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on Econometrics |
| By: | Yukai Yang (Uppsala University); Luc Bauwens (Université catholique de Louvain) |
| Abstract: | We develop novel multivariate state-space models wherein the latent states evolve on the Stiefel manifold and follow a conditional matrix Langevin distribution. The latent states correspond to time-varying reduced rank parameter matrices, like the loadings in dynamic factor models and the parameters of cointegrating relations in vector error-correction models. The corresponding nonlinear filtering algorithms are developed and evaluated by means of simulation experiments. |
| Keywords: | State-space models, Stiefel manifold, matrix Langevin distribution, filtering, smoothing, Laplace method, dynamic factor model, cointegration |
| JEL: | C32 C51 |
| Date: | 2411 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2018-30&r=ecm |
| By: | Nadja Klein; Thomas Kneib; Giampiero Marra; Rosalba Radice; Slawa Rokicki; Mark E. McGovern |
| Abstract: | Bivariate copula regression allows for the flexible combination of two arbitrary, continuous marginal distributions with regression effects being placed on potentially all parameters of the resulting bivariate joint response distribution. Motivated by the risk factors for adverse birth outcomes, many of which are dichotomous, we consider mixed binary-continuous responses that extend the bivariate continuous framework to the situation where one response variable is discrete (more precisely binary) while the other response remains continuous. Utilizing the latent continuous representation of binary regression models, we implement a penalized likelihood based approach for the resulting class of copula regression models and employ it in the context of modelling gestational age and the presence/absence of low birth weight. The analysis demonstrates the advantage of the flexible specification of regression impacts including nonlinear effects of continuous covariates and spatial effects. Our results imply that racial and spatial inequalities in the risk factors for infant mortality are even greater than previously suggested. |
| Keywords: | Adverse Birth Outcomes, Copula, Latent Variable, Mixed Discrete-continuous Distributions, Penalised Maximum Likelihood, Penalised Splines |
| JEL: | I14 C30 I10 |
| Date: | 2018–10 |
| URL: | http://d.repec.org/n?u=RePEc:qub:charms:1806&r=ecm |
| By: | Vladim\'ir Hol\'y; Petra Tomanov\'a |
| Abstract: | When stock prices are observed at high frequencies, more information can be utilized in estimation of parameters of the price process. However, high-frequency data are contaminated by the market microstructure noise which causes significant bias in parameter estimation when not taken into account. We propose an estimator of the Ornstein-Uhlenbeck process based on the maximum likelihood which is robust to the noise and utilizes irregularly spaced data. We also show that the Ornstein-Uhlenbeck process contaminated by the independent Gaussian white noise and observed at discrete equidistant times follows an ARMA(1,1) process. To illustrate benefits of the proposed noise-robust approach, we analyze an intraday pairs trading strategy based on the mean-variance optimization. In an empirical study of 7 Big Oil companies, we show that the use of the proposed estimator of the Ornstein-Uhlenbeck process leads to an increase in profitability of the pairs trading strategy. |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1811.09312&r=ecm |
| By: | Matthew Norton; Valentyn Khokhlov; Stan Uryasev |
| Abstract: | Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR), also called the superquantile and quantile, are frequently used to characterize the tails of probability distribution's and are popular measures of risk. Buffered Probability of Exceedance (bPOE) is a recently introduced characterization of the tail which is the inverse of CVaR, much like the CDF is the inverse of the quantile. These quantities can prove very useful as the basis for a variety of risk-averse parametric engineering approaches. Their use, however, is often made difficult by the lack of well-known closed-form equations for calculating these quantities for commonly used probability distribution's. In this paper, we derive formulas for the superquantile and bPOE for a variety of common univariate probability distribution's. Besides providing a useful collection within a single reference, we use these formulas to incorporate the superquantile and bPOE into parametric procedures. In particular, we consider two: portfolio optimization and density estimation. First, when portfolio returns are assumed to follow particular distribution families, we show that finding the optimal portfolio via minimization of bPOE has advantages over superquantile minimization. We show that, given a fixed threshold, a single portfolio is the minimal bPOE portfolio for an entire class of distribution's simultaneously. Second, we apply our formulas to parametric density estimation and propose the method of superquantile's (MOS), a simple variation of the method of moment's (MM) where moment's are replaced by superquantile's at different confidence levels. With the freedom to select various combinations of confidence levels, MOS allows the user to focus the fitting procedure on different portions of the distribution, such as the tail when fitting heavy-tailed asymmetric data. |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1811.11301&r=ecm |
| By: | Chang, Yoosoon; Lu, Ye; Park, Joon Y. |
| Abstract: | In this paper, we analyze regressions with observations collected at small time interval over long period of time. For the formal asymptotic analysis, we assume that samples are obtained from continuous time stochastic processes, and let the sampling interval δ shrink down to zero and the sample span T increase up to infinity. In this setup, we show that the standard Wald statistic diverges to infinity and the regression becomes spurious as long as δ → 0 sufficiently fast relative to T → ∞. Such a phenomenon is indeed what is frequently observed in practice for the type of regressions considered in the paper. In contrast, our asymptotic theory predicts that the spuriousness disappears if we use the robust version of the Wald test with an appropriate longrun variance estimate. This is supported, strongly and unambiguously, by our empirical illustration. |
