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on Econometric Time Series |
| By: | Federico Carlini (Aarhus University and CREATES); Katarzyna Lasak (VU Amsterdam & Tinbergen Institute) |
| Abstract: | In this paper we consider the Fractional Vector Error Correction model proposed in Avarucci (2007), which is characterized by a richer lag structure than models proposed in Granger (1986) and Johansen (2008, 2009). We discuss the identification issues of the model of Avarucci (2007), following the ideas in Carlini and Santucci de Magistris (2014) for the model of Johansen (2008, 2009). We propose a 4-step estimation procedure that is based on the switching algorithm employed in Carlini and Mosconi (2014) and the GLS procedure in Mosconi and Paruolo (2014). The proposed procedure provides estimates of the long run parameters of the fractional cointegrated system that are consistent and unbiased, which we demonstrate by a Monte Carlo experiment. |
| Keywords: | Error correction model, Gaussian VAR model, Fractional Cointegration, Estimation algorithm, Maximum likelihood estimation, Switching Algorithm, Reduced Rank Regression |
| JEL: | C13 C32 |
| Date: | 2014–04–29 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2014-15&r=ets |
| By: | Mario Bonino; Matteo Camelia; Paolo Pigato |
| Abstract: | We study a bivariate mean reverting stochastic volatility model, finding an explicit expression for the decay of cross-asset correlations over time. We compare our result with the empirical time series of the Dow Jones Industrial Average and the Financial Times Stock Exchange 100 in the period 1984-2013, finding an excellent agreement. The main features of the model consist in the jumps in the volatilities and a nonlinear mean reversion. Based on these features, we propose an algorithm for the detection of jumps in the volatility. |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1404.7632&r=ets |
| By: | Hajo Holzmann; Matthias Eulert |
| Abstract: | Predictions are issued on the basis of certain information. If the forecasting mechanisms are correctly specified, a larger amount of available information should lead to better forecasts. For point forecasts, we show how the effect of increasing the information set can be quantified by using strictly consistent scoring functions, where it results in smaller average scores. Further, we show that the classical Diebold-Mariano test, based on strictly consistent scoring functions and asymptotically ideal forecasts, is a consistent test for the effect of an increase in a sequence of information sets on $h$-step point forecasts. For the value at risk (VaR), we show that the average score, which corresponds to the average quantile risk, directly relates to the expected shortfall. Thus, increasing the information set will result in VaR forecasts which lead on average to smaller expected shortfalls. We illustrate our results in simulations and applications to stock returns for unconditional versus conditional risk management as well as univariate modeling of portfolio returns versus multivariate modeling of individual risk factors. The role of the information set for evaluating probabilistic forecasts by using strictly proper scoring rules is also discussed. |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1404.7653&r=ets |
| By: | Stefan Skowronek; Stanislav Volgushev; Tobias Kley; Holger Dette; Marc Hallin |
| Keywords: | time series; spectral analysis; periodogram; quantile regression; copulas; ranks; local stationarity |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/159999&r=ets |
| By: | Hännikäinen, Jari |
| Abstract: | This paper analyzes the relative performance of multi-step forecasting methods in the presence of breaks and data revisions. Our Monte Carlo simulations indicate that the type and the timing of the break affect the relative accuracy of the methods. The iterated method typically performs the best in unstable environments, especially if the parameters are subject to small breaks. This result holds regardless of whether data revisions add news or reduce noise. Empirical analysis of real-time U.S. output and inflation series shows that the alternative multi-step methods only episodically improve upon the iterated method. |
| Keywords: | structural breaks, multi-step forecasting, intercept correction, real-time data |
| JEL: | C22 C53 C82 |
| Date: | 2014–05–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:55816&r=ets |
| By: | YONGMIAO HONG; YOON-JIN LEE |
| Abstract: | Economic theories in time series contexts usually have implications on and only on the conditional mean dynamics of underlying economic variables. We propose a new class of specification tests for time series conditional mean models, where the dimension of the conditioning information set may be infinite. Both linear and nonlinear conditional mean specifications are covered. The tests can detect a wide range of model misspecifications in mean while being robust to conditional heteroscedasticity and higher order time-varying moments of unknown form. They check a large number of lags, but naturally discount higher order lags, which is consistent with the stylized fact that economic behaviours are more affected by the recent past events than by the remote past events. No specific estimation method is required, and the tests have the appealing “nuisance parameter free†property that parameter estimation uncertainty has no impact on the limit distribution of the tests. A simulation study shows that it is important to take into account the impact of conditional heteroscedasticity; failure to do so will cause overrejection of a correct conditional mean model. In a horse race competition on testing linearity in mean, our tests have omnibus and robust power against a variety of alternatives relative to some existing tests. In an application, we find that after removing significant but possibly spurious autocorrelations due to nonsynchronous trading, there still exists significant predictable nonlinearity in mean for S&P 500 and NASDAQ daily returns. