection bias |
| JEL: | C2 C5 I18 |
| Date: | 2013–12–15 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:14/02&r=ecm |
| By: | Simon A. Broda; Raymond Kan (University of Toronto) |
| Abstract: | A large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables. If the denominator variable is positive, then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random variables. If in addition, the joint characteristic function of numerator and denominator is known, then standard Fourier inversion techniques can be used to reconstruct the distribution function from it. Most research in this field has been based on this correspondence, but which breaks down when both numerator and denominator are supported on the entire real line. The present manuscript derives inversion formulae and saddlepoint approximations that remain valid in this case, and reduce to known results when the denominator is almost surely positive. Applications include the IV estimator of a structural parameter in a just identified equation. |
| Date: | 2013–12–22 |
| URL: | http://d.repec.org/n?u=RePEc:ame:wpaper:1310&r=ecm |
| By: | Roberto Leon-Gonzalez (National Graduate Institute for Policy Studies); Fuyu Yang (University of East Anglia) |
| Abstract: | A stationary bilinear (SB) model can be used to describe processes with a time-varying degree of persistence that depends on past shocks. The SB model has been used to model highly persistent but stationary macroeconomic time series such as inflation. This study develops methods for Bayesian inference, model comparison, and forecasting in the SB model. Using U.K. inflation data, we find that the SB model outperforms the random walk and first order autoregressive AR(1) models, in terms of root mean squared forecast errors for the one-step-ahead out-of-sample forecast. In addition, the SB model is superior to these two models in terms of predictive likelihood for almost all of the forecast observations. |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:uea:aepppr:2012_55&r=ecm |
| By: | Arias, Jonas E.; Rubio-Ramírez, Juan F.; Waggoner, Daniel F. |
| Abstract: | Are optimism shocks an important source of business cycle fluctuations? Are deficit-financed tax cuts better than deficit-financed spending to increase output? These questions have been previously studied using SVARs identified with sign and zero restrictions and the answers have been positive and definite in both cases. While the identification of SVARs with sign and zero restrictions is theoretically attractive because it allows the researcher to remain agnostic with respect to the responses of the key variables of interest, we show that current implementation of these techniques does not respect the agnosticism of the theory. These algorithms impose additional sign restrictions on variables that are seemingly unrestricted that bias the results and produce misleading confidence intervals. We provide an alternative and efficient algorithm that does not introduce any additional sign restriction, hence preserving the agnosticism of the theory. Without the additional restrictions, it is hard to support the claim that either optimism shocks are an important source of business cycle fluctuations or deficit-financed tax cuts work best at improving output. Our algorithm is not only correct but also faster than current ones. |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpm:dynare:030&r=ecm |
| By: | Ting Ting Chen; Tetsuya Takaishi |
| Abstract: | We use the GARCH model with a fat-tailed error distribution described by a rational function and apply it for the stock price data on the Tokyo Stock Exchange. To determine the model parameters we perform the Bayesian inference to the model. The Bayesian inference is implemented by the Metropolis-Hastings algorithm with an adaptive multi-dimensional Student's t-proposal density. In order to compare the model with the GARCH model with the standard normal errors we calculate information criterions: AIC and DIC, and find that both criterions favor the GARCH model with a rational error distribution. We also calculate the accuracy of the volatility by using the realized volatility and find that a good accuracy is obtained for the GARCH model with a rational error distribution. Thus we conclude that the GARCH model with a rational error distribution is superior to the GARCH model with the normal errors and it can be used as an alternative GARCH model to those with other fat-tailed distributions. |
| Date: | 2013–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1312.7057&r=ecm |
| By: | Jiaqi Chen; Michael L. Tindall |
| Abstract: | This paper describes the structure of a rule-based econometric forecasting system designed to produce multi-equation econometric models. The paper describes the functioning of a working system which builds the econometric forecasting equation for each series submitted and produces forecasts of the series. The system employs information criteria and cross validation in the equation building process, and it uses Bayesian model averaging to combine forecasts of individual series. The system outperforms standard benchmarks for a variety of national economic datasets. |
| Keywords: | Econometrics |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:fip:feddop:2013_001&r=ecm |
| By: | Ngoc Mai Tran; Maria Osipenko; Wolfgang Karl Härdle; |
