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on Econometric Time Series |
| By: | Bin Chen (University of Rochester); Jinho Choi (Bank of Korea); Juan Carlos Escanciano (Indiana University) |
| Abstract: | We propose a test for invertibility or fundamentalness of structural vector autoregressive moving average models generated by non-Gaussian independent and identically distributed (iid) structural shocks. We prove that in these models and under some regularity conditions the Wold innovations are a martingale difference sequence (mds) if and only if the structural shocks are fundamental. This simple but powerful characterization suggests an empirical strategy to assess invertibility. We propose a test based on a generalized spectral density to check for the mds property of the Wold innovations. This approach does not require to specify and estimate the economic agent?'s information ?flows or to identify and estimate the structural parameters and the non-invertible roots. Moreover, the proposed test statistic uses all lags in the sample and it has a convenient asymptotic N(0; 1) distribution under the null hypothesis of invertibility, and hence, it is straightforward to implement. In case of rejection, the test can be further used to check if a given set of additional variables provides sufficient informational content to restore invertibility. A Monte Carlo study is conducted to examine the ?finite-sample performance of our test. Finally, the proposed test is applied to two widely cited works on the effects of ?fiscal shocks by Blanchard and Perotti (2002) and Ramey (2011). |
| Keywords: | Fundamental Representations; Generalized Spectrum; Identi?cation; Invertible Moving Average |
| Date: | 2015–12 |
| URL: | http://d.repec.org/n?u=RePEc:inu:caeprp:2015022&r=ets |
| By: | Pooyan Amir Ahmadi; Harald Uhlig |
| Abstract: | We propose a novel identification strategy of imposing sign restrictions directly on the impulse responses of a large set of variables in a Bayesian factor-augmented vector autoregression. We conceptualize and formalize conditions under which every additional sign restriction imposed can be qualified as either relevant or irrelevant for structural identification up to a limiting case of point identification. Deriving exact conditions we establish that, (i) in a two dimensional factor model only two out of potentially infinite sign restrictions are relevant and (ii) in contrast, in cases of higher dimension every additional sign restriction can be relevant improving structural identification. The latter result can render our approach a blessing in high dimensions. In an empirical application for the US economy we identify monetary policy shocks imposing conventional wisdom and find modest real effects avoiding various unreasonable responses specifically present and pronounced combining standard recursive identification with FAVARs. |
| JEL: | C22 E5 |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:21738&r=ets |
| By: | Rangan Gupta (Department of Economics, University of Pretoria); Eric Olson (College of Business and Economics, West Virginia University, Morgantown, WV 26506, USA.); Mark E. Wohar (College of Business Administration, University of Nebraska at Omaha, 6708 Pine Street, Omaha, NE 68182, USA, and School of Business and Economics, Loughborough University, Leicestershire, LE11 3TU, UK.) |
| Abstract: | In this paper, we first extract 8 factors from a monthly data set of 130 macroeconomic and financial variables. Then these extracted factors are used to construct a Factor-Augmented Qualitative VAR (FA-Qual VAR) model to forecast industrial production growth, inflation, the Federal funds rate and the term spread based on a pseudo real-time recursive forecasting exercise over an out-of-sample period of 1980:1-2014:12, using an in-sample period of 1960:1-1979:12. Short-, medium- and long-run horizons of one-, six, twelve- and twenty-four-month(s)-ahead are considered. The forecasts from the FA-Qual VAR is compared with that of a standard VAR model (comprising of output, prices, interest rate and the term spread), and that of a Qualitative VAR (Qual VAR) model (which includes the variables in the VAR and the latent business cycle index generated based on the information from the industrial production growth, inflation, the Federal Funds rate and the term spread). In general, we observe that the FA-QualVAR tends to perform significantly better than the VAR and Qual VAR for the one-month-ahead and six-months-ahead forecast horizons for the key US variables under consideration. In other words, adding information from a large data set (through the use of factors) tend to produce forecasting gains at short- to medium-run horizons. |
| Keywords: | Vector Autoregressions, Business Cycle Turning Points, Factors, Forecasting |
| JEL: | C32 C53 E37 E47 |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:pre:wpaper:201585&r=ets |