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002062&r=ets |
| By: | Ching-Kang Ing; Chor-Yiu Sin |
| Abstract: | In this article asymptotic expressions for the final prediction error (FPE) and the accumulated prediction error (APE) of the least squares predictor are obtained in regression models with nonstationary regressors. It is shown that the term of order 1/n in FPE and the term of order log n in APE share the same constant, where n is the sample size. Since the model includes the random walk model as a special case, these asymptotic expressions extend some of the results in Wei (1987) and Ing (2001). In addition, we also show that while the FPE of the least squares predictor is not affected by the contemporary correlation between the innovations in input and output variables, the mean squared error of the least squares estimate does vary with this correlation. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002063&r=ets |
| By: | Cheng Hsiao; Siyan Wang |
| Abstract: | We consider the estimation of a structural vector autoregressive model of nonstationary and possibly cointegrated variables without the prior knowledge of unit roots or rank of cointegration. We propose two modified two-stage least-squares estimators that are consistent and have limiting distributions that are either normal or mixed normal. Limited Monte Carlo studies are also conducted to evaluate their finite sample properties. r 2005 Elsevier B.V. All rights reserved. |
| Keywords: | Structural vector autoregression; Unit root; Cointegration; Asymptotic properties; Hypothesis testing |
| JEL: | C32 C12 C13 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002065&r=ets |
| By: | Yongmiao Hong; Yoon-Jin Lee |
| Abstract: | Dynamic economic theories usually have implications on and only on the conditional mean dynamics of economic processes. Using a generalized spectral derivative approach, Hong and Lee (2005, Review of Economic Studies 72, 499–541) recently proposed a new class of omnibus nonparametric specification tests for linear and nonlinear time series conditional mean models, where the dimension of the conditioning information set may be infinite. The tests can detect a wide range of model misspecifications in mean while being robust to conditional heteroskedasticity and time-varying higher order moments of unknown form. They enjoy an asymptotic “nuisance parameter–free†property in the sense that parameter estimation uncertainty has no impact on the asymptotic N(0,1) distribution of the test statistics As a result, only the estimated residuals from the null parametric model are needed to implement the tests, and no specific estimation is required. Although parameter estimation uncertainty has no impact on the asymptotic distribution of the tests, it may have significant impact on the finite-sample distribution, and such an impact may become more substantial as the number of estimated parameters increases In this paper, we adopt the Wooldridge (1990, Econometric Theory 6, 17– 43) device for parametric m-tests to the Hong and Lee (2005) nonparametric tests to reduce the impact of parameter estimation uncertainty Asymptotic size and power properties of the modified tests are investigated, and simulation studies show that the modified tests generally have better sizes in finite samples and are robust to parameter estimation uncertainty In the meantime, the size improvement does not cause loss of power against a wide range of alternatives when using the empirical critical values for the tests. These results suggest that the modified generalized spectral derivative tests can be a useful tool in time series conditional mean modeling. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002069&r=ets |
| By: | Zongwu Cai; Qi Li; Joon Y. Park |
| Abstract: | This paper studies functional coefficient regression models with nonstationary time series data, allowing also for stationary covariates. A local linear fitting scheme is developed to estimate the coefficient functions. The asymptotic distributions of the estimators are obtained, showing different convergence rates for the stationary and nonstationary covariates. A two-stage approach is proposed to achieve estimation optimality in the sense of minimizing the asymptotic mean squared error.When the coefficient function is a function of a nonstationary variable, the new findings are that the asymptotic bias of its nonparametric estimator is the same as the stationary covariate case but convergence rate differs, and further, the asymptotic distribution is a mixed normal, associated with the local time of a standard Brownian motion. The asymptotic behavior at boundaries is also investigated. |
