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on Econometric Time Series |
| By: | Mark Podolskij (University of Heidelberg and CREATES); Mathieu Rosenbaum (École Polytechnique Paris) |
| Abstract: | In practice, the choice of using a local volatility model or a stochastic volatility model is made according to their respective ability to fit implied volatility surfaces. In this paper, we adopt an opposite point of view. Indeed, based on historical data, we design a statistical procedure aiming at testing the assumption of a local volatility model for the price dynamics, against the alternative of a stochastic volatility model. |
| Keywords: | Local Volatility Models, Stochastic Volatility Models, Test Statistics, Semi-Martingales, Limit Theorems. |
| JEL: | C10 C13 C14 |
| Date: | 2011–01–13 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2011-04&r=ets |
| By: | Roxana Halbleib (European Center for Advanced Research in Economics and Statistics (ECARES), Université libre de Bruxelles, Solvay Brussels School of Economics and Management and CoFE); Valeri Voev (School of Economics and Management, Aarhus University and CREATES) |
| Abstract: | This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows for flexible dependence patterns for volatilities and correlations, and can be applied to covariance matrices of large dimensions. The separate modeling of volatility and correlation forecasts considerably reduces the estimation and measurement error implied by the joint estimation and modeling of covariance matrix dynamics. Our empirical results show that the new mixing approach provides superior forecasts compared to multivariate volatility specifications using single sources of information. |
| Keywords: | Volatility forecasting, High-frequency data, Realized variance |
| JEL: | C32 C53 G11 |
| Date: | 2011–01–18 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2011-03&r=ets |
| By: | Vasco Gabriel (University of Surrey and NIPE-UM, Portugal); Luis Martins (UNIDE, ISCTE-LUI, Portugal) |
| Abstract: | We examine the properties of several residual-based cointegration tests when long run parameters are subject to multiple shifts driven by an unobservable Markov process. Unlike earlier work, which considered one-off deterministic breaks, our approach has the advantage of allowing for an unspeci?ed number of stochastic breaks. We illustrate this issue by exploring the possibility of Markov switching cointegration in the stock-price dividend relationship and showing that this case is empirically relevant. Our subsequent Monte Carlo analysis reveals that standard cointegration tests are generally reliable, their performance often being robust for a number of plausible regime shift parameterizations. |
| Keywords: | Present value model, Cointegration tests, Markov switching |
| JEL: | C32 G12 E44 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:sur:surrec:0910&r=ets |
| By: | Morten Ørregaard Nielsen (Queen's University and CREATES) |
| Abstract: | This paper proves consistency and asymptotic normality for the conditional-sum-of-squares (CSS) estimator in fractional time series models. The models are parametric and quite general. The novelty of the consistency result is that it applies to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in probablity thus making the proof much more challenging than usual. The neighborhood around the critical point where uniform convergence fails is handled using a truncation argument. The only other consistency proof for such models that applies to an arbitrarily large set of admissible parameter values appears to be Hualde and Robinson (2010), who require all moments of the innovation process to exist. In contrast, the present proof requires only a few moments of the innovation process to be finite (four in the simplest case). Finally, all arguments, assumptions, and proofs in this paper are stated entirely in the time domain, which is somewhat remarkable for this literature. |
| Keywords: | Asymptotic normality, conditional-sum-of-squares estimator, consistency, fractional integration, fractional time series, likelihood inference, long memory, nonstationary, uniform convergence |
| JEL: | C22 |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1259&r=ets |
| By: | David Stephen Pollock |
| Abstract: | Discrete-time ARMA processes can be placed in a one-to-one correspondence with a set of continuous-time processes that are bounded in frequency by the Nyquist value of ? radians per sample period. It is well known that, if data are sampled from a continuous process of which the maximum frequency exceeds the Nyquist value, then there will be a problem of aliasing. However, if the sampling is too rapid, then other problems will arise that will cause the ARMA estimates to be severely biased. The paper reveals the nature of these problems and it shows how they may be overcome. It is argued that the estimation of macroeconomic processes may be compromised by a failure to take account of their limits in frequency. |
| Keywords: | Stochastic Differential Equations; Band-Limited Stochastic Processes; Oversampling |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:lec:leecon:11/14&r=ets |
| By: | David Stephen Pollock |
