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on Econometric Time Series |
| By: | H. Peter Boswijk (University of Amsterdam); Michael Jansson (UC Berkeley and CREATES); Morten Ørregaard Nielsen (Queen's University and CREATES) |
| Abstract: | We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but of course the asymptotic results apply more generally. The power gains relative to existing tests are due to two factors. First, instead of basing our tests on the conditional (with respect to the initial observations) likelihood, we follow the recent unit root literature and base our tests on the full likelihood as in, e.g., Elliott, Rothenberg, and Stock (1996). Secondly, our tests incorporate a ?sign?restriction which generalizes the one-sided unit root test. We show that the asymptotic local power of the proposed tests dominates that of existing cointegration rank tests. |
| Keywords: | Cointegration rank, efficiency, likelihood ratio test, vector autoregression |
| JEL: | C12 C32 |
| Date: | 2012–09–19 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-39&r=ets |
| By: | Pier Paolo Peiranno (CFM - Capital Fund Management - Capital Fund Management); Damien Challet (MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris) |
| Abstract: | Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently proposed a powerful and consistent way to build a model describing the time evolution of a financial index. We first make it fully explicit by using Student distributions instead of power law-truncated Lévy distributions and show that the analytic tractability of the model extends to the larger class of symmetric generalized hyperbolic distributions and provide a full computation of their multivariate characteristic functions; more generally, we show that the stochastic processes arising in this framework are representable as mixtures of Wiener processes. The basic Baldovin and Stella model, while mimicking well volatility relaxation phenomena such as the Omori law, fails to reproduce other stylized facts such as the leverage effect or some time reversal asymmetries. We discuss how to modify the dynamics of this process in order to reproduce real data more accurately. |
| Keywords: | Stochastic volatility model, long memory, stylized fact, fat tails |
| Date: | 2012–08–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-00734355&r=ets |
| By: | Markku Lanne (Department of Political and Economic Studies, University of Helsinki); Mika Meitz (Department of Economics, Koç University); Pentti Saikkonen (Department of Mathematics and Statistics, University of Helsinki) |
| Abstract: | We develop likelihood-based tests for autocorrelation and predictability in a first order non-Gaussian and noninvertible ARMA model. Tests based on a special case of the general model, referred to as an all-pass model, are also obtained. Data generated by an all-pass process are uncorrelated but, in the non-Gaussian case, dependent and nonlinearly predictable. Therefore, in addition to autocorrelation the proposed tests can also be used to test for nonlinear predictability. This makes our tests different from their previous counterparts based on conventional invertible ARMA models. Unlike in the invertible case, our tests can also be derived by standard methods that lead to chi-squared or standard normal limiting distributions. A further convenience of the noninvertible ARMA model is that, to some extent, it can allow for conditional heteroskedasticity in the data which is useful when testing for predictability in economic and financial data. This is also illustrated by our empirical application to U.S. stock returns, where our tests indicate the presence of nonlinear predictability. |
| Keywords: | Non-Gaussian time series, noninvertible ARMA model, all-pass process. |
| JEL: | C58 G12 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:koc:wpaper:1225&r=ets |
| By: | Mika Meitz (Department of Economics, Koç University); Pentti Saikkonen (Department of Mathematics and Statistics, University of Helsinki) |
| Abstract: | We consider maximum likelihood estimation of a particular noninvertible ARMA model with autoregressive conditionally heteroskedastic (ARCH) errors. The model can be seen as an extension to so-called all-pass models in that it allows for autocorrelation and for more fl exible forms of conditional heteroskedasticity. These features may be attractive especially in economic and financial applications. Unlike in previous literature on maximum likelihood estimation of noncausal and/or noninvertible ARMA models and all-pass models, our estimation theory does allow for Gaussian innovations. We give conditions under which a strongly consistent and asymptotically normally distributed solution to the likelihood equations exists, and we also provide a consistent estimator of the limiting covariance matrix. |
| Keywords: | Maximum likelihood estimation, autoregressive moving average, ARMA, autoregressive conditional heteroskedasticity, ARCH, noninvertible, noncausal, all-pass, nonminimum phase. |
| JEL: | C22 C51 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:koc:wpaper:1226&r=ets |
| By: | Giraitis, L.; Kapetanios, G.; Price, S. |
