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on Econometric Time Series |
| By: | esposito, francesco paolo; cummins, mark |
| Abstract: | In this article we use a partial integral-differential approach to construct and extend a non-linear filter to include jump components in the system state. We employ the enhanced filter to estimate the latent state of multivariate parametric jump-diffusions. The devised procedure is flexible and can be applied to non-affine diffusions as well as to state dependent jump intensities and jump size distributions. The particular design of the system state can also provide an estimate of the jump times and sizes. With the same approch by which the filter has been devised, we implement an approximate likelihood for the parameter estimation of models of the jump-diffusion class. In the development of the estimation function, we take particular care in designing a simplified algorithm for computing. The likelihood function is then characterised in the application to stochastic volatility models with jumps. In the empirical section we validate the proposed approach via Monte Carlo experiments. We deal with the volatility as an intrinsic latent factor, which is partially observable through the integrated variance, a new system state component that is introduced to increase the filtered information content, allowing a closer tracking of the latent volatility factor. Further, we analyse the structure of the measurement error, particularly in relation to the presence of jumps in the system. In connection to this, we detect and address an issue arising in the update equation, improving the system state estimate. |
| Keywords: | latent state-variables, non-linear filtering, finite difference method, multi-variate jump-diffusions, likelihood estimation |
| JEL: | C13 |
| Date: | 2015–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:64987&r=ets |
| By: | Christopher G. Gibbs (School of Economics, UNSW Business School, UNSW) |
| Abstract: | This paper proposes a new dynamic forecast combination strategy for forecasting inflation. The procedure draws on explanations of why the forecast combination puzzle exists and the stylized fact that Phillips curve forecasts of inflation exhibit significant time-variation in forecast accuracy. The forecast combination puzzle is the empirical observation that a simple average of point forecasts is often the best forecasting strategy. The forecast combination puzzle exists because many dynamic weighting strategies tend to shift weights toward Phillips curve forecasts after they exhibit a significant period of relative forecast improvement, which is often when their forecast accuracy begins to deteriorate. The proposed strategy in this paper weights forecasts according to their expected performance rather than their past performance to anticipate these changes in forecast accuracy. The forward-looking approach is shown to robustly beat equal weights combined and benchmark univariate forecasts of inflation in real-time out-of-sample exercises on U.S. and New Zealand inflation data. |
| Keywords: | Forecast combination, inflation, forecast pooling, forecast combination puzzle, Phillips curve |
| JEL: | E17 E47 C53 |
| Date: | 2015–04 |
| URL: | http://d.repec.org/n?u=RePEc:swe:wpaper:2015-09&r=ets |
| By: | Naoto Kunitomo (Faculty of Economics, The University of Tokyo); Seisho Sato (Faculty of Economics, The University of Tokyo) |
| Abstract: | The use of seasonally adjusted (official) data may have statistical problem because it is a common practice to use <i>X-12-ARIMA</i> in <i>the official seasonal adjustment</i>, which adopts the univariate ARIMA time series modeling with some renements. Instead of using the seasonally adjusted data, for estimating the structural parameters and relationships among non-stationary economic time series with seasonality and noise, we propose a new method called the Separating Information Maximum Likelihood (SIML) estimation. We show that the SIML estimation can identify the nonstationary trend, the seasonality and the noise components, which have been observed in many macro-economic time series, and recover the structural parameters and relationships among the non-stationary trends with seasonality. The SIML estimation is consistent and it has the asymptotic normality when the sample size is large. Based on simulations, we nd that the SIML estimator has reasonable nite sample properties and thus it would be useful for practice. -- |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2015cf977&r=ets |
| By: | Abdelkamel Alj; Christophe Ley; Guy Melard |
| Keywords: | non-stationary process; multivariate time series; time-varying models |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/200183&r=ets |