| Abstract: | A theory of band-limited linear stochastic processes is described and it is related to the familiar theory of ARMA models in discrete time. By ignoring the limitation on the frequencies of the forcing function, in the process of fitting a conventional ARMA model, one is liable to derive estimates that are severely biased. If the maximum frequency in the sampled data is less than the Nyquist value, then the underlying continuous function can be reconstituted by sinc function or Fourier interpolation. The estimation biases can be avoided by re-sampling the continuous process at a rate corresponding to the maximum frequency of the forcing function. Then, there is a direct correspondence between the parameters of the band-limited ARMA model and those of an equivalent continuous-time process. |
| Keywords: | Stochastic Differential Equations; Band-Limited Stochastic Processes; Aliasing and Interference |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:lec:leecon:11/11&r=ets |
| By: | David Stephen Pollock; Emi Mise |
| Abstract: | Alternative methods for the seasonal adjustment of economic data are described that operate in the time domain and in the frequency domain. The time-domain method, which employs a classical comb filter, mimics the effects of the model-based procedures of the SEATS–TRAMO and STAMP programs. The frequency-domain method eliminates the sinusoidal elements of which, in the judgment of the user, the seasonal component is composed. It is proposed that, in some circumstances, seasonal adjustment is best achieved by eliminating all elements in excess of the frequency that marks the upper limit of the trend-cycle component of the data. It is argued that the choice of the method seasonal adjustment is liable to affect the determination of the turning points of the business cycle. |
| Keywords: | Wiener–Kolmogorov Filtering; Frequency-Domain Methods; The Trend-Cycle Component |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:lec:leecon:11/12&r=ets |
| By: | Vogelsang, Timothy J. (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria); Wagner, Martin (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria) |
| Abstract: | This paper is concerned with parameter estimation and inference in a cointegrating regression, where as usual endogenous regressors as well as serially correlated errors are considered. We propose a simple, new estimation method based on an augmented partial sum (integration) transformation of the regression model. The new estimator is labeled Integrated Modified Ordinary Least Squares (IM-OLS). IM-OLS is similar in spirit to the fully modified approach of Phillips and Hansen (1990) with the key difference that IM-OLS does not require estimation of long run variance matrices and avoids the need to choose tuning parameters (kernels, bandwidths, lags). Inference does require that a long run variance be scaled out, and we propose traditional and fixed-b methods for obtaining critical values for test statistics. The properties of IM-OLS are analyzed using asymptotic theory and finite sample simulations. IM-OLS performs well relative to other approaches in the literature. |
| Keywords: | Bandwidth, cointegration, fixed-b asymptotics, Fully Modified OLS, IM-OLS, kernel |
| JEL: | C31 C32 |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihsesp:263&r=ets |
| By: | Roxana Halbleib; Valerie Voev |
| Abstract: | This paper analyzes the forecast accuracy of the multivariate realized volatility model introduced by Chiriac and Voev (2010), subject to different degrees of model parametrization and economic evaluation criteria. By modelling the Cholesky factors of the covariance matrices, the model generates positive definite, but biased covariance forecasts. In this paper, we provide empirical evidence that parsimonious versions of the model generate the best covariance forecasts in the absence of bias correction. Moreover, we show by means of stochastic dominance tests that any risk averse investor, regardless of the type of utility function or return distribution, would be better-off from using this model than from using some standard approaches. |
| Keywords: | Forecasting; Fractional integration; Stochastic dominance; Portfolio optimization; Realized covariance |
| JEL: | C32 C53 G11 |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/73585&r=ets |
| By: | Roxana Halbleib |
| Abstract: | This note solves the puzzle of estimating degenerate Wishart Autoagressive processes, introduced by Gourieroux, Jasiak and Sufana (2009)to model multivariate stochastic volatility. It derives the asymptotic and empirical properties of the Method of Moment estimator of the Wishart degrees of freedom subject to different stationarity asumptions and specific distributional settings of the underlying processes. |
| Keywords: | Wishart autoagressive process; asymptotic properties; realized covariance; log-normal distribution |
| JEL: | C32 C46 C51 |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/73606&r=ets |
| By: | Gianluca Cubadda (:Faculty of Economics, University of Rome "Tor Vergata"); Umberto Triacca (Università dell'Aquila) |
| Abstract: | This note concerns with the marginal models associated with a given vector autoregressive model. In particular, it is shown that a reduction in the orders of the univariate ARMA marginal models can be determined by the presence of variables integrated with different orders. The concepts and methods of the paper are illustrated via an empirical investigation of the low-frequency properties of hours worked in the US. |
| Keywords: | VAR Models; ARIMA Models; Final Equations |
| JEL: | C32 |
| Date: | 2011–01–24 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:184&r=ets |