| Keywords: | Nonstationary; Nonlinearity; Semiparametric estimation. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002096&r=ets |
| By: | Sung Y. Park; Anil K. Bera |
| Abstract: | In many applications, it has been found that the autoregressive conditional heteroskedasticity (ARCH) model under the conditional normal or Student’s t distributions are not general enough to account for the excess kurtosis in the data. Moreover, asymmetry in the financial data is rarely modeled in a systematic way. In this paper, we suggest a general density function based on the maximum entropy (ME) approach that takes account of asymmetry, excess kurtosis and also of high peakedness. The ME principle is based on the efficient use of available information, and as is well known, many of the standard family of distributions can be derived from the ME approach. We demonstrate how we can extract information functional from the data in the form of moment functions. We also propose a test procedure for selecting appropriate moment functions. Our procedure is illustrated with an application to the NYSE stock returns. The empirical results reveal that the ME approach with a fewer moment functions leads to a model that captures the stylized facts quite effectively. |
| Keywords: | Maximum entropy density; ARCH models; Excess kurtosis; Asymmetry; Peakedness of distribution; Stock returns data |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002099&r=ets |
| By: | Yongmiao Hong; Yoon-Jin Lee |
| Abstract: | We develop a general theory to test correct specification of multiplicative error models of non-negative time-series processes, which include the popular autoregressive conditional duration (ACD) models. Both linear and nonlinear conditional expectation models are covered, and standardized innovations can have time-varying conditional dispersion and higher-order conditional moments of unknown form. No specific estimation method is required, and the tests have a convenient null asymptotic N(0,1) distribution. To reduce the impact of parameter estimation uncertainty in finite samples, we adopt Wooldridge’s (1990a) device to our context and justify its validity. Simulation studies show that in the context of testing ACD models, finite sample correction gives better sizes in finite samples and are robust to parameter estimation uncertainty. And, it is important to take into account timevarying conditional dispersion and higher-order conditional moments in standardized innovations; failure to do so can cause strong overrejection of a correctly specified ACD model. The proposed tests have reasonable power against a variety of popular linear and nonlinear ACD alternatives. |
| Keywords: | Autoregressive conditional duration; dispersion clustering; finite sample correction; generalized spectral derivative; nonlinear time series; parameter estimation uncertainty; Wooldridge’s Device |
| JEL: | C4 C2 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002120&r=ets |
| By: | Hongquan Li; Yongmiao Hong |
| Abstract: | The classical volatility models, such as GARCH, are return-based models, which are constructed with the data of closing prices. It might neglect the important intraday information of the price movement, and will lead to loss of information and efficiency. This study introduces and extends the range-based autoregressive volatility model to make up for these weaknesses. The empirical results consistently show that the new model successfully captures the dynamics of the volatility and gains good performance relative to GARCH model. |
| Keywords: | Volatility modeling; Price range; Forecasting performance; Intraday information;�GARCH |
| JEL: | G32 C01 C53 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002128&r=ets |
| By: | Nadine McCloud; Yongmiao Hong |
| Abstract: | We introduce a class of generally applicable specification tests for constant and dynamic structures of conditional correlations in multivariate GARCH models. The tests are robust to the presence of time-varying higher-order conditional moments of unknown form and are pure significance tests. The tests can identify linear and nonlinear misspecifications in conditional correlations. Our approach does not necessitate a particular parameter estimation method and distributional assumption on the error process. The asymptotic distribution of the tests is invariant to the uncertainty in parameter estimation. We assess the finite sample performance of our tests using simulated and real data. |
| Keywords: | Constant conditional correlation; Dynamic conditional correlation; Generalized cross-spectrum; Financial Econometrics; Multivariate GARCH model; Specification testing. |
| JEL: | C12 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002141&r=ets |
| By: | Bin Chen; Yongmiao Hong |