| By: | Violetta Dalla (National and Kapodistrian University of Athens); Liudas Giraitis (Queen Mary University of London); Peter C.B. Phillips (Yale University, University of Auckland, University of Southampton, Singapore Management University) |
| Abstract: | Time series models are often fitted to the data without preliminary checks for stability of the mean and variance, conditions that may not hold in much economic and financial data, particularly over long periods. Ignoring such shifts may result in fitting models with spurious dynamics that lead to unsupported and controversial conclusions about time dependence, causality, and the effects of unanticipated shocks. In spite of what may seem as obvious differences between a time series of independent variates with changing variance and a stationary conditionally heteroskedastic (GARCH) process, such processes may be hard to distinguish in applied work using basic time series diagnostic tools. We develop and study some practical and easily implemented statistical procedures to test the mean and variance stability of uncorrelated and serially dependent time series. Application of the new methods to analyze the volatility properties of stock market returns leads to some unexpected surprising findings concerning the advantages of modeling time varying changes in unconditional variance. |
| Keywords: | Heteroskedasticity, KPSS test, Mean stability, Variance stability, VS test |
| JEL: | C22 C23 |
| Date: | 2015–12 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp765&r=ets |
| By: | Liudas Giraitis (Queen Mary University of London); Donatas Surgailis (Vilnius University); Andrius Škarnulis (Vilnius University) |
| Abstract: | Although the properties of the ARCH(∞) model are well investigated, the existence of long memory FIGARCH and IARCH solution was not established in the literature. These two popular ARCH type models which are widely used in applied literature, were causing theoretical controversy because of the suspicion that other solutions besides the trivial zero one, do not exist. Since ARCH models with non-zero intercept have a unique stationary solution and exclude long memory, the existence of finite variance FIGARCH and IARCH models and, thus, the possibility of long memory in the ARCH setting was doubtful. The present paper solves this controversy by showing that FIGARCH and IARCH equations have a non-trivial covariance stationary solution, and that such a solution exhibits long memory. The existence and uniqueness of stationary Integrated AR(∞) processes is also discussed, and long memory, as an inherited feature, is established. Summarizing, we show that covariance stationary IARCH, FIEGARCH and IAR(∞) processes exist, their class is wide, and they always have long memory. |
| Keywords: | AR, FIGARCH, IARCH, Long memory |
| JEL: | C15 C22 |
| Date: | 2015–12 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp766&r=ets |
| By: | Liudas Giraitis (Queen Mary University of London); George Kapetanios (Queen Mary University of London); Tony Yates (Unversity of Bristol) |
| Abstract: | In this paper we introduce the general setting of a multivariate time series autoregressive model with stochastic time-varying coefficients and time-varying conditional variance of the error process. This allows modeling VAR dynamics for non-stationary times series and estimation of time varying parameter processes by well-known rolling regression estimation techniques. We establish consistency, convergence rates and asymptotic normality for kernel estimators of the paths of coefficient processes and provide pointwise valid standard errors. The method is applied to a popular 7 variable data set to analyze evidence of time-variation in empirical objects of interest for the DSGE literature. The results of this paper serve as a starting point for further research on numerous open problems including establishing estimation results of time-varying parameters that are uniform in time <i>t</i>, constructing Bonferroni-type correction to the pointwise standard error bands and developing a valid test of the null hypothesis of no time variation. |
| Keywords: | Kernel estimation, Time-varying VAR, Structural change, Monetary policy shock |
| JEL: | C10 C14 E52 E61 |
| Date: | 2015–12 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp767&r=ets |
| By: | Liudas Giraitis (Queen Mary University of London); George Kapetanios (Queen Mary University of London); Konstantinos Theodoridis (Bank of England); Tony Yates (University of Bristol and Centre for Macroeconomics) |
| Abstract: | Following Giraitis, Kapetanios, and Yates (2014b), this paper uses kernel methods to estimate a seven variable time-varying (TV) vector autoregressive (VAR) model on the data set constructed by Smets and Wouters (2007). We apply an indirect inference method to map from this TV VAR to time variation in implied Dynamic Stochastic General Equilibrium (DSGE) parameters. We find that many parameters change substantially, particularly those defining nominal rigidities, habits and investment adjustment costs. In contrast to the 'Great Moderation' literature our monetary policy parameter estimates suggest that authorities tried to deliver a low and stable inflation from 1975 onwards, however, the severe adverse supply shocks in the 70s could have caused these policies to fail. |
