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on Econometrics |
| By: | Jiti Gao; Peter M. Robinson |
| Abstract: | A semiparametric model is proposed in which a parametric filtering of a non-stationary time series, incorporating fractionally differencing with short memory correction, removes correlation but leaves a nonparametric deterministic trend. Estimates of the memory parameter and other dependence parameters are proposed, and shown to be consistent and asymptotically normally distributed with parametric rate. Unit root tests with standard asymptotics are thereby justified. Estimation of the trend function is also considered. We include a Monte Carlo study of finite-sample performance. |
| Keywords: | fractional time series; fixed design nonparametric regression; non-stationary time series; unit root tests. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2013-15&r=ecm |
| By: | Rothe, Christoph (Columbia University); Firpo, Sergio (Sao Paulo School of Economics) |
| Abstract: | We study semiparametric two-step estimators which have the same structure as parametric doubly robust estimators in their second step, but retain a fully nonparametric specification in the first step. Such estimators exist in many economic applications, including a wide range of missing data and treatment effect models. We show that these estimators are √n-consistent and asymptotically normal under weaker than usual conditions on the accuracy of the first stage estimates, have smaller first order bias and second order variance, and that their finite-sample distribution can be approximated more accurately by classical first order asymptotics. We argue that because of these refinements our estimators are useful in many settings where semiparametric estimation and inference are traditionally believed to be unreliable. We also illustrate the practical relevance of our approach through simulations and an empirical application. |
| Keywords: | semiparametric model, missing data, treatment effects, doubly robust estimation, higher order asymptotics |
| JEL: | C14 C21 C31 C51 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp7564&r=ecm |
| By: | Jiti Gao; Peter C.B. Phillips |
| Abstract: | This paper studies a general class of nonlinear varying coefficient time series models with possible nonstationarity in both the regressors and the varying coefficient components. The model accommodates a cointegrating structure and allows for endo-geneity with contemporaneous correlation among the regressors, the varying coefficient drivers, and the residuals. This framework allows for a mixture of stationary and non-stationary data and is well suited to a variety of models that are commonly used in applied econometric work. Nonparametric and semiparametric estimation methods are proposed to estimate the varying coefficient functions. The analytical findings reveal some important differences, including convergence rates, that can arise in the conduct of semiparametric regression with nonstationary data. The results include some new asymptotic theory for nonlinear functionals of nonstationary and stationary time series that are of wider interest and applicability and subsume much earlier research on such systems. The finite sample properties of the proposed econometric methods are analyzed in simulations. An empirical illustration examines nonlinear dependencies in aggregate consumption function behavior in the US over the period 1960 - 2009. |
| Keywords: | fractional Aggregate consumption, Asymptotic theory, cointegration, density, local time, nonlinear functional, nonparametric estimation, semiparametric, time series, varying coefficient model. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2013-16&r=ecm |
| By: | Biqing Cai; Jiti Gao |
| Abstract: | This paper discusses nonparametric series estimation of integrable cointegration models using Hermite functions. We establish the uniform consistency and asymptotic normality of the series estimator. The Monte Carlo simulation results show that the performance of the estimator is numerically satisfactory. We then apply the estimator to estimate the stock return predictive function. The out-of-sample evaluation results suggest that dividend yield has nonlinear predictive power for stock returns while book-to-market ratio and earning-price ratio have little predictive power. |
| Keywords: | Cointegration, Hermite Functions, Return Predictability, Series Estimator, Unit Root |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2013-17&r=ecm |
| By: | Zhenlin Yang (School of Economics, Singapore Management University) |