| Abstract: | We consider time series forecasting in the presence of ongoing structural change where both the time series dependence and the nature of the structural change are unknown. Methods that downweight older data, such as rolling regressions, forecast averaging over different windows and exponentially weighted moving averages, known to be robust to historical structural change, are found to be also useful in the presence of ongoing structural change in the forecast period. A crucial issue is how to select the degree of downweighting, usually defined by an arbitrary tuning parameter. We make this choice data dependent by minimizing forecast mean square error, and provide a detailed theoretical analysis of our proposal. Monte Carlo results illustrate the methods. We examine their performance on 191 UK and US macro series. Forecasts using data-based tuning of the data discount rate are shown to perform well. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:cty:dpaper:12/02&r=ets |
| By: | Ioannis Kasparis; Elena Andreou; Peter C. B. Phillips |
| Abstract: | A unifying framework for inference is developed in predictive regressions where the predictor has unknown integration properties and may be stationary or nonstationary. Two easily implemented nonparametric F-tests are proposed. The test statistics are related to those of Kasparis and Phillips (2012) and are obtained by kernel regression. The limit distribution of these predictive tests holds for a wide range of predictors including stationary as well as non-stationary fractional and near unit root processes. In this sense the proposed tests provide a unifying framework for predictive inference, allowing for possibly nonlinear relationships of unknown form, and offering robustness to integration order and functional form. Under the null of no predictability the limit distributions of the tests involve functionals of independent ÷² variates. The tests are consistent and divergence rates are faster when the predictor is stationary. Asymptotic theory and simulations show that the proposed tests are more powerful than existing parametric predictability tests when deviations from unity are large or the predictive regression is nonlinear. Some empirical illustrations to monthly SP500 stock returns data are provided. |
| Keywords: | Functional regression, Nonparametric predictability test, Nonparametric regression, Stock returns, Predictive regression |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:ucy:cypeua:14-2012&r=ets |
| By: | Michael Vogt; Oliver Linton (Institute for Fiscal Studies and Cambridge University) |
| Abstract: | In this paper, we study a nonparametric regression model including a periodic component, a smooth trend function, and a stochastic error term. We propose a procedure to estimate the unknown period and the function values of the periodic component as well as the nonparametric trend function. The theoretical part of the paper establishes the asymptotic properties of our estimators. In particular, we show that our estimator of the period is consistent. In addition, we derive the convergence rates as well as the limiting distributions of our estimators of the periodic component and the trend function. The asymptotic results are complemented with a simulation study that investigates the small sample behaviour of our procedure. Finally, we illustrate our method by applying it to a series of global temperature anomalies. |
| Keywords: | Nonparametric estimation; penalized least squares; periodic sequence; temperature anomaly data. |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:23/12&r=ets |
| By: | Michael Vogt |
| Abstract: | In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coecients. We introduce a kernel-based method to estimate the time-varying regression function and provide asymptotic theory for our estimates. Moreover, we show that the main conditions of the theory are satised for a large class of nonlinear autoregressive processes with a time-varying regression function. Finally, we examine structured models where the regression function splits up into time-varying additive components. As will be seen, estimation in these models does not suer from the curse of dimensionality. We complement the technical analysis of the paper by an application to nancial data. |
| Keywords: | local stationarity, nonparametric regression, smooth backfitting |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:22/12&r=ets |
| By: | Mahesh S. Khadka; K. M. George; N. Park |
| Abstract: | This paper presents performance analysis of hybrid model comprise of concordance and Genetic Programming (GP) to forecast financial market with some existing models. This scheme can be used for in depth analysis of stock market. Different measures of concordances such as Kendalls Tau, Ginis Mean Difference, Spearmans Rho, and weak interpretation of concordance are used to search for the pattern in past that look similar to present. Genetic Programming is then used to match the past trend to present trend as close as possible. Then Genetic Program estimates what will happen next based on what had happened next. The concept is validated using financial time series data (S&P 500 and NASDAQ indices) as sample data sets. The forecasted result is then compared with standard ARIMA model and other model to analyse its performance. |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1209.4608&r=ets |