| Abstract: | Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal process- ing, mechanical ingeneering, psychometrics, and other fields under different names. It still bears the same mathematical idea: the decomposition of variation of a high dimensional object into uncorrelated factors or components. However, in many of the above applications, one is interested in capturing the tail variables of the data rather than variation around the mean. Such applications include weather related event curves, expected shortfalls, and speeding analysis among others. These are all high dimensional tail objects which one would like to study in a PCA fashion. The tail character though requires to do the dimension reduction in an asymmet- ric norm rather than the classical L2-type orthogonal projection. We develop an analogue of PCA in an asymmetric norm. These norms cover both quantiles and expectiles, another tail event measure. The difficulty is that there is no natural basis, no 'principal components', to the k-dimensional subspace found. We propose two definitions of principal components and provide algorithms based on iterative least squares. We prove upper bounds on their convergence times, and compare their performances in a simulation study. We apply the algorithms to a Chinese weather dataset with a view to weather derivative pricing. |
| Keywords: | principal components; asymmetric norm; dimension reduction; quan- tile; expectile |
| JEL: | C38 C61 C63 |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2014-001&r=ecm |
| By: | Jakub Nowotarski; Rafal Weron |
| Abstract: | We examine possible accuracy gains from forecast averaging in the context of interval forecasts of electricity spot prices. First, we test whether constructing empirical prediction intervals (PI) from combined electricity spot price forecasts leads to better forecasts than those obtained from individual methods. Next, we propose a new method for constructing PI, which utilizes the concept of quantile regression (QR) and a pool of point forecasts of individual (i.e. not combined) time series models. While the empirical PI from combined forecasts do not provide significant gains, the QR based PI are found to be more accurate than those of the best individual model - the smoothed nonparametric autoregressive model. |
| Keywords: | Prediction interval; Quantile regression; Forecasts combination; Electricity spot price |
| JEL: | C22 C24 C53 Q47 |
| Date: | 2013–12–31 |
| URL: | http://d.repec.org/n?u=RePEc:wuu:wpaper:hsc1312&r=ecm |
| By: | Emmanuel Bacry; Jean-Francois Muzy |
| Abstract: | We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix by a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the kernel matrix is the unknown) possesses a unique causal solution and consequently that the second-order properties fully characterize Hawkes processes. The numerical inversion of the system of integral equations allows us to propose a fast and efficient method to perform a non-parametric estimation of the Hawkes kernel matrix. We discuss the estimation error and provide some numerical examples. Applications to high frequency trading events in financial markets and to earthquakes occurrence dynamics are considered. |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1401.0903&r=ecm |
| By: | Dimitris, Korobilis |
| Abstract: | We use Bayesian factor regression models to construct a financial conditions index (FCI) for the U.S. Within this context we develop Bayesian model averaging methods that allow the data to select which variables should be included in the FCI or not. We also examine the importance of different sources of instability in the factors, such as stochastic volatility and structural breaks. Our results indicate that ignoring structural breaks in the loadings can be quite costly in terms of the forecasting performance of the FCI. Additionally, Bayesian model averaging can improve in specific cases the performance of the FCI, by means of discarding irrelevant financial variables during the estimation of the factor. |
| Keywords: | financial stress; stochastic search variable selection; early-warning system; forecasting |
| JEL: | C11 C22 C52 C53 C63 E17 G01 G17 |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:52724&r=ecm |
| By: | Joshua Angrist |
| Abstract: | Individual outcomes are highly correlated with group average outcomes, a fact often interpreted as a causal peer effect. Without covariates, however, outcome-on-outcome peer effects are vacuous, either unity or, if the average is defined as leave-out, determined by a generic intraclass correlation coefficient. When pre-determined peer characteristics are introduced as covariates in a model linking individual outcomes with group averages, the question of whether peer effects or social spillovers exist is econometrically identical to that of whether a 2SLS estimator using group dummies to instrument individual characteristics differs from OLS estimates of the effect of these characteristics. The interpretation of results from models that rely solely on chance variation in peer groups is therefore complicated by bias from weak instruments. With systematic variation in group composition, the weak IV issue falls away, but the resulting 2SLS estimates can be expected to exceed the corresponding OLS estimates as a result of measurement error and other reasons unrelated to social effects. Randomized and quasi-experimental research designs that manipulate peer characteristics in a manner unrelated to individual characteristics provide the strongest evidence on the nature of social spillovers. As an empirical matter, designs of this sort have uncovered little in the way of socially significant causal effects. |
| JEL: | C18 C31 C36 I21 I31 |
| Date: | 2013–12 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:19774&r=ecm |
| By: | Leonardo Bargigli (DISEI, Università degli Studi di Firenze) |
| Abstract: | Real markets can be naturally represented as networks, and they share with other social networks the fundamental property of sparsity, whereby agents are connected by l = O (n) relationships. The exponential networks model introduced by Park and Newman can be extended in order to deal with this property. When compared with alternative statistical models of a given real network, this extended model provides a better statistical justification for the observed network values. Consequently, it provides more reliable maximum entropy estimates of partially known networks than previously known ME techniques. |
| Keywords: | networks |
| JEL: | C49 C63 D85 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:frz:wpaper:wp2013_25.rdf&r=ecm |