| Abstract: | To test the existence of spatial dependence in an econometric model, a convenient test is the Lagrange Multiplier (LM) test. However, evidence shows that, infinite samples, the LM test referring to asymptotic critical values may suffer from the problems of size distortion and low power, which become worse with a denser spatial weight matrix. In this paper, residual-based bootstrap methods are introduced for asymptotically refined approximations to the finite sample critical values of the LM statistics. Conditions for their validity are clearly laid out and formal justifications are given in general, and in details under several popular spatial LM tests using Edgeworth expansions. Monte Carlo results show that when the conditions are not fully met, bootstrap may lead to unstable critical values that change significantly with the alternative, whereas when all conditions are met, bootstrap critical values are very stable, approximate much better the finite sample critical values than those based on asymptotics, and lead to significantly improved size and power. The methods are further demonstrated using more general spatial LM tests, in connection with local misspecification and unknown heteroskedasticity. |
| Keywords: | Asymptotic refinements; Bootstrap; Edgeworth expansion; LM Tests; Spatial dependence; Size; Power; Local misspecification; heteroskedasticity; Wild bootstrap. |
| JEL: | C12 C15 C18 C21 |
| Date: | 2013–05 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:03-2013&r=ecm |
| By: | Giorgio Calzolari (University of Florence); Laura Magazzini (Department of Economics (University of Verona)) |
| Keywords: | panel data, dynamic model, GMM estimation, test of overidentifying restrictions |
| JEL: | C23 C12 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:ver:wpaper:14/2013&r=ecm |
| By: | Yuanhua Feng (University of Paderborn); Sarah Forstinger (University of Paderborn); Christian Peitz (University of Paderborn) |
| Abstract: | This paper discusses the detailed performance of an iterative plug-in (IPI) bandwidth selector for estimating the diurnal duration pattern in a recently proposed semiparametric autoregressive conditional duration (SemiACD) model. For this purpose an alternative formula of the asymptotically optimal bandwidth is proposed. A large simulation study was carried out based on this new formula. The effect of different factors, which affect the selected bandwidth is discussed in detail. It is shown that the proposed IPI algorithm works very well in practice and that the SemiACD model in general, is clearly superior to the parametric ACD model, if there is a deterministic trend in the duration data. It is also shown that the quality of the bandwidth selection, the diurnal pattern estimate and the parametric estimation will all be clearly improved, if the sample size is enlarged. Furthermore, according to the goodness-of-fit of the estimated diurnal pattern, a best combination of the above mentioned factors is found. |
| Keywords: | Autoregressive conditional duration, diurnal duration patterns, local linear estimator, iterative plug-in, simulation |
| JEL: | C14 C41 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:wpaper:66&r=ecm |
| By: | Yuanhua Feng (University of Paderborn) |
| Abstract: | This paper introduces a spatial framework for high-frequency returns and a faster double-conditional smoothing algorithm to carry out bivariate kernel estimation of the volatility surface. A spatial multiplicative component GARCH with random effects is proposed to deal with multiplicative random effects found from the data. It is shown that the probabilistic properties of the stochastic part and the asymptotic properties of the kernel volatility surface estimator are all strongly affected by the multiplicative random effects. Data example shows that the volatility surface before, during and after the 2008 financial crisis forms a volatility saddle. |
| Keywords: | Spatial multiplicative component GARCH, high-frequency returns, double-conditional smoothing, multiplicative random effect, volatility arch, volatility saddle. |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:wpaper:65&r=ecm |
| By: | Daniel Levin; Terry Lyons; Hao Ni |
| Abstract: | Regression analysis aims to use observational data from multiple observations to develop a functional relationship relating explanatory variables to response variables, which is important for much of modern statistics, and econometrics, and also the field of machine learning. In this paper, we consider the special case where the explanatory variable is a stream of information, and the response is also potentially a stream. We provide an approach based on identifying carefully chosen features of the stream which allows linear regression to be used to characterise the functional relationship between explanatory variables and the conditional distribution of the response; the methods used to develop and justify this approach, such as the signature of a stream and the shuffle product of tensors, are standard tools in the theory of rough paths and seem appropriate in this context of