| By: | Jouchi Nakajima (Department of Statistical Science, Duke University); Tsuyoshi Kunihama (Department of Statistical Science, Duke University); Yasuhiro Omori (Faculty of Economics, University of Tokyo); Sylvia Fruhwirth-Schnatter (Department of Applied Statistics, Johannes Kepler University Linz) |
| Abstract: | A new state space approach is proposed to model the time-dependence in an extreme value process. The generalized extreme value distribution is extended to incorporate the time-dependence using a state space representation where the state variables either fol- low an autoregressive (AR) process or a moving average (MA) process with innovations arising from a Gumbel distribution. Using a Bayesian approach, an efficient algorithm is proposed to implement Markov chain Monte Carlo method where we exploit an accu- rate approximation of the Gumbel distribution by a ten-component mixture of normal distributions. The methodology is illustrated using extreme returns of daily stock data. The model is tted to a monthly series of minimum returns and the empirical results support strong evidence of time-dependence among the observed minimum returns. |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2010cf782&r=ets |
| By: | Zhu, Junjun; Xie, Shiyu |
| Abstract: | We construct one triple-threshold GARCH model to analyze the asymmetric response of mean and conditional volatility. In parameter estimation, we apply Griddy-Gibbs sampling method, which require less work in selection of starting values and pre-run. As we apply this model in Chinese stock market, we find that 12-days-average return plays an important role in defining different regimes. While the down regime is characterized by negative 12-days-average return, the up regime has positive 12-days-average return. The conditional mean responds differently between down and up regime. In down regime, the return at date t is affected negatively by lag 2 negative return, while in up regime the return responds significantly to both positive and negative lag 1 past return. Moreover, our model shows that volatility reacts asymmetrically to positive and negative innovations, and this asymmetric reaction varies between down and up regimes. In down regime, volatility becomes more volatile when negative innovation impacts the market than when positive one does, while in up regime positive innovation leads to more volatile market than negative one. |
| Keywords: | Threshold; Griddy-Gibbs sampling; MCMC method; GARCH |
| JEL: | G15 C22 C11 |
| Date: | 2010–06–18 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:28195&r=ets |
| By: | Ardia, David; Lennart, Hoogerheide; Nienke, Corré |
| Abstract: | Using well-known GARCH models for density prediction of daily S&P 500 and Nikkei 225 index returns, a comparison is provided between frequentist and Bayesian estimation. No significant difference is found between the qualities of the forecasts of the whole density, whereas the Bayesian approach exhibits significantly better left-tail forecast accuracy. |
| Keywords: | GARCH; Bayesian; KLIC; censored likelihood |
| JEL: | C52 C22 C11 |
| Date: | 2011–01–17 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:28259&r=ets |
| By: | Pötscher, Benedikt M. |
| Abstract: | Bounds on the order of magnitude of sums of negative powers of integrated processes are derived. |
| Keywords: | integrated proesses; sums of negative powers; order of magnitude; martingale transform |
| JEL: | C22 |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:28287&r=ets |
| By: | Buss, Ginters |
| Abstract: | The paper proposes an extension of the symmetric Baxter-King band pass filter to an asymmetric Baxter-King filter. The optimal correction scheme of the ideal filter weights is the same as in the symmetric version, i.e, cut the ideal filter at the appropriate length and add a constant to all filter weights to ensure zero weight on zero frequency. Since the symmetric Baxter-King filter is unable to extract the desired signal at the very ends of the series, the extension to an asymmetric filter is useful whenever the real time estimation is needed. The paper uses Monte Carlo simulation to compare the proposed filter's properties in extracting business cycle frequencies to the ones of the original Baxter-King filter and Christiano-Fitzgerald filter. Simulation results show that the asymmetric Baxter-King filter is superior to the asymmetric default specification of Christiano-Fitzgerald filter in real time signal extraction exercises. |
| Keywords: | real time estimation; Christiano-Fitzgerald filter; Monte Carlo simulation; band pass filter |
| JEL: | C13 C22 C15 |
| Date: | 2011–01–17 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:28176&r=ets |
| By: | Ulrich K. Müller; James H. Stock |
| Abstract: | We propose a Bayesian procedure for exploiting small, possibly long-lag linear predictability in the innovations of a finite order autoregression. We model the innovations as having a log-spectral density that is a continuous mean-zero Gaussian process of order 1/√T. This local embedding makes the problem asymptotically a normal-normal Bayes problem, resulting in closed-form solutions for the best forecast. When applied to data on 132 U.S. monthly macroeconomic time series, the method is found to improve upon autoregressive forecasts by an amount consistent with the theoretical and Monte Carlo calculations. |
| JEL: | C11 C22 C32 |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:16714&r=ets |