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on Econometric Time Series |
| By: | Niels Haldrup (Aarhus University and CREATES); Robinson Kruse (Leibniz University Hannover and CREATES) |
| Abstract: | Fractionally integrated processes have become a standard class of models to describe the long memory features of economic and financial time series data. However, it has been demonstrated in numerous studies that structural break processes and non-linear features can often be confused as being long memory. The question naturally arises whether it is possible empirically to determine the source of long memory as being genuinely long memory in the form of a fractionally integrated process or whether the long range dependence is of a di¤erent nature. In this paper we suggest a testing procedure that helps discriminating between such processes. The idea is based on the feature that nonlinear transformations of stationary fractionally integrated Gaussian processes decrease the order of memory in a speci?c way which is determined by the Hermite rank of the transformation. In principle, a non-linear transformation of the series can make the series short memory I(0). We suggest using the Wald test of Shimotsu (2007) to test the null hypothesis that a vector time series of properly transformed variables is I(0). Our testing procedure is designed such that even non-stationary fractionally integrated processes are permitted under the null hypothesis. The test is shown to have good size and to be robust against certain types of deviations from Gaussianity. The test is also shown to be consistent against a broad class of processes that are non-fractional but still exhibit (spurious) long memory. In particular, the test is shown to have excellent power against a class of stationary and non-stationary random level shift models as well as Markov switching GARCH processes where the break and transition probabilities are allowed to be time varying. |
| Keywords: | Long memory, fractional integration, non-linear models, structural breaks, random level shifts, Hermite polynomials, realized volatility, in?ation. |
| JEL: | C12 C2 C22 |
| Date: | 2014–06–26 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2014-19&r=ets |
| By: | Federico Carlini (CREATES, Aarhus University, Denmark); Katarzyna Lasak (VU University Amsterdam) |
| 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 fractionally 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: | 2014–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140052&r=ets |
| By: | Francisco Blasques (VU University Amsterdam); Siem Jan Koopman (VU University Amsterdam, the Netherlands); and André Lucas (VU University Amsterdam, the Netherlands, and Aarhus University, Denmark) |
| Abstract: | The strong consistency and asymptotic normality of the maximum likelihood estimator in observation-driven models usually requires the study of the model both as a filter for the time-varying parameter and as a data generating process (DGP) for observed data. The probabilistic properties of the filter can be substantially different from those of the DGP. This difference is particularly relevant for recently developed time varying parameter models. We establish new conditions under which the dynamic properties of the true time varying parameter as well as of its filtered counterpart are both well-behaved and We only require the verification of one rather than two sets of conditions. In particular, we formulate conditions under which the (local) invertibility of the model follows directly from the stable behavior of the true time varying parameter. We use these results to prove the local strong consistency and asymptotic normality of the maximum likelihood estimator. To illustrate the results, we apply the theory to a number of empirically relevant models. |
| Keywords: | Observation-driven models; stochastic recurrence equations; contraction conditions; invertibility; stationarity; ergodicity; generalized autoregressive score models |
| JEL: | C13 C22 C12 |
| Date: | 2014–06–20 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140074&r=ets |
| By: | Doukhan, Paul; Lang, Gabriel; Leucht, Anne; Neumann, Michael H. |
| Abstract: | In this paper, we propose a model-free bootstrap method for the empirical process under absolute regularity. More precisely, consistency of an adapted version of the so-called dependent wild bootstrap, that was introduced by Shao (2010) and is very easy to implement, is proved under minimal conditions on the tuning parameter of the procedure. We apply our results to construct confidence intervals for unknown parameters and to approximate critical values for statistical tests. A simulation study shows that our method is competitive to standard block bootstrap methods in finite samples. |
| Keywords: | Absolute regularity , bootstrap , empirical process , time series , V -statistics , quantiles , Kolmogorov-Smirnov test |
| JEL: | C |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:mnh:wpaper:35246&r=ets |