regression as well and provide a surprisingly unified and non-parametric approach. To illustrate the approach we consider the problem of using data to predict the conditional distribution of the near future of a stationary, ergodic time series and compare it with probabilistic approaches based on first fitting a model. We believe our reduction of this regression problem for streams to a linear problem is clean, systematic, and efficient in minimizing the effective dimensionality. The clear gradation of finite dimensional approximations increases its usefulness. Although the approach is non-parametric, it presents itself in computationally tractable and flexible restricted forms in examples we considered. Popular techniques in time series analysis such as AR, ARCH and GARCH can be seen to be special cases of our approach, but it is not clear if they are always the best or most informative choices. |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1309.0260&r=ecm |
| By: | Peter C. B. Phillips (Yale University, University of Auckland, University of Southampton & Singapore Management University); Shu-Ping Shi (The Australian National University); Jun Yu (Singapore Management University) |
| Abstract: | Recent work on econometric detection mechanisms has shown the effectiveness of recursive procedures in identifying and dating financial bubbles. These procedures are useful as warning alerts in surveillance strategies conducted by central banks and fiscal regulators with real time data. Use of these methods over long historical periods presents a more serious econometric challenge due to the complexity of the nonlinear structure and break mechanisms that are inherent in multiple bubble phenomena within the same sample period. To meet this challenge the present paper develops a new recursive flexible window method that is better suited for practical implementation with long historical time series. The method is a generalized version of the sup ADF test of Phillips, Wu and Yu (2011, PWY) and delivers a consistent date-stamping strategy for the origination and termination of multiple bubbles. Simulations show that the test significantly improves discriminatory power and leads to distinct power gains when multiple bubbles occur. An empirical application of the methodology is conducted on S&P 500 stock market data over a long historical period from January 1871 to December 2010. The new approach successfully identi.es the well-known historical episodes of exuberance and collapse over this period, whereas the strategy of PWY and a related CUSUM dating procedure locate far fewer episodes in the same sample range. |
| Keywords: | Date-stamping strategy; Flexible window; Generalized sup ADF test; Multiple bubbles, Rational bubble; Periodically collapsing bubbles; Sup ADF test; |
| JEL: | C15 C22 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:04-2013&r=ecm |
| By: | Jakob W. Messner; Georg J. Mayr; Achim Zeileis; Daniel S. Wilks |
| Abstract: | To achieve well calibrated probabilistic forecasts, ensemble forecasts often need to be statistically post-processed. One recent ensemble-calibration method is extended logistic regression which extends the popular logistic regression to yield full probability distribution forecasts. Although the purpose of this method is to post-process ensemble forecasts, mostly only the ensemble mean is used as predictor variable, whereas the ensemble spread is neglected because it does not improve the forecasts. In this study we show that when simply used as ordinary predictor variable in extended logistic regression, the ensemble spread only affects the location but not the variance of the predictive distribution. Uncertainty information contained in the ensemble spread is therefore not utilized appropriately. To solve this drawback we propose a simple new approach where the ensemble spread is directly used to predict the dispersion of the predictive distribution. With wind speed data and ensemble forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF) we show that using this approach, the ensemble spread can be used effectively to improve forecasts from extended logistic regression. |
| Keywords: | probabilistic forecasting, extended logistic regression, heteroskedasticity, ensemble spread |
| JEL: | C53 C25 Q42 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:inn:wpaper:2013-21&r=ecm |
| By: | Andrea Carriero (Queen Mary, University of London); Haroon Mumtaz (Bank of England); Konstantinos Theodoridis (Bank of England); Angeliki Theophilopoulou (University of Westminister) |
