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on Econometric Time Series |
| By: | Merce, Emilian; Merce, Cristian Calin; Pocol, Cristina Bianca |
| Abstract: | The paper demonstrates that autocorrelation is an accidental statistical phenomenon, whose origin is the incomplete data base. It also shows that the attempts to redistribute factors interactions have focused on the development of methods of solving the effect rather than identifying the cause that generates collinearity. Three possible methods for collinearity removal are analysed comparatively. The premise for two of these methods is autocorrelation redistribution, and the third reveals the cause of collinearity and, implicitly, its cancellation. The three methods are named as follows: 1. Classic method [1,7]; 2. Method of Merce E., Merce C.C.[6]; 3. Method of Merce E., Merce C.C.[5]; It is demonstrated that the first two methods are conventional approximations on the distribution of factors’ interaction, with possible subjective consequences. The ideal solution is the use of a complete data base. If this is not possible, as is often the case with databases of economic or sociological research, solving can be the completion of information with theoretical values, obtained by adjusting the causal relationship, in the hypothesis of a certain regression model, a procedure that represents, in fact and implicitly, a way of redistributing the interaction on the influence factors included in the causal model. |
| Keywords: | autocorrelation, statistic, method |
| JEL: | C1 C15 Q1 R0 |
| Date: | 2017–11–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:85090&r=ets |
| By: | Offer Lieberman (Bar-Ilan University); Peter C.B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | Two approaches have dominated formulations designed to capture small departures from unit root autoregressions. The first involves deterministic departures that include local-to-unity (LUR) and mildly (or moderately) integrated (MI) specifications where departures shrink to zero as the sample size tends to infinity. The second approach allows for stochastic departures from unity, leading to stochastic unit root (STUR) specifications. This paper introduces a hybrid local stochastic unit root (LSTUR) specification that has both LUR and STUR components and allows for endogeneity in the time varying coefficient that introduces structural elements to the autoregression. This hybrid model generates trajectories that, upon normalization, have non-linear diffusion limit processes that link closely to models that have been studied in mathematical finance, particularly with respect to option pricing. It is shown that some LSTUR parameterizations have a mean and variance which are the same as a random walk process but with a kurtosis exceeding 3, a feature which is consistent with much financial data. We develop limit theory and asymptotic expansions for the process and document how inference in LUR and STUR autoregressions is affected asymptotically by ignoring one or the other component in the more general hybrid generating mechanism. In particular, we show how confidence belts constructed from the LUR model are affected by the presence of a STUR component in the generating mechanism. The import of these findings for empirical research are explored in an application to the spreads on US investment grade corporate debt. |
| Keywords: | Autoregression, Nonlinear diffusion, Stochastic unit roo, Time-varying coefficient |
| JEL: | C22 |
| Date: | 2017–11 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2113&r=ets |
| By: | Yubo Tao (School of Economics, Singapore Management University); Peter C.B. Phillips (Cowles Foundation, Yale University); Jun Yu (School of Economics and Lee Kong Chian School of Business, Singapore Management University) |
| Abstract: | This paper studies a continuous time dynamic system with a random persistence parameter. The exact discrete time representation is obtained and related to several discrete time random coefficient models currently in the literature. The model distinguishes various forms of unstable and explosive behaviour according to specific regions of the parameter space that open up the potential for testing these forms of extreme behaviour. A two-stage approach that employs realized volatility is proposed for the continuous system estimation, asymptotic theory is developed, and test statistics to identify the different forms of extreme sample path behaviour are proposed. Simulations show that the proposed estimators work well in empirically realistic settings and that the tests have good size and power properties in discriminating characteristics in the data that differ from typical unit root behaviour. The theory is extended to cover models where the random persistence parameter is endogenously determined. An empirical application based on daily real S\&P 500 index data over 1964-2015 reveals strong evidence against parameter constancy after early 1980, which strengthens after July 1997, leading to a long duration of what the model characterizes as extreme behaviour in real stock prices. |
| Keywords: | Continuous time models, Explosive path, Extreme behaviour, Random coefficient autoregression, Infill asymptotics, Bubble testing |
| JEL: | C13 C22 G13 |
| Date: | 2017–12 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2114&r=ets |
