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on Econometric Time Series |
| By: | Marco Avarucci (Maastricht University); Eric Beutner (Maastricht University); Paolo Zaffaroni (Imperial College London and Università di Roma "La Sapienza") |
| Abstract: | This paper questions whether it is possible to derive consistency and asymptotic normality of the Gaussian quasi-maximum likelihood estimator (QMLE) for possibly the simplest VEC-GARCH model, namely the multivariate ARCH(1) model of the BEKK form, under weak moment conditions similar to the univariate case. In contrast to the univariate specification, we show that the expectation of the loglikelihood function is unbounded, away from the true parameter value, if (and only if) the observable has unbounded second moment. Despite this non-standard feature, consistency of the Gaussian QMLE is still warranted. The same moment condition proves to be necessary and sucient for the stationarity of the score, when evaluated at the true parameter value. This explains why high moment conditions, typically bounded sixth moment and above, have been used hitherto in the literature to establish the asymptotic normality of the QMLE in the multivariate framework. |
| Keywords: | multivariate ARCH models. moment conditions. VEC-GARCH. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:sas:wpaper:20121&r=ets |
| By: | Peter Martey Addo (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne); Monica Billio (Università Ca' Foscari of Venice - Department of Economics); Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris) |
| Abstract: | In ESTAR models it is usually quite difficult to obtain parameter estimates, as it is discussed in the literature. The problem of properly distinguishing the transition function in relation to extreme parameter combinations often leads to getting strongly biased estimators. This paper proposes a new procedure to test for the unit root in a nonlinear framework, and contributes to the existing literature in three separate directions. First, we propose a new alternative model - the MT-STAR model - which has similar properties as the ESTAR model but reduces the effects of the identification problem and can also account for cases where the adjustment mechanism towards equilibrium is not symmetric. Second, we develop a testing procedure to detect the presence of a nonlinear stationary process by establishing the limiting non-standard asymptotic distributions of the proposed test-statistics. Finally, we perform Monte Carlo simulations to assess the small sample performance of the test and then to highlight its power gain over existing tests for a unit root. We proposed two applications. |
| Keywords: | Nonlinearity, smooth transition, unit root testing, Monte Carlo simulations. |
| Date: | 2011–11 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00659158&r=ets |
| By: | Mario Forni (Universita' di Modena e Reggio Emilia, CEPR and RECent); Marc Hallin (ECARES, Université Libre de Bruxelles); Marco Lippi (Università di Roma La Sapienza and EIEF); Paolo Zaffaroni (Imperial College London) |
| Abstract: | In the present paper we study a semiparametric version of the Generalized Dynamic Factor Model introduced in Forni, Hallin, Lippi and Reichlin (2000). Precisely, we suppose that the common components have rational spectral density, while no parametric structure is assumed for the idiosyncratic components. The parametric structure assumed for the common components does not imply that the model has a static representation (though the converse implication holds), a strong restriction which is shared by most of the literature on large-dimensional dynamic factor models. We use recent results on singular stationary processes with rational spectral density, to obtain a finite autoregressive representation for the common components. We construct an estimator for the model parameters and the common shocks. Consistency and rates of convergence are obtained. An empirical section, based on US macroeconomic time series, compares estimates based on our model with those based on the usual static representation restriction. We find convincing evidence that the latter is not supported by the data. |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:eie:wpaper:1106&r=ets |
| By: | Tommaso Proietti (The University of Sydney Business School) |
| Abstract: | The Beveridge-Nelson decomposition defines the trend component in terms of the eventual forecast function, as the value the series would take if it were on its long-run path. The paper introduces the multistep Beveridge-Nelson decomposition, which arises when the forecast function is obtained by the direct autoregressive approach, which optimizes the predictive ability of the AR model at forecast horizons greater than one. We compare our proposal with the standard Beveridge-Nelson decomposition, for which the forecast function is obtained by iterating the one-stepahead predictions via the chain rule. We illustrate that the multistep Beveridge-Nelson trend is more efficient than the standard one in the presence of model misspecification and we subsequently assess the predictive validity of the extracted transitory component with respect to future growth. |
| Keywords: | Trend and Cycle. Forecasting. Filtering. Misspecification |
| JEL: | C22 C52 E32 |
| Date: | 2011–10 |
| URL: | http://d.repec.org/n?u=RePEc:syb:wpbsba:09/2011&r=ets |
| By: | Tommaso Proietti (The University of Sydney Business School and Università degli Studi di Roma "Tor Vergata"); Helmut Lütkepohl (European University Institute) |
| Abstract: | The paper investigates whether transforming a time series leads to an improvement in forecasting accuracy. The class of transformations that is considered is the Box-Cox power transformation, which applies to series measured on a ratio scale. We propose a nonparametric approach for estimating the optimal transformation parameter based on the frequency domain estimation of the prediction error variance, and also conduct an extensive recursive forecast experiment on a large set of seasonal monthly macroeconomic time series related to industrial production and retail turnover. In about one fifth of the series considered the Box-Cox transformation produces forecasts significantly better than the untransformed data at one-step-ahead horizon; in most of the cases the logarithmic transformation is the relevant one. As the forecast horizon increases, the evidence in favour of a transformation becomes less strong. Typically, the naïve predictor that just reverses the transformation leads to a lower mean square error than the optimal predictor at short forecast leads. We also discuss whether the preliminary in-sample frequency domain assessment conducted provides a reliable guidance which series should be transformed for improving significantly the predictive performance. |
| Keywords: | Forecasts comparisons. Multi-step forecasting. Rolling forecasts. Nonparametric estimation of prediction error variance. |
| Date: | 2011–10 |
| URL: | http://d.repec.org/n?u=RePEc:syb:wpbsba:08/2011&r=ets |
| By: | Tommaso Proietti (The University of Sydney Business School); Stefano Grassi (CREATES, Aarhus University) |
| Abstract: | An important issue in modelling economic time series is whether key unobserved components representing trends, seasonality and calendar components, are deterministic or evolutive. We address it by applying a recently proposed Bayesian variable selection methodology to an encompassing linear mixed model that features, along with deterministic effects, additional random explanatory variