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on Econometrics |
| By: | Gabriele Fiorentini (Università di Firenze); Enrique Sentana (CEMFI, Centro de Estudios Monetarios y Financieros) |
| Abstract: | We derive simple algebraic expressions for score tests of serial correlation in the levels and squares of common and idiosyncratic factors in static factor models with (semi) parametrically specified elliptical distributions even though one must generally compute the likelihood by simulation. We also robustify our Gaussian tests against non-normality. The orthogonality conditions resemble the orthogonality conditions of models with observed factors but the weighting matrices reflect their unobservability. Our Monte Carlo exercises assess the finite sample reliability and power of our proposed tests, and compare them to other existing procedures. Finally, we apply our methods to monthly US stock returns. |
| Keywords: | ARCH, Financial returns, Kalman filter, LM tests, Non-Gaussian state space models, Predictability. |
| JEL: | C32 C12 C13 C14 C38 C46 C58 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:cmf:wpaper:wp2012_1211&r=ecm |
| By: | David Pacini |
| Abstract: | This paper investigates the identification and estimation of the least square linear predictor for the conditional expectation of an outcome variable Y given covariates (X;Z0) from data consisting of two independent random samples; the first sample contains replications of the variables (Y;Z0) but not X, while the second sample contains replications of (X;Z0) but not Y . The contribution is to characterize the identified set of the least square linear predictor when no assumption on the joint distribution of (Y;X;Z0), except for the existence of second order moments, is imposed. We show that the identified set is not a singleton, so the least square linear predictor of interest is set identified. The characterization is used to construct a sample analog estimator of the identified set. The asymptotic properties of the estimator are established and its implementation is illustrated via Monte Carlo exercises. |
| Keywords: | Network Identification; Least Square Linear Prediction; Two samples |
| JEL: | C21 C26 |
| Date: | 2012–11 |
| URL: | http://d.repec.org/n?u=RePEc:bri:uobdis:12/631&r=ecm |
| By: | Halkos, George; Kevork, Ilias |
| Abstract: | This paper considers the classical newsvendor model when, (a) demand is autocorrelated, (b) the parameters of the marginal distribution of demand are unknown, and (c) historical data for demand are available for a sample of successive periods. An estimator for the optimal order quantity is developed by replacing in the theoretical formula which gives this quantity the stationary mean and the stationary variance with their corresponding maximum likelihood estimators. The statistical properties of this estimator are explored and general expressions for prediction intervals for the optimal order quantity are derived in two cases: (a) when the sample consists of two observations, and (b) when the sample is considered as sufficiently large. Regarding the asymptotic prediction intervals, specifications of the general expression are obtained for the time-series models AR(1), MA(1), and ARMA(1,1). These intervals are estimated in finite samples using in their theoretical expressions, the sample mean, the sample variance, and estimates of the theoretical autocorrelation coefficients at lag one and lag two. To assess the impact of this estimation procedure on the optimal performance of the newsvendor model, four accuracy implication metrics are considered which are related to: (a) the mean square error of the estimator, (b) the accuracy and the validity of prediction intervals, and (c) the actual probability of running out of stock during the period when the optimal order quantity is estimated. For samples with more than two observations, these metrics are evaluated through simulations, and their values are presented to appropriately constructed tables. The general conclusion is that the accuracy and the validity of the estimation procedure for the optimal order quantity depends upon the critical fractile, the sample size, the autocorrelation level, and the convergence rate of the theoretical autocorrelation function to zero. |
| Keywords: | Newsvendor model; accuracy implication metrics; time-series models; prediction intervals; Monte-Carlo simulations |
| JEL: | C13 M11 C53 C22 M21 |
| Date: | 2013–02–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:44189&r=ecm |
| By: | Chau, Tak Wai |
| Abstract: | In this simulation study, I compare the efficiency and finite sample bias of parameter estimators for popular income dynamic models using various forms of autocovariances. The dynamic models have a random walk or a heterogeneous growth permanent component, a persistent autoregressive component and a white noise transitory component. I compare the estimators using autocovariances in level, first differences (FD), and autocovariances between level and future first differences (LD), where the last one is new in the literature of income dynamics. To maintain the same information used as in using level covariances, I also augment the FD and LD covariances with level variances in the estimation. The results show that using level covariances can give rise to larger finite sample biases and larger standard errors than using covariances in FD and LD augmented by level variance. Without augmenting the level variances, LD provides more efficient estimators than FD in estimating the non-permanent components. I also show that LD provides a convenient test between random walk and heterogeneous growth models with good power. |