| Abstract: | A growing empirical literature has considered the impact of uncertainty using SVAR models that include proxies for uncertainty shocks as endogenous variables. In this paper we consider the possible impact of measurement error in the uncertainty shock proxies on the estimated impulse responses from these SVAR models. We show via a Monte Carlo experiment that measurement error can result in attenuation bias in the SVAR impulse responses. In contrast, the proxy SVAR that uses the uncertainty shock proxy as an instrument to identify the underlying shock does not suffer from this bias. Applying this proxy SVAR method to the Bloom (2009) data set results in estimated impulse responses to uncertainty shocks that are larger in magnitude and persistence than those obtained from a standard recursive SVAR. |
| Keywords: | Uncertainty shocks, Proxy SVAR, Non-linear DSGE models |
| JEL: | C15 C32 E32 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp707&r=ecm |
| By: | Peter C. B. Phillips (Yale University, University of Auckland, University of Southampton & Singapore Management University); Shu-Ping Shi (The Australian National University); Jun Yu (Singapore Management University) |
| Abstract: | This paper provides the limit theory of real time dating algorithms for bubble detection that were suggested in Phillips, Wu and Yu (2011, PWY) and Phillips, Shi and Yu (2013b, PSY). Bubbles are modeled using mildly explosive bubble episodes that are embedded within longer periods where the data evolves as a stochastic trend, thereby capturing normal market behavior as well as exuberance and collapse. Both the PWY and PSY estimates rely on recursive right tailed unit root tests (each with a different recursive algorithm) that may be used in real time to locate the origination and collapse dates of bubbles. Under certain explicit conditions, the moving window detector of PSY is shown to be a consistent dating algorithm even in the presence of multiple bubbles. The other algorithms are consistent detectors for bubbles early in the sample and, under stronger conditions, for subsequent bubbles in some cases. These asymptotic results and accompanying simulations guide the practical implementation of the procedures. They indicate that the PSY moving window detector is more reliable than the PWY strategy, sequential application of the PWY procedure and the CUSUM procedure. |
| Keywords: | Bubble duration, Consistency, Dating algorithm, Limit theory, Multiple bubbles, Real time detector. |
| JEL: | C15 C22 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:05-2013&r=ecm |
| By: | In Choi (Department of Economics, Sogang University, Seoul) |
| Abstract: | This paper surveys the literature on panel cointegration. It starts by dis- cussing cointegrating panel regressions for both cross-sectionally independent and correlated panels. It then introduces three groups of tests for panel coin-tegration : residual-based tests for the null of noncointegration, residual-based tests for the null of cointegration, and tests based on vector autoregression. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:sgo:wpaper:1208&r=ecm |
| By: | Herrera Gómez, Marcos |
| Abstract: | This paper presents a collection of spatial econometrics tools to detect global and local spatial dependence. These tools are used to analyze the spatial structure of the unemployment rate in Argentina in Census 2001 and 2010. Detailed study enables identification and comparison of persistent spatial structures in the departamental distribution of unemployment. |
| Keywords: | Spatial Autocorrelation, LISA, Getis-Ord Test, Symbolic Entropy, Unemployment |
| JEL: | C12 C21 J64 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:49407&r=ecm |
| By: | Vladimir Filimonov; Didier Sornette |
| Abstract: | We present a careful analysis of a set of effects that lead to significant biases in the estimation of the branching ratio n that quantifies the degree of endogeneity of how much past events trigger future events. We report (i) evidence of strong upward biases on the estimation of n when using power law memory kernels in the presence of a few outliers, (ii) strong effects on n resulting from the form of the regularization part of the power law kernel, (iii) strong edge effects on the estimated n when using power law kernels, and (iv) the need for an exhaustive search of the absolute maximum of the log-likelihood function due to its complicated shape. Moreover, we demonstrate that the calibration of the Hawkes process on mixtures of pure Poisson process with changes of regime leads to completely spurious apparent critical values for the branching ratio (n=1) while the true value is actually n=0. More generally, regime shifts on the parameters of the Hawkes model and/or on the generating process itself are shown to systematically lead to a significant upward bias in the estimation of the branching ratio. Many of these effects are present in high-frequency financial data, which is studied as an illustration. Altogether, our careful exploration of the caveats of the calibration of the Hawkes process stresses the need for considering all the above issues before any conclusion can be sustained. In this respect, because the above effects are plaguing their analyses, the claim by Hardiman, Bercot and Bouchaud (2013) that financial market have been continuously functioning at or close to criticality (n=1) cannot be supported. In contrast, our previous results on E-mini S&P 500 Futures Contracts and on major commodity future contracts are upheld. |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1308.6756&r=ecm |