| By: | Ole Peters; William Klein |
| Abstract: | Geometric Brownian motion is non-stationary. It is non-ergodic in the sense that the time-average growth rate observed in a single realization differs from the growth rate of the ensemble average. We prove that the time-average growth rate of averages over a finite number, N, of realizations is independent of N. A stability analysis shows that the time at which such averages begin to deviate from ensemble-average behavior increases logarithmically with N. |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1209.4517&r=ets |
| By: | Dominique, C-Rene; Rivera-Solis, Luis Eduardo |
| Abstract: | The capital market is a reflexive dynamical input/output construct whose output (time series) is usually assessed by an index of roughness known as Hurst’s exponent (H). Oddly enough, H has no theoretical foundation, but recently it has been found experimentally to vary from persistence (H > 1/2) or long-term dependence to anti-persistence (H < 1/2) or short-term dependence. This paper uses the thrown-offs of quadratic maps (modeled asymptotically) and singularity spectra of fractal sets to characterize H, the alternateness of dependence, and market crashes while proposing a simpler method of computing the correlation dimension than the Grassberger-Procaccia procedure. |
| Keywords: | Hurst Exponent; anti-persistence; fractal attractors; SDIC; chaos; inherent noise; market crashes; Renyi’s generalized fractal dimensions |
| JEL: | G1 C6 A1 G01 |
| Date: | 2012–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:41408&r=ets |
| By: | Francq, Christian; Wintenberger, Olivier; Zakoian, Jean-Michel |
| Abstract: | This paper studies the probabilistic properties and the estimation of the asymmetric log-GARCH($p,q$) model. In this model, the log-volatility is written as a linear function of past values of the log-squared observations, with coefficients depending on the sign of the observations, and past log-volatility values. Conditions are obtained for the existence of solutions and finiteness of their log-moments. We also study the tail properties of the solution. Under mild assumptions, we show that the quasi-maximum likelihood estimation of the parameters is strongly consistent and asymptotically normal. Simulations illustrating the theoretical results and an application to real financial data are proposed. |
| Keywords: | log-GARCH: Quasi-Maximum Likelihood: Strict stationarity: Tail index |
| JEL: | C13 C22 |
| Date: | 2012–09–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:41373&r=ets |
| By: | Fernández-Villaverde, Jesús; Guerron-Quintana, Pablo A.; Rubio-Ramírez, Juan Francisco |
| Abstract: | We propose a novel method to estimate dynamic equilibrium models with stochastic volatility. First, we characterize the properties of the solution to this class of models. Second, we take advantage of the results about the structure of the solution to build a sequential Monte Carlo algorithm to evaluate the likelihood function of the model. The approach, which exploits the profusion of shocks in stochastic volatility models, is versatile and computationally tractable even in large-scale models, such as those often employed by policy-making institutions. As an application, we use our algorithm and Bayesian methods to estimate a business cycle model of the U.S. economy with both stochastic volatility and parameter drifting in monetary policy. Our application shows the importance of stochastic volatility in accounting for the dynamics of the data. |
| Keywords: | Bayesian methods.; Dynamic equilibrium models; Parameter drifting; Stochastic volatility |
| JEL: | C11 E10 E30 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9130&r=ets |
| By: | Cogley, Timothy; Startz, Richard |
| Abstract: | Standard estimation of ARMA models in which the AR and MA roots nearly cancel, so that individual coefficients are only weakly identified, often produces inferential ranges for individual coefficients that give a spurious appearance of accuracy. We remedy this problem with a model that mixes inferential ranges from the estimated model with those of a more parsimonious model. The mixing probability is derived using Bayesian methods, but we show that the method works well in both Bayesian and frequentist setups. In particular, we show that our mixture procedure weights standard results heavily when given data from a well-identified ARMA model (which does not exhibit near root cancellation) and weights heavily an uninformative inferential region when given data from a weakly-identified ARMA model (with near root cancellation). When our procedure is applied to a well-identified process the investigator gets the “usual results,†so there is no important statistical cost to using our procedure. On the other hand, when our procedure is applied to a weakly-identified process, the investigator learns that the data tell us little about the parameters—and is thus protected against making spurious inferences. We recommend that mixture models be computed routinely when inference about ARMA coefficients is of interest. |
| Keywords: | Econometrics and Quantitative Economics, ARMA, bayesian, weak identification |
| Date: | 2012–05–15 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:ucsbec:qt0cw056qz&r=ets |