| By: | W. Robert Reed (University of Canterbury) |
| Abstract: | This paper demonstrates that unit root tests can suffer from inflated Type I error rates when data are cointegrated. Results from Monte Carlo simulations show that three commonly used unit root tests – the ADF, Phillips-Perron, and DF-GLS tests – frequently overreject the true null of a unit root for at least one of the cointegrated variables. The reason for this overrejection is that unit root tests, designed for random walk data, are often misspecified when data are cointegrated. While the addition of lagged differenced (LD) terms can eliminate the size distortion, this “success” is spurious, driven by collinearity between the lagged dependent variable and the LD explanatory variables. Accordingly, standard diagnostics such as (i) testing for serial correlation in the residuals and (ii) using information criteria to select among different lag specifications are futile. The implication of these results is that researchers should be conservative in the weight |
| Keywords: | Unit root testing, cointegration, DF-GLS test, Augmented Dickey-Fuller test, Phillips-Perron test, simulation |
| JEL: | C32 C22 C18 |
| Date: | 2015–05–30 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:15/11&r=ets |
| By: | Rasmus Søndergaard Pedersen (University of Copenhagen); Anders Rahbek (University of Copenhagen and CREATES) |
| Abstract: | Consistency and asymptotic normality are established for the maximum likelihood estimators in the nonstationary ARCH and GARCH models with general t-distributed innovations. The results hold for joint estimation of (G)ARCH effects and the degrees of freedom parameter parametrizing the t-distribution. With T denoting sample size, classic square-root T-convergence is shown to hold with closed form expressions for the multivariate covariances. |
| Keywords: | ARCH, GARCH, asymptotic normality, asymptotic theory, consistency, t-distribution, maximum likelihood, nonstationarity |
| JEL: | C32 |
| Date: | 2015–04–10 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2015-27&r=ets |
| By: | Joshua C.C. Chan; Eric Eisenstat |
| Abstract: | Empirical work in macroeconometrics has been mostly restricted to using VARs, even though there are strong theoretical reasons to consider general VARMAs. A number of articles in the last two decades have conjectured that this is because estimation of VARMAs is perceived to be challenging and proposed various ways to simplify it. Nevertheless, VARMAs continue to be largely dominated by VARs, particularly in terms of developing useful extensions. We address these computational challenges with a Bayesian approach. Specifically, we develop a Gibbs sampler for the basic VARMA, and demonstrate how it can be extended to models with time-varying VMA coefficients and stochastic volatility. We illustrate the methodology through a macroeconomic forecasting exercise. We show that in a class of models with stochastic volatility, VARMAs produce better density forecasts than VARs, particularly for short forecast horizons. |
| Keywords: | state space, stochastic volatility, factor model, macroeconomic forecasting, density forecast |
| JEL: | C11 C32 C53 |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2015-19&r=ets |
| By: | Joshua C.C. Chan; Angelia L. Grant |
| Abstract: | We compare a number of GARCH and stochastic volatility (SV) models using nine series of oil, petroleum product and natural gas prices in a formal Bayesian model comparison exercise. The competing models include the standard models of GARCH(1,1) and SV with an AR(1) log-volatility process and more flexible models with jumps, volatility in mean and moving average innovations. We find that: (1) SV models generally compare favorably to their GARCH counterparts; (2) the jump component substantially improves the performance of the standard GARCH, but is unimportant for the SV model; (3) the volatility feedback channel seems to be superfluous; and (4) the moving average component markedly improves the fit of both GARCH and SV models. Overall, the SV model with moving average innovations is the best model for all nine series. |
| Keywords: | Bayesian model comparison, crude oil, natural gas, moving average, jumps |
| JEL: | C11 C52 Q41 |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2015-20&r=ets |
| By: | Dan Xu; Christian Beck |