| Keywords: | high frequency regression; spurious regression; continuous time model; asymptotics; longrun variance estimation |
| Date: | 2018–07 |
| URL: | http://d.repec.org/n?u=RePEc:syd:wpaper:2018-10&r=ecm |
| By: | Brinca, Pedro; Iskrev, Nikolay; Loria, Francesca |
| Abstract: | Since its introduction by Chari et al. (2018), Business Cycle Accounting (BCA) exercises have become widespread. Much attention has been devoted to the results of such exercises and to methodological departures from the baseline methodology. Little attention has been paid to identification issues within these classes of models, despite the methodology typically involving estimating relatively large scale dynamic stochastic general equilibrium models. In this paper we investigate whether such issues are of concern in the original methodology and in an extension proposed by Sustek (2011) called Monetary BCA. We resort to two types of identification tests in population. One concerns strict identification as theorized by Komuner and Ng (2011), while the other deals both with strict and weak identification as in Iskrev (2015). As to the former, when restricting the estimation to the parameters governing the latent variable's laws of motion, we find that both in the BCA and MBCA framework, all parameters fulfill the requirements for strict identification. If instead we estimate all structural parameters of the model jointly, both frameworks show strict identification failures in several parameters. These results hold for both tests. We show that restricting estimation of some deep parameters can obviate such failures. When we explore weak identification issues, we find that they affect both models. They arise from the fact that many of the estimated parameters do not have a distinct effect on the likelihood. Most importantly, we explore the extent to which these weak identification problems affect the main economic takeaways and find that the identification deficiencies are not relevant for the standard BCA model. Finally, we compute some statistics of interest to practitioners of the BCA methodology. |
| Keywords: | Business Cycle Accounting, Identification, Maximum Likelihood Estimation |
| JEL: | C32 C51 C52 E27 E32 E37 |
| Date: | 2018–11–26 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:90250&r=ecm |
| By: | Victor Chernozhukov; Iv\'an Fern\'andez-Val; Siyi Luo |
| Abstract: | We develop a distribution regression model under endogenous sample selection. This model is a semiparametric generalization of the Heckman selection model that accommodates much rich patterns of heterogeneity in the selection process and effect of the covariates. The model applies to continuous, discrete and mixed outcomes. We study the identification of the model, and develop a computationally attractive two-step method to estimate the model parameters, where the first step is a probit regression for the selection equation and the second step consists of multiple distribution regressions with selection corrections for the outcome equation. We construct estimators of functionals of interest such as actual and counterfactual distributions of latent and observed outcomes via plug-in rule. We derive functional central limit theorems for all the estimators and show the validity of multiplier bootstrap to carry out functional inference. We apply the methods to wage decompositions in the UK using new data. Here we decompose the difference between the male and female wage distributions into four effects: composition, wage structure, selection structure and selection sorting. We uncover positive sorting for single men and negative sorting for married women that accounts for a substantial fraction of the gender wage gap at the top of the distribution. These findings can be interpreted as evidence of assortative matching in the marriage market and glass-ceiling in the labor market. |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1811.11603&r=ecm |
| By: | Isabel Casas (BCAM; and Department of Business Economics, University of Southern Denmark); Jiti Gao (Monash University); Shangyu Xie (University of International Business and Economics) |
| Abstract: | Income elasticity dynamics of health expenditure is considered for the OECD and the Eurozone over the period 1995-2014. This paper studies a novel non-linear cointegration model with fixed effects, controlling for cross-section dependence and unobserved heterogeneity. Most importantly, its coefficients can vary over time and its variables can be non-stationary. The resulting asymptotic theory is fundamentally different with a faster rate of convergence to similar kernel smoothing methodologies. A fully modified kernel regression method is also proposed to reduce the asymptotic bias. Results show a steep increase in the income elasticity for the OECD and a small increase for the Eurozone. |
| Keywords: | Cross-sectional dependence, Health expenditure, Income elasticity, Nonparametric kernel smoothing, Non-stationarity, Super-consistency. |
| JEL: | C14 C23 G13 H51 |
| Date: | 2111 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2018-29&r=ecm |
| By: | Ben Moews; J. Michael Herrmann; Gbenga Ibikunle |
| Abstract: | Trend change prediction in complex systems with a large number of noisy time series is a problem with many applications for real-world phenomena, with stock markets as a notoriously difficult to predict example of such systems. We approach predictions of directional trend changes via complex lagged correlations between them, excluding any information about the target series from the respective inputs to achieve predictions purely based on such correlations with other series. We propose the use of deep neural networks that employ step-wise linear regressions with exponential smoothing in the preparatory feature engineering for this task, with regression slopes as trend strength indicators for a given time interval. We apply this method to historical stock market data from 2011 to 2016 as a use case example of lagged correlations between large numbers of time series that are heavily influenced by externally arising new information as a random factor. The results demonstrate the viability of the proposed approach, with state-of-the-art accuracies and accounting for the statistical significance of the results for additional validation, as well as important implications for modern financial economics. |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1811.11287&r=ecm |