| Keywords: | covariance structure; income dynamics; random walk; heterogeneous growth profi le; finite sample bias; efficiency |
| JEL: | C51 J31 C33 |
| Date: | 2013–01–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:44106&r=ecm |
| By: | Robert Kollmann |
| Keywords: | DSGE Models; Kalman Filter; smoothing |
| JEL: | E37 C32 C68 |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/139176&r=ecm |
| By: | Marcello Galeotti (Dipartimento di Statistica, Informatica e Applicazioni, Universita' degli Studi di Firenze) |
| Abstract: | We prove the convergence of a deterministic algorithm to compute the distribution function of the sum of d >1 dependent random variables, with given joint distribution, via the approximation of the probability measure of a d-dimensional symplex by overlapping hypercubes. |
| Keywords: | algorithm convergence, dependent random variables, measure theory |
| JEL: | C6 |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:flo:wpaper:2013-01&r=ecm |
| By: | Senay Sokullu |
| Abstract: | This paper considers an empirical semiparametric model for two-sided markets. Contrary to existing empirical literature on two-sided markets, we do not rely on linear network effects. Instead, network effects and probability distribution functions of net benefits of two sides are specified nonparametrically. The demand functions and the network effect functions of readers and advertisers are estimated by nonparametric IV estimation using a data set from German magazine industry. The ill-posed inverse problem faced during the estimation is solved by Tikhonov Regularization. We show that semiparametric specification is supported by the data and the network effects on readers' side are neither linear nor monotonic. With a numerical illustration we demonstrate that the mark-up of the magazine on readers' side is 27% higher with the nonlinearly specified network effects than in the case with linear network effects. |
| Keywords: | Two-sided markets, Network externality, Nonparametric IV, Ill-posed inverse problems, Tikhonov Regularization |
| JEL: | C14 C30 L14 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:bri:uobdis:12/628&r=ecm |
| By: | Wolfgang Karl Härdle; Elena Silyakova; ; |
| Abstract: | Equity basket correlation is an important risk factor. It characterizes the strength of linear dependence between assets and thus measures the degree of portfolio diversification. It can be estimated both under the physical measure from return series, and under the risk neutral measure from option prices. The difference between the two estimates motivates a so called "dispersion strategy". We study the performance of this strategy on the German market over the recent 2 years and propose several hedging schemes based on implied correlation (IC) forecasts. Modeling IC is a challenging task both in terms of computational burden and estimation error. First the number of correlation coefficients to be estimated would grow with the size of the basket. Second, since the IC is implied from option prices it is not constant over maturities and strikes. Finally, the IC changes over time. The dimensionality of the problem is reduced by an assumption that the correlation between all pairs of equities is constant (equicorrelation). The IC surface (ICS) is then approximated from implied volatilities of stocks and implied volatility of the basket. To analyze this structure and the dynamics of the ICS we employ a dynamic semiparametric factor model (DSFM). |
| Keywords: | correlation risk, dimension reduction, dispersion strategy, dynamic factor models, implied correlation |
| JEL: | C14 C32 G12 G13 G15 G17 |
| Date: | 2012–11 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2012-066&r=ecm |
| By: | Massimiliano Marcellino (European University Institute and Bocconi University); Mario Porqueddu (Bank of Italy); Fabrizio Venditti (Bank of Italy) |
| Abstract: | In this paper we develop a mixed frequency dynamic factor model featuring stochastic shifts in the volatility of both the latent common factor and the idiosyncratic components. We take a Bayesian perspective and derive a Gibbs sampler to obtain the posterior density of the model parameters. This new tool is then used to investigate business cycle dynamics and to forecast GDP growth at short-term horizons in the euro area. We discuss three sets of empirical results. First, we use the model to evaluate the impact of macroeconomic releases on point and density forecast accuracy and on the width of forecast intervals. Second, we show how our setup allows us to make a probabilistic assessment of the contribution of releases to forecast revisions. Third, we design a pseudo out-of-sample forecasting exercise and examine point and density forecast accuracy. In line with findings in literature on Bayesian Vector Autoregressions (BVAR), we find that stochastic volatility contributes to an improvement in density forecast accuracy. |
| Keywords: | forecasting, business cycle, mixed-frequency data, nonlinear models, nowcasting |
| JEL: | E32 C22 E27 |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:bdi:wptemi:td_896_13&r=ecm |