| By: | Jentsch, Carsten; Paparoditis, Efstathios; Politis, Dimitris N. |
| Abstract: | We develop some asymptotic theory for applications of block bootstrap resampling schemes to multivariate integrated and cointegrated time series. It is proved that a multivariate, continuous-path block bootstrap scheme applied to a full rank integrated process, succeeds in estimating consistently the distribution of the least squares estimators in both, the regression and the spurious regression case. Furthermore, it is shown that the same block resampling scheme does not succeed in estimating the distribution of the parameter estimators in the case of cointegrated time series. For this situation, a modified block resampling scheme, the so-called residual based block bootstrap, is investigated and its validity for approximating the distribution of the regression parameters is established. The performance of the proposed block bootstrap procedures is illustrated in a short simulation study. |
| Keywords: | Block bootstrap , bootstrap consistency , spurious regression , functional limit theorem , continuous-path block bootstrap , model-based block bootstrap |
| JEL: | C15 C32 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:mnh:wpaper:36668&r=ets |
| By: | Proietti, Tommaso |
| Abstract: | Extracting and forecasting the volatility of financial markets is an important empirical problem. Time series of realized volatility or other volatility proxies, such as squared returns, display long range dependence. Exponential smoothing (ES) is a very popular and successful forecasting and signal extraction scheme, but it can be suboptimal for long memory time series. This paper discusses possible long memory extensions of ES and finally implements a generalization based on a fractional equal root integrated moving average (FerIMA) model, proposed originally by Hosking in his seminal 1981 article on fractional differencing. We provide a decomposition of the process into the sum of fractional noise processes with decreasing orders of integration, encompassing simple and double exponential smoothing, and introduce a lowpass real time filter arising in the long memory case. Signal extraction and prediction depend on two parameters: the memory (fractional integration) parameter and a mean reversion parameter. They can be estimated by pseudo maximum likelihood in the frequency domain. We then address the prediction of volatility by a FerIMA model and carry out a recursive forecasting experiment, which proves that the proposed generalized exponential smoothing predictor improves significantly upon commonly used methods for forecasting realized volatility. |
| Keywords: | Realized Volatility. Signal Extraction. Permanent-Transitory Decomposition. Fractional equal-root IMA model. |
| JEL: | C22 C53 G17 |
| Date: | 2014–07–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:57230&r=ets |
| By: | Abdelhamid Ouakasse; Guy Melard |
| Abstract: | Recursive estimation methods for time series models usually make use of recurrences for the vector of parameters, the modelerror and its derivatives with respect to the parameters, plus a recurrence for the Hessian of the model error. An alternativemethod is proposed in the case of an autoregressive-moving average model, where the Hessian is not updated but is replaced,at each time, by the inverse of the Fisher information matrix evaluated at the current parameter. The asymptotic properties,consistency and asymptotic normality, of the new estimator are obtained. Monte Carlo experiments indicate that the estimatesmay converge faster to the true values of the parameters than when the Hessian is updated. The paper is illustrated by anexample on forecasting the speed of wind. |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:ulb:ulbeco:2013/13844&r=ets |
| By: | Giorgio Calzolari (University of Florence); Laura Magazzini (Department of Economics (University of Verona)) |
| Abstract: | Within the framework of dynamic panel data models with mean stationarity, one additional moment condition may remarkably increase the efficiency of the system GMM estimator. This additional condition is essentially a condition of “homoskesdasticity” of the individual effects; it is “implicitly satisfied” in all the Monte Carlo simulations on dynamic panel data models available in the literature (including the experiments with heteroskedasticity, which is always confined to the idiosyncratic errors), but not “explicitly” exploited. Monte Carlo experiments show remarkable efficiency improvements when the distribution of individual effects, and thus of yi0, are skewed, thus including the very important cases in economic applications that include variables like individual wages, sizes of the firms, number of employees, etc. |
| Keywords: | panel data, dynamic model, GMM estimation, mean stationarity, skewed individual effects |
| JEL: | C23 C13 |
| Date: | 2014–07 |
| URL: | http://d.repec.org/n?u=RePEc:ver:wpaper:12/2014&r=ets |