| By: | Henderson, Daniel J. (University of Alabama); Souto, Anne-Charlotte (University of Alabama) |
| Abstract: | In this article we overview nonparametric (spline and kernel) regression methods and illustrate how they may be used in labor economic applications. We focus our attention on issues commonly found in the labor literature such as how to account for endogeneity via instrumental variables in a nonparametric setting. We showcase these methods via data from the Current Population Survey. |
| Keywords: | endogeneity, kernel, labor, nonparametic, regression, spline |
| JEL: | C14 C26 I24 J24 J31 |
| Date: | 2018–10 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp11914&r=ecm |
| By: | Eric Benhamou |
| Abstract: | In this paper, we revisit the Kalman filter theory. After giving the intuition on a simplified financial markets example, we revisit the maths underlying it. We then show that Kalman filter can be presented in a very different fashion using graphical models. This enables us to establish the connection between Kalman filter and Hidden Markov Models. We then look at their application in financial markets and provide various intuitions in terms of their applicability for complex systems such as financial markets. Although this paper has been written more like a self contained work connecting Kalman filter to Hidden Markov Models and hence revisiting well known and establish results, it contains new results and brings additional contributions to the field. First, leveraging on the link between Kalman filter and HMM, it gives new algorithms for inference for extended Kalman filters. Second, it presents an alternative to the traditional estimation of parameters using EM algorithm thanks to the usage of CMA-ES optimization. Third, it examines the application of Kalman filter and its Hidden Markov models version to financial markets, providing various dynamics assumptions and tests. We conclude by connecting Kalman filter approach to trend following technical analysis system and showing their superior performances for trend following detection. |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1811.11618&r=ecm |
| By: | Yoosoon Chang (Indiana University); Junior Maih (Norges Bank and BI Norwegian Business School); Fei Tan (Department of Economics, Chaifetz School of Business, Saint Louis University and Center for Economic Behavior and Decision-Making, Zhejiang University of Finance and Economics) |
| Abstract: | This article studies the estimation of state space models whose parameters are switching endogenously between two regimes, depending on whether an autoregressive latent factor crosses some threshold level. Endogeneity stems from the sustained impacts of transition innovations on the latent factor, absent from which our model reduces to one with exogenous Markov switching. Due to the flexible form of state space representation, this class of models is vastly broad, including classical regression models and the popular dynamic stochastic general equilibrium (DSGE) models as special cases. We develop a computationally efficient filtering algorithm to estimate the non-linear model. Calculations are greatly simplified by appropriate augmentation of the transition equation and exploiting the conditionally linear and Gaussian structure. The algorithm is shown to be accurate in approximating both the likelihood function and filtered state variables. We also apply the filter to estimate a small-scale DSGE model with threshold-type switching in monetary policy rule, and find apparent empirical evidence of endogeneity in the U.S. monetary policy shifts. Overall, our approach provides a greater scope for understanding the complex interaction between regime switching and measured economic behavior. |
| Keywords: | state space model; regime switching; endogenous feedback; filtering; DSGE model |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:inu:caeprp:2018011&r=ecm |
| By: | Jiang, Bibo; Lu, Ye; Park, Joon Y. |
| Abstract: | The high frequency behavior of the KPSS test, which is most commonly used to test for stationarity, is analyzed in a continuous time framework. Our asymptotics show that the test has no discriminatory power at high frequency: It either always rejects stationarity or has no nontrivial power at high frequency. The test becomes valid at high frequency only when the bandwidth of its longrun variance estimate is chosen suitably in our framework. We also analyze the residual-based KPSS test for cointegration. |
| Keywords: | KPSS test; testing for stationarity; testing for cointegration; continuous time process; high frequency observation |
| Date: | 2018–07 |
| URL: | http://d.repec.org/n?u=RePEc:syd:wpaper:2018-09&r=ecm |
| By: | Anne Lundgaard Hansen (Department of Economics, University of Copenhagen, Denmark) |
| Abstract: | It is well-known that interest rates and inflation rates are extremely persistent, yet they are best modeled and understood as stationary processes. These properties are contradictory in the workhorse Gaussian affine term structure model in which the persistent data often result in unit roots that imply non-stationarity. We resolve this puzzle by proposing a macro-finance term structure model with volatility-induced stationarity. Our model employs a level-dependent conditional volatility that maintains stationarity despite presence of unit roots in the characteristic polynomial corresponding to the conditional mean. Compared to the Gaussian affine term structure model, we improve out-of-sample forecasting of the yield curve and estimate term premia that are economically plausible and consistent with survey data. Moreover, we show that volatility-induced stationarity affects the error-correcting mechanism in a system of interest rates, inflation, and real activity. |
| Keywords: | Yield curve, error-correction, unit root, volatility-induced stationarity, macro-finance term structure model, level-dependent conditional volatility |
| JEL: | E43 E44 G12 |
| Date: | 2018–12–03 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:1812&r=ecm |