| Keywords: | DSGE, Structural change, Kernel estimation, Time-varying VAR, Monetary policy shocks |
| JEL: | E52 E61 E66 C14 C18 |
| Date: | 2015–12 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp768&r=ets |
| By: | Ana Beatriz Galvão (University of Warwick); Liudas Giraitis (Queen Mary University of London); George Kapetanios (Queen Mary University of London); Katerina Petrova (Queen Mary University of London) |
| Abstract: | We build a time varying DSGE model with financial frictions in order to evaluate changes in the responses of the macroeconomy to financial friction shocks. Using US data, we find that the transmission of the financial friction shock to economic variables, such as output growth, has not changed in the last 30 years. The volatility of the financial friction shock, however, has changed, so that output responses to a one-standard deviation shock increase twofold in the 2007-2011 period in comparison with the 1985-2006 period. The time varying DSGE model with financial frictions improves the accuracy of forecasts of output growth and inflation during the tranquil period of 2000-2006, while delivering similar performance to the fixed coefficient DSGE model for the 2007-2012 period. |
| Keywords: | DSGE models, Financial frictions, Local likelihood, Bayesian methods, Time varying parameters |
| JEL: | C11 C53 E27 E52 |
| Date: | 2015–12 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp769&r=ets |
| By: | Ana Beatriz Galvão (University of Warwick); Liudas Giraitis (Queen Mary University of London); George Kapetanios (Queen Mary University of London); Katerina Petrova (Queen Mary University of London) |
| Abstract: | DSGE models have recently received considerable attention in macroeconomic analysis and forecasting. They are usually estimated using Bayesian methods, which require the computation of the likelihood function under the assumption that the parameters of the model remain fixed throughout the sample. This paper presents a Local Bayesian Likelihood method suitable for estimation of DSGE models that can accommodate time variation in all parameters of the model. There are two advantages in allowing the parameters to vary over time. The first is that it enables us to assess the possibilities of regime changes, caused by shifts in the policy preferences or the volatility of shocks, as well as the possibility of misspecification in the design of DSGE models. The second advantage is that we can compute predictive densities based on the most recent parameters' values that could provide us with more accurate forecasts. The novel Bayesian Local Likelihood method applied to the Smets and Wouters (2007) model provides evidence of time variation in the policy parameters of the model as well as the volatility of the shocks. We also show that allowing for time variation improves considerably density forecasts in comparison to the fixed parameter model and we interpret this result as evidence for the presence of stochastic volatility in the structural shocks. |
| Keywords: | DSGE models, Local likelihood, Bayesian methods, Time varying parameters |
| JEL: | C11 C53 E27 E52 |
| Date: | 2015–12 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp770&r=ets |
| By: | Peter C. B. Phillips (Yale University); Ye Chen (Singapore Management University); Jun Yu (Singapore Management University) |
| Abstract: | Limit theory is developed for continuous co-moving systems with mildly explosive regressors. The theory uses double asymptotics with in ll (as the sampling interval tends to zero) and large time span asymptotics. The limit theory explicitly involves initial conditions, allows for drift in the system, is provided for single and multiple explosive regressors, and is feasible to implement in practice. Simulations show that double asymptotics deliver a good approximation to the nite sample distribution, with both nite sample and asymptotic distributions showing sensitivity to initial conditions. The methods are implemented in the US real estate market for an empirical application, illustrating the usefulness of double asymptotics in practical work. |
| Keywords: | Cointegrated system; Explosive Process; Moderate Deviations from Unity; Double Asymptotics; Real Estate Market. |
| JEL: | C12 C13 C58 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:03-2015&r=ets |
| By: | Su Liangjun (Singapore Management University); Zhang Yonghui (Renmin University of China) |