| By: | Alessandro Casini; Pierre Perron |
| Abstract: | Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2017a) for inference in structural change models, we propose a Laplace-based (Quasi-Bayes) procedure for the construction of the estimate and confidence set for the date of a structural change. The procedure relies on a Laplace-type estimator defined by an integration-based rather than an optimization-based method. A transformation of the leastsquares criterion function is evaluated in order to derive a proper distribution, referred to as the Quasi-posterior. For a given choice of a loss function, the Laplace-type estimator is defined as the minimizer of the expected risk with the expectation taken under the Quasi-posterior. Besides providing an alternative estimate that is more precise---lower mean absolute error (MAE) and lower root-mean squared error (RMSE)---than the usual least-squares one, the Quasi-posterior distribution can be used to construct asymptotically valid inference using the concept of Highest Density Region. The resulting Laplace-based inferential procedure proposed is shown to have lower MAE and RMSE, and the confidence sets strike the best balance between empirical coverage rates and average lengths of the confidence sets relative to traditional long-span methods, whether the break size is small or large. |
| Date: | 2018–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1804.00232&r=ets |
| By: | Miranda-Agrippino, Silvia; Ricco, Giovanni |
| Abstract: | This article reviews Bayesian inference methods for Vector Autoregression models, commonly used priors for economic and financial variables, and applications to structural analysis and forecasting. |
| Keywords: | Bayesian inference; Vector Autoregression Models; BVAR; SVAR; forecasting |
| JEL: | C30 C32 E0 E00 |
| Date: | 2018–03–23 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:87393&r=ets |
| By: | Joris de Wind (CPB Netherlands Bureau for Economic Policy Analysis) |
| Abstract: | In this paper, I present a novel implementation of the exact nonlinear and non-Gaussian Kalman smoother that can also deal with implicit functions in the measurement and/or state equations as well as equality constraints. Read the accompanying paper CPB Discussion Paper 360 . My approach has the additional advantage that it can be fully automated, on the basis of which I have developed a toolbox that can handle a wide class of discrete-time state space models. The toolbox is documented in an accompanying paper, while the technical details are presented in the current one. |
| JEL: | C21 C22 C25 J64 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:cpb:discus:359&r=ets |
| By: | Joris de Wind (CPB Netherlands Bureau for Economic Policy Analysis) |
| Abstract: | In this paper, I present a new toolbox that implements the exact nonlinear and non-Gaussian Kalman smoother for a wide class of discrete-time state space models, including models with implicit functions and equality constraints. Read also CPB Discussion Paper 359 . The technical details are presented in an accompanying paper, while the toolbox is documented in the current one. The toolbox, which is built on top of Dynare, is very user-friendly and only requires the user to provide the state space model to be analyzed, while the toolbox automatically solves the smoothing problem. The toolbox can also be applied for conditional forecasting, which is demonstrated on the basis of a nonlinear macroeconomic model with forward-looking variables. |
| JEL: | C21 C22 C25 J64 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:cpb:discus:360&r=ets |
| By: | Ke Zhu |
| Abstract: | This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute deviations estimator (LADE) for the model. Second, we develop the random weighting (RW) method to estimate its asymptotic covariance matrix, leading to the implementation of the Wald test. Third, we construct a portmanteau test for model checking, and use the RW method to obtain its critical values. As a special weighted LADE, the feasible adaptive LADE (ALADE) is proposed and proved to have the same efficiency as its infeasible counterpart. The importance of our entire methodology based on the feasible ALADE is illustrated by simulation results and the real data analysis on three U.S. economic data sets. |
| Date: | 2018–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1804.02348&r=ets |
| By: | Qiying Wang (University of Sydney); Peter C.B. Phillips (Cowles Foundation, Yale University); Ioannis Kasparis (Dept. of Economics, University of Cyprus) |
| Abstract: | This paper studies the asymptotic properties of empirical nonparametric regressions that partially misspecify the relationships between nonstationary variables. In particular, we analyze nonparametric kernel regressions in which a potential nonlinear cointegrating regression is misspecified through the use of a proxy regressor in place of the true regressor. Such regressions arise naturally in linear and nonlinear regressions where the regressor suffers from measurement error or where the true regressor is a latent variable. The model considered allows for endogenous regressors as the latent variable and proxy variables that cointegrate asymptotically with the true latent variable. Such a framework includes correctly specified systems as well as misspecified models in which the actual regressor serves as a proxy variable for the true regressor. The system is therefore intermediate between nonlinear nonparametric cointegrating regression (Wang and Phillips, 2009a, 2009b) and completely misspecified nonparametric regressions in which the relationship is entirely spurious (Phillips, 2009). The asymptotic results relate to recent work on dynamic misspecification in nonparametric nonstationary systems by Kasparis and Phillips (2012) and Duffy (2014). The limit theory accommodates regressor variables with autoregressive roots that are local to unity and whose errors are driven by long memory and short memory innovations, thereby encompassing applications with a wide range of economic and financial time series. |