| Abstract: | Share price returns on different time scales can be well modelled by a superstatistical dynamics. Here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales. It is shown that while chi-square superstatistics works well on a time scale of days, on a much smaller time scale of minutes the price changes are better described by lognormal superstatistics. The system dynamics thus exhibits a transition from lognormal to chi-square superstatistics as a function of time scale. We discuss a more general model interpolating between both statistics which fits the observed data very well. We also present results on correlation functions of the extracted superstatistical volatility parameter, which exhibits exponential decay for returns on large time scales, whereas for returns on small time scales there are long-range correlations and power-law decay. |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1506.01660&r=ets |
| By: | Chevillon, Guillaume (ESSEC Business School); Hecq , Alain (Maastricht University (Department of Quantitative Economics)); Laurent, Sébastien (Aix-Marseille University (Aix-Marseille School of Economics)) |
| Abstract: | This paper shows that large dimensional vector autoregressive (VAR) models of fi nite order can generate long memory in the marginalized univariate series. We derive high-level assumptions under which the fi nal equation representation of a VAR(1) leads to univariate fractional white noises and verify the validity of these assumptions for two speci fic models. We consider the implications of our findings for the variances of asset returns where the so-called golden-rule of realized variances states that they tend always to exhibit fractional integration of a degree close to 0:4. |
| Keywords: | Long memory; Vector Autoregressive Model; Marginalization; Final Equation Representation; Volatility |
| JEL: | C10 C32 C58 |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:ebg:essewp:dr-15007&r=ets |
| By: | Violetta Dalla; Javier Hidalgo |
| Keywords: | Nonparametric regression, Breaks/smoothness, Strong dependence, Extreme-values distribution, Frequency domain bootstrap algorithms. |
| JEL: | C14 C22 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:cep:stiecm:/2015/584&r=ets |
| By: | Bent Jesper Christensen (Aarhus University and CREATES); Rasmus T. Varneskov (Aarhus University and CREATES) |
| Abstract: | This paper introduces a new estimator of the fractional cointegrating vector between stationary long memory processes that is robust to low-frequency contamination such as level shifts, i.e., structural changes in the means of the series, and deterministic trends. In particular, the proposed medium band least squares (MBLS) estimator uses sample dependent trimming of frequencies in the vicinity of the origin to account for such contamination. Consistency and asymptotic normality of the MBLS estimator are established, a feasible inference procedure is proposed, and rigorous tools for assessing the cointegration strength and testing MBLS against the existing narrow band least squares estimator are developed. Finally, the asymptotic framework for the MBLS estimator is used to provide new perspectives on volatility factors in an empirical application to long-span realized variance series for S&P 500 equities. |
| Keywords: | Deterministic Trends, Factor Models, Fractional Cointegration, Long Memory, Realized Variance, Semiparametric Estimation, Structural Change |
| JEL: | C12 C14 C32 C58 |
| Date: | 2015–05–27 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2015-25&r=ets |
| By: | Ulrich Hounyo (Oxford-Man Institute, University of Oxford, and Aarhus University and CREATES); Rasmus T. Varneskov (Aarhus University and CREATES) |
| Abstract: | We provide a new resampling procedure - the local stable bootstrap - that is able to mimic the dependence properties of realized power variations for pure-jump semimartingales observed at different frequencies. This allows us to propose a bootstrap estimator and inference procedure for the activity index of the underlying process, ß, as well as a bootstrap test for whether it obeys a jump-diffusion or a pure-jump process, that is, of the null hypothesis H0: ß=2 against the alternative H1: ß<2. We establish first-order asymptotic validity of the resulting bootstrap power variations, activity index estimator, and diffusion test for H0. Moreover, the finite sample size and power properties of the proposed diffusion test are compared to those of benchmark tests using Monte Carlo simulations. Unlike existing procedures, our bootstrap test is correctly sized in general settings. Finally, we illustrate use and properties of the new bootstrap diffusion test using high-frequency data on three FX series, the S&P 500, and the VIX. |
| Keywords: | Activity index, Bootstrap, Blumenthal-Getoor index, Confidence Intervals, Highfrequency Data, Hypothesis Testing, Realized Power Variation, Stable Processes |
| JEL: | C12 C14 C15 G1 |
| Date: | 2015–05–27 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2015-26&r=ets |