| Abstract: | In this paper, we study a partially linear dynamic panel data model with fixed effects, where either exogenous or endogenous variables or both enter the linear part, and the lagged dependent variable together with some other exogenous variables enter the nonparametric part. Two types of estimation methods are proposed for the first-differenced model. One is composed of a semiparametric GMM estimator for the finite dimensional parameter and a local polynomial estimator for the infinite dimensional parameter based on the empirical solutions to Fredholm integral equations of the second kind, and the other is a sieve IV estimate of the parametric and nonparametric components jointly. We study the asymptotic properties for these two types of estimates when the number of individuals tends to ∞ and the time period is fixed. We also propose a specification test for the linearity of the nonparametric component based on a weighted square distance between the parametric estimate under the linear restriction and the semiparametric estimate under the alternative. Monte Carlo simulations suggest that the proposed estimators and tests perform well in finite samples. We apply the model to study the relationship between intellectual property right (IPR) protection and economic growth, and find that IPR has a nonlinear positive effect on the economic growth rate. |
| Keywords: | Additive structure, Fredholm integral equation, Generated covariate, GMM, Local polynomial regression, Partially linear model, Sieve method, Time effect |
| JEL: | C14 C33 C36 |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:06-2015&r=ets |
| By: | Su Liangjun (Singapore Management University); Junhui Qian (Shanghai Jiao Tong University) |
| Abstract: | In this paper we consider estimation and inference of common breaks in panel data models via adaptive group fused lasso. We consider two approaches — penalized least squares (PLS) for firstdifferenced models without endogenous regressors, and penalized GMM (PGMM) for first-differenced models with endogeneity. We show that with probability tending to one both methods can correctly determine the unknown number of breaks and estimate the common break dates consistently. We establish the asymptotic distributions of the Lasso estimators of the regression coefficients and their post Lasso versions. We also propose and validate a data-driven method to determine the tuning parameter used in the Lasso procedure. Monte Carlo simulations demonstrate that both the PLS and PGMM estimation methods work well in finite samples. We apply our PGMM method to study the effect of foreign direct investment (FDI) on economic growth using a panel of 88 countries and regions from 1973 to 2012 and find multiple breaks in the model. |
| Keywords: | Adaptive Lasso; Change point; Group fused Lasso; Panel data; Penalized least squares; Penalized GMM; Structural change |
| JEL: | C13 C23 C33 C51 |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:07-2015&r=ets |
| By: | Su Liangjun (Singapore Management University); Xia Wang (University of Chinese Academy of Sciences) |
| Abstract: | Conventional factor models assume that factor loadings are fixed over a long horizon of time, which appears overly restrictive and unrealistic in applications. In this paper, we introduce a time-varying factor model where factor loadings are allowed to change smoothly over time. We propose a local version of the principal component method to estimate the latent factors and time-varying factor loadings simultaneously. We establish the limiting distributions of the estimated factors and factor loadings in the standard large and large framework. We also propose a BIC-type information criterion to determine the number of factors, which can be used in models with either time-varying or time-invariant factor models. Based on the comparison between the estimates of the common components under the null hypothesis of no structural changes and those under the alternative, we propose a consistent test for structural changes in factor loadings. We establish the null distribution, the asymptotic local power property, and the consistency of our test. Simulations are conducted to evaluate both our nonparametric estimates and test statistic. We also apply our test to investigate Stock and Watson’s (2009) U.S. macroeconomic data set and find strong evidence of structural changes in the factor loadings. |
| Keywords: | Factor model, Information criterion, Local principal component, Local smoothing, Structural change, Test, Time-varying parameter. |
| JEL: | C12 C14 C33 C38 |
| Date: | 2015–07 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:08-2015&r=ets |
| By: | Su Liangjun (Singapore Management University); Xi Qu (Shanghai Jiao Tong University) |
| Abstract: | This paper considers a simple test for the correct specification of linear spatial autoregressive models, assuming that the choice of the weight matrix is true. We derive the limiting distributions of the test under the null hypothesis of correct specification and a sequence of local alternatives. We show that the test is free of nuisance parameters asymptotically under the null and prove the consistency of our test. To improve the finite sample performance of our test, we also propose a residual-based wild bootstrap and justify its asymptotic validity. We conduct a small set of Monte Carlo simulations to investigate the finite sample properties of our tests. Finally, we apply the test to two empirical datasets: the vote cast and the economic growth rate. We reject the linear spatial autoregressive model in the vote cast example but fail to reject it in the economic growth rate example. |