| Abstract: | The Markov property is a fundamental property in time series analysis and is often assumed in economic and �nancial modelling. We develop a new test for the Markov property using the conditional characteristic function embedded in a frequency domain approach, which checks the implication of the Markov property in every conditional moment (if exists) and over many lags. The proposed test is applicable to both univariate and multivariate time series with discrete or continuous distributions. Simulation studies show that with the use of a smoothed nonparametric transition density-based bootstrap procedure, the proposed test has reasonable sizes and all-around power against several popular non-Markov alternatives in �nite samples. We apply the test to a number of �nancial time series and �nd some evidence against the Markov property. |
| Keywords: | Conditional characteristic function, Generalized cross-spectrum, Markov property, Smoothed nonparametric bootstrap |
| JEL: | C1 C4 G0 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002143&r=ets |
| By: | Haiqiang Chen; Terence Tai-Leung Chong; Jushan Bai |
| Abstract: | A growing body of threshold models has been developed over the past two decades to capture the nonlinear movement of financial time series. Most of these models, however, contain a single threshold variable only. In many empirical applications, models with two or more threshold variables are needed. This article develops a new threshold autoregressive model which contains two threshold variables. A likelihood ratio test is proposed to determine the number of regimes in the model. The finite-sample performance of the estimators is evaluated and an empirical application is provided. |
| Keywords: | Bootstrapping; Likelihood ratio test; Misspecification; Threshold autoregressive model. |
| JEL: | C22 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002152&r=ets |
| By: | Bing-Yi Jing; Cui-Xia Li; Zhi Liu |
| Abstract: | In this paper, we consider the estimation of covariation of two asset prices which contain jumps and microstructure noise, based on high frequency data. We propose a realized covariance estimator, which combines pre-averaging method to remove the microstructure noise and the threshold method to reduce the jumps effect. The asymptotic properties, such as consistency and asymptotic normality, are investigated. The estimator allows very general structure of jumps, for example, binfinity activity or even infinity variation. Simulation is also included to illustrate the performance of the proposed procedure. |
| Keywords: | Ito semi-martingale; High frequency data; Microstructure noise; Covolatility; Jumps; Central limit theorem. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002161&r=ets |
| By: | Muyi Li; Wai Keung Li; Guodong Li |
| Abstract: | We propose a new volatility model, which is called the mixture memory GARCH (MM-GARCH) model. The MM-GARCH model has two mixture components, of which one is a short memory GARCH and the other is the long memory FIGARCH. The new model, a special ARCH(∞) process with random coefficients, possesses both the properties of long memory volatility and covariance stationarity. The existence of its stationary solution is discussed. A dynamic mixture of the proposed model is also introduced. Other issues, such as the EM algorithm as a parameter estimation procedure, the observed information matrix which is relevant in calculating the theoretical standard errors, and a model selection criterion are also investigated. Monte Carlo experiments demonstrate our theoretical findings. Empirical application of the MM-GARCH model to the daily S&P 500 index illustrates its capabilities. |
| Keywords: | long memory in volatility, covariance stationarity, mixture ARCH(∞), EM algorithm. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002190&r=ets |
| By: | Haiqiang Chen |
| Abstract: | This paper studies the robust estimation and inference of threshold models with integrated regressors. We derive the asymptotic distribution of the profiled least squares (LS) estimator under the diminishing threshold effect assumption that the size of the threshold effect converges to zero. Depending on how rapidly this sequence converges, the model may be identified or only weakly identified and asymptotic theorems are developed for both cases. As the convergence rate is unknown in practice, a model-selection procedure is applied to determine the model identification strength and to construct robust confidence intervals, which have the correct asymptotic size irrespective of the magnitude of the threshold effect. The model is then generalized to incorporate endogeneity and serial correlation in error terms, under which, we design a Cochrane-Orcutt feasible generalized least squares (FGLS) estimator which enjoys efficiency gains and robustness against different error specifications, including both I(0) and I(1) errors. Based on this FGLS estimator, we further develop a sup-Wald statistic to test for the existence of the threshold effect. Monte Carlo simulations show that our estimators and test statistics perform well. |
| Keywords: | Threshold effects; Integrated processes; Nonlinear cointegration; Weak identification. |
| JEL: | C12 C22 C52 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002203&r=ets |
| By: | Cindy Shin-Huei Wang; Luc Bauwens; Cheng Hsiao |