| By: | Niels Framroze Møller (DTU Management Engineering, Energy Systems Analysis, Technical University of Denmark) |
| Abstract: | What explains the persistence of unemployment? The literature on hysteresis, which is based on unit root testing in autoregressive models, consists of a vast number of univariate studies, i.e. that analyze unemployment series in isolation, but few multivariate analyses that focus on the sources of hysteresis. As a result, this question remains largely unanswered. This paper presents a multivariate econometric framework for analyzing hysteresis, which allows one to test different hypotheses about non-stationarity of unemployment against one another. For example, whether this is due to a persistently changing equilibrium, slow adjustment towards the equilibrium (persistent ?uctuations), or perhaps even a combination of the two. Different hypotheses of slow adjustment, as implied by theories of hysteresis, nominal rigidities or labor hoarding can also be compared. A small illustrative application to UK quarterly data on prices, wages, output, unemployment and crude oil prices, suggests that, for the period 1988 up to the onset of the financial crisis, the non-stationarity of UK unemployment cannot be explained as a result of slow adjustment, including sluggish wage formation as emphasized by the hysteresis theories. Instead, it is the equilibrium that has evolved persistently as a consequence of exogenous oil prices shifting the price setting relation (in the unemployment-real wage space) in a non-stationary manner. |
| Keywords: | Hysteresis, Unemployment Hysteresis, Persistence, Cointegration, Structural VAR, Equilibrium unemployment, Multivariate Time series analysis, Price- and Wage Setting, Wage formation, Crude oil prices, UK unemployment |
| JEL: | C1 C32 E00 E24 |
| Date: | 2013–08–28 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:1306&r=ecm |
| By: | Monica Billio (Department of Economics, University of Venice Cà Foscari); Roberto Casarin (Department of Economics, University of Venice Cà Foscari); Francesco Ravazzolo (Norges Bank and BI Norwegian Business School); Herman K. van Dijk (Econometric Institute, Erasmus University Rotterdam and Econometrics Department VU University Amsterdam) |
| Abstract: | Interactions between the eurozone and US booms and busts and among major eurozone economies are analyzed by introducing a panel Markov-switching VAR model well suitable for a multi-country cyclical analysis. The model accommodates changes in low and high data frequencies and endogenous time-varying transition matrices of the country-specific Markov chains. The transition matrix of each Markov chain depends on its own past history and on the history of the other chains, thus allowing for modelling of the interactions between cycles. An endogenous common eurozone cycle is derived by aggregating country-specific cycles. The model is estimated using a simulation based Bayesian approach in which an efficient multi-move strategy algorithm is defined to draw common time-varying Markov-switching chains. Our results show that the US and eurozone cycles are not fully synchronized over the 1991-2013 sample period, with evidence of more recessions in the eurozone, in particular during the 90's when the monetary union was planned. Larger synchronization occurs at beginning of the Great Financial Crisis. Shocks affect the US 1-quarter in advance of the eurozone, but these spread very rapidly among economies. There exist reinforcement effects in the recession probabilities and in the probabilities of exiting recessions for both eurozone and US cycles, and substantial differences in the phase transitions within the eurozone. An increase in the number of eurozone countries in recession increases the probability of the US to stay within recession, while the US recession indicator has a negative impact on the probability to stay in recession for eurozone countries. Moreover, turning point analysis shows that the cycles of Germany, France and Italy are closer to the US cycle than other countries. Belgium, Spain, and Germany, provide more timely information on the aggregate recession than Netherlands and France. |
| Keywords: | Bayesian Model; Panel VAR; Markov-switching; International Business Cycles; Interaction mechanisms. |
| JEL: | C1 C11 C15 C32 F31 G15 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2013:17&r=ecm |