| Keywords: | Generalized method of moments; Nonlinearity; Spatial autoregression; Spatial dependence; Specification test |
| JEL: | C12 C14 C21 |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:10-2015&r=ets |
| By: | Degui Li (University of York); Junhui Qian (Shanghai Jiao Tong University); Su Liangjun (Singapore Management University) |
| Abstract: | In this paper we consider estimation of common structural breaks in panel data models with unobservable interactive fixed effects. We introduce a penalized principal component (PPC) estimation procedure with an adaptive group fused LASSO to detect the multiple structural breaks in the models. Under some mild conditions, we show that with probability approaching one the proposed method can correctly determine the unknown number of breaks and consistently estimate the common break dates. Furthermore, we estimate the regression coefficients through the post-LASSO method and establish the asymptotic distribution theory for the resulting estimators. The developed methodology and theory are applicable to the case of dynamic panel data models. Simulation results demonstrate that the proposed method works well in finite samples with low false detection probability when there is no structural break and high probability of correctly estimating the break numbers when the structural breaks exist. We finally apply our method to study the environmental Kuznets curve for 74 countries over 40 years and detect two breaks in the data. |
| Keywords: | Change point; Interactive fixed effects; LASSO; Panel data; Penalized estimation; Principal component analysis. |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:12-2015&r=ets |
| By: | Stelios D. Bekiros; Alessia Paccagnini |
| Abstract: | Advanced Bayesian methods are employed in estimating dynamic stochastic general equilibrium (DSGE) models. Although policymakers and practitioners are particularly interested in DSGE models, these are typically too stylized to be taken directly to the data and often yield weak prediction results. Hybrid models can deal with some of the DSGE model misspecifications. Major advances in Bayesian estimation methodology could allow these models to outperform well-known time series models and effectively deal with more complex real-world problems as richer sources of data become available. A comparative evaluation of the out-of-sample predictive performance of many different specifications of estimated DSGE models and various classes of VAR models is performed, using datasets from the US economy. Simple and hybrid DSGE models are implemented, such as DSGE–VAR and Factor Augmented DSGEs and tested against standard, Bayesian and Factor Augmented VARs. Moreover, small scale models including the real gross domestic product, the harmonized consumer price index and the nominal short-term federal funds interest rate, are comparatively assessed against medium scale models featuring additionally sticky nominal prices, wage contracts, habit formation, variable capital utilization and investment adjustment costs. The investigated period spans 1960:Q4–2010:Q4 and forecasts are produced for the out-of-sample testing period 1997:Q1–2010:Q4. This comparative validation can be useful to monetary policy analysis and macro-forecasting with the use of advanced Bayesian methods. |
| Keywords: | Bayesian estimation; Forecasting; Metropolis–Hastings; Markov Chain Monte Carlo; Marginal data density; Factor augmented DSGE |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:ucn:oapubs:10197/7322&r=ets |
| By: | Cubadda G.; Guardabascio B.; Hecq A.W. (GSBE) |
| Abstract: | This paper introduces a new modelling for detecting the presence of commonalities in a set of realized volatility measures. In particular, we propose a multivariate generalization of the heterogeneous autoregressive model HAR that is endowed with a common index structure. The Vector Heterogeneous Autoregressive Index model has the property to generate a common index that preserves the same temporal cascade structure as in the HAR model, a feature that is not shared by other aggregation methods e.g., principal components. The parameters of this model can be easily estimated by a proper switching algorithm that increases the Gaussian likelihood at each step. We illustrate our approach with an empirical analysis aiming at combining several realized volatility measures of the same equity index for three different markets. |
| Keywords: | Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; |
| JEL: | C32 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2015033&r=ets |