| Keywords: | Cointegrating regression, Kernel regression, Latent variable, Local time, Misspecification, Nonlinear nonparametric nonstationary regression |
| JEL: | C23 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2111&r=ets |
| By: | Anna Bykhovskaya (Department of Economics, Yale University); Peter C. B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | Limit theory for regressions involving local to unit roots (LURs) is now used extensively in time series econometric work, establishing power properties for unit root and cointegration tests, assisting the construction of uniform confidence intervals for autoregressive coefficients, and enabling the development of methods robust to departures from unit roots. The present paper shows how to generalize LUR asymptotics to cases where the localized departure from unity is a time varying function rather than a constant. Such a functional local unit root (FLUR) model has much greater generality and encompasses many cases of additional interest, including structural break formulations that admit subperiods of unit root, local stationary and local explosive behavior within a given sample. Point optimal FLUR tests are constructed in the paper to accommodate such cases. It is shown that against FLUR\ alternatives, conventional constant point optimal tests can have extremely low power, particularly when the departure from unity occurs early in the sample period. Simulation results are reported and some implications for empirical practice are examined. |
| Keywords: | Functional local unit root, Local to unity, Uniform confidence interval, Unit root model |
| JEL: | C22 C65 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2107&r=ets |
| By: | Degui Li (University of York); Peter C.B. Phillips (Cowles Foundation, Yale University); Jiti Gao (Dept. of Econometrics and Business Statistics, Monash University) |
| Abstract: | This paper studies nonlinear cointegrating models with time-varying coefficients and multiple nonstationary regressors using classic kernel smoothing methods to estimate the coefficient functions. Extending earlier work on nonstationary kernel regression to take account of practical features of the data, we allow the regressors to be cointegrated and to embody a mixture of stochastic and deterministic trends, complications which result in asymptotic degeneracy of the kernel-weighted signal matrix. To address these complications new \textsl{local} and \textsl{global rotation} techniques are introduced to transform the covariate space to accommodate multiple scenarios of induced degeneracy. Under certain regularity conditions we derive asymptotic results that differ substantially from existing kernel regression asymptotics, leading to new limit theory under multiple convergence rates. For the practically important case of endogenous nonstationary regressors we propose a fully-modified kernel estimator whose limit distribution theory corresponds to the prototypical pure (i.e., exogenous covariate) cointegration case, thereby facilitating inference using a generalized Wald-type test statistic. These results substantially generalize econometric estimation and testing techniques in the cointegration literature to accommodate time variation and complications of co-moving regressors. Finally an empirical illustration to aggregate US data on consumption, income, and interest rates is provided. |
| Keywords: | Cointegration, FM-kernel estimation, Generalized Wald test, Global rotation, Kernel degeneracy, Local rotation, Super-consistency, Time-varying coefficients |
| JEL: | C22 C65 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2109&r=ets |
| By: | Anna Bykhovskaya (Department of Economics, Yale University); Peter C. B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | This paper studies functional local unit root models (FLURs) in which the autoregressive coefficient may vary with time in the vicinity of unity. We extend conventional local to unity (LUR) models by allowing the localizing coefficient to be a function which characterizes departures from unity that may occur within the sample in both stationary and explosive directions. Such models enhance the flexibility of the LUR framework by including break point, trending, and multi-directional departures from unit autoregressive coefficients. We study the behavior of this model as the localizing function diverges, thereby determining the impact on the time series and on inference from the time series as the limits of the domain of definition of the autoregressive coefficient are approached. This boundary limit theory enables us to characterize the asymptotic form of power functions for associated unit root tests against functional alternatives. Both sequential and simultaneous limits (as the sample size and localizing coefficient diverge) are developed. We find that asymptotics for the process, the autoregressive estimate, and its $t$ statistic have boundary limit behavior that differs from standard limit theory in both explosive and stationary cases. Some novel features of the boundary limit theory are the presence of a segmented limit process for the time series in the stationary direction and a degenerate process in the explosive direction. These features have material implications for autoregressive estimation and inference which are examined in the paper. |