| Abstract: | We develop an easy-to-implement method for forecasting a stationary autoregressive fractionally integrated moving average (ARFIMA) process subject to structural breaks with unknown break dates. We show that an ARFIMA process subject to a mean shift and a change in the long memory parameter can be well approximated by an autoregressive (AR) model and suggest using an information criterion (AIC or Mallows’ Cp) to choose the order of the approximate AR model. Our method avoids the issue of estimation inaccuracy of the long memory parameter and the issue of spurious breaks in finite sample. Insights from our theoretical analysis are confirmed by Monte Carlo experiments, through which we also find that our method provides a substantial improvement over existing prediction methods. An empirical application to the realized volatility of three exchange rates illustrates the usefulness of our forecasting procedure. The empirical success of the HAR-RV model can be explained, from an econometric perspective, by our theoretical and simulation results. |
| Keywords: | Forecasting, Long memory process, Structural break, HAR model |
| JEL: | C22 C53 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002213&r=ets |
| By: | Bin Chen; Yongmiao Hong |
| Abstract: | Detecting and modelling structural changes in GARCH processes have attracted increasing attention in time series econometrics. In this paper, we propose a new approach to testing structural changes in GARCH models. The idea is to compare the log likelihoods of a time-varying parameter GARCH model and a constant parameter GARCH model, where the time-varying GARCH parameters are estimated by a local quasi-maximum likelihood estimator (QMLE) and the constant GARCH parameters are estimated by a standard QMLE. The test does not require any prior information about the alternatives of structural changes. It has an asymptotic N(0,1) distribution under the null hypothesis of parameter constancy and is consistent against a vast class of smooth structural changes as well as abrupt structural breaks with possibly unknown break points. A consistent parametric bootstrap is employed to provide a reliable inference infinite samples and the simulation study highlights the merits of our approach. |
| Keywords: | GARCH, Local smoothing, Parameter constancy, QMLE, Smooth structural change |
| JEL: | C1 C4 E0 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002019&r=ets |
| By: | Bin Chen; Yongmiao Hong |
| Abstract: | Modeling conditional distributions in time series has attracted increasing attention in economics and finance. We develop a new class of generalized Cramer-von Mises (GCM) specification tests for time series conditional distribution models using a novel approach, which embeds the empirical distribution function in a spectral framework. Our tests check a large number of lags and are therefore expected to be powerful against neglected dynamics at higher order lags, which is particularly useful for nonMarkovian processes. Despite using a large number of lags, our tests do not suffer much from loss of a large number of degrees of freedom, because our approach naturally downweights higher order lags, which is consistent with the stylized fact that economic or financial markets are more affected by recent past events than by remote past events. Unlike the existing methods in the literature, the proposed GCM tests cover both univariate and multivariate conditional distribution models in a unified framework. They exploit the information in the joint conditional distribution of underlying economic processes. Moreover, a class of easy-to-interpret diagnostic procedures are supplemented to gauge possible sources of model misspecifications. Distinct from conventional CM and Kolmogorov-Smirnov (KS) tests, which are also based on the empirical distribution function, our GCM test statistics follow a convenient asymptotic N (0; 1) distribution and enjoy the appealing "nuisance parameter free" property that parameter estimation uncertainty has no impact on the asymptotic distribution of the test statistics. Simulation studies show that the tests provide reliable inference for sample sizes often encountered in economics and finance. |
| Keywords: | Diagnostic procedure, Empirical distribution function, Frequency domain, Generalized Cramer-von Mises test, Kernel method, Non-Markovian process, Time series conditional distribution model |
| JEL: | C4 G0 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002024&r=ets |
| By: | Ming Lin; Changjiang Liu; Linlin Niu |
| Abstract: | The Wishart autoregressive (WAR) process is a powerful tool to model multivariate stochastic volatility (MSV) with correlation risk and derive closed-form solutions in various asset pricing models. However, making inferences of the WAR stochastic volatility (WAR-SV) model is challenging because the latent volatility series does not have a closed-form transition density. Based on an alternative representation of the WAR process with lag order p=1 and integer degrees of freedom, we develop an effective two-step procedure to estimate parameters and the latent volatility series. The procedure can be applied to study other varying-dimension problems. We show the effectiveness of this procedure with a simulated example. Then this method is used to study the time-varying correlation of US and China stock market returns. |
| Keywords: | Bayesian posterior probability, Markov chain Monte Carlo, Multivariate stochastic volatility, Sequential Monte Carlo, Wishart autoregressive process |
| JEL: | G13 G17 C11 C58 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002054&r=ets |