| Keywords: | Boundary asymptotics, Functional local unit root, Local to unity, Sequential limits, Simultaneous limits, Unit root model |
| JEL: | C22 C65 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2108&r=ets |
| By: | Elmar Mertens; James M. Nason |
| Abstract: | This paper studies the joint dynamics of real-time U.S. inflation and average inflation predictions of the Survey of Professional Forecasters (SPF) based on sample ranging from 1968Q4 to 2017Q2. The joint data generating process (DGP) comprises an unobserved components (UC) model of inflation and a sticky information (SI) prediction mechanism for the SPF predictions. We add drifting gap inflation persistence to a UC model in which stochastic volatility (SV) affects trend and gap inflation. Another innovation puts a time-varying frequency of inflation forecast updating into the SI prediction mechanism. The joint DGP is a nonlinear state space model (SSM). We estimate the SSM using Bayesian tools grounded in a Rao-Blackwellized auxiliary particle filter, particle learning, and a particle smoother. The estimates show that (i) longer horizon average SPF inflation predictions inform estimates of trend inflation; (ii) gap inflation persistence is procyclical and SI inflation updating is frequent before the Volcker disinflation; and (iii) subsequently, gap inflation persistence turns countercyclical and SI inflation updating becomes infrequent. |
| Keywords: | inflation; unobserved components;professional forecasts; sticky information; stochastic volatility; time-varying parameters; Bayesian; particle filter |
| JEL: | E31 C11 C32 |
| Date: | 2018–04 |
| URL: | http://d.repec.org/n?u=RePEc:bis:biswps:713&r=ets |
| By: | Haroon Mumtaz (Queen Mary University of London); |
| Abstract: | This paper introduces a VAR with stochastic volatility in mean where the residuals of the volatility equations and the observation equations are allowed to be correlated. This implies that exogeneity of shocks to volatility is not assumed apriori and structural shocks can be identified ex-post by applying standard SVAR techniques. The paper provides a Gibbs algorithm to approximate the posterior distribution and demonstrates the proposed methods by estimating the impact of financial uncertainty shocks on the US economy. |
| Keywords: | VAR, Stochastic volatility in mean, error covariance |
| JEL: | C2 C11 E3 |
| Date: | 2018–03–06 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:855&r=ets |
| By: | Lisa Sella (Department of Economics and Statistics Cognetti de Martiis, University of Torino, Torino, Italy, IRCrES - Research Institute on Sustainaible Economic Growth (CNR - Consiglio Nazionale delle Ricerche)); Gianna Vivaldo (IMT - School for Advanced Studies Lucca); Andreas Groth (CERES-ERTI - Centre d'Enseignement et de Recherche sur l'Environnement et la Societé / Environmental Research and Teaching Institute - ENS Paris - École normale supérieure - Paris); Michael Ghil (Department of Atmospheric Sciences, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095-1565, United States, CERES-ERTI - Centre d'Enseignement et de Recherche sur l'Environnement et la Societé / Environmental Research and Teaching Institute - ENS Paris - École normale supérieure - Paris) |
| Abstract: | The present work applies singular spectrum analysis (SSA) to the study of macroeconomic fluctuations in three European countries: Italy, The Netherlands, and the United Kingdom. This advanced spectral method provides valuable spatial and frequency information for multivariate data sets and goes far beyond the classical forms of time domain analysis. In particular, SSA enables us to identify dominant cycles that characterize the deterministic behavior of each time series separately, as well as their shared behavior. We demonstrate its usefulness by analyzing several fundamental indicators of the three countries’ real aggregate economy in a univariate, as well as a multivariate setting. Since business cycles are international phenomena, which show common characteristics across countries, our aim is to uncover supranational behavior within the set of representative European economies selected herein. Finally, the analysis is extended to include several indicators from the U.S. economy, in order to examine its influence on the European economies under study and their interrelationships. |
| Keywords: | Spectral analysis,Synchronization,Business cycles synchronization,Advanced spectral methods, Business cycles, European Union,Frequency domain, Time domain,JEL classification: C15, C60, E32 * Corresponding author |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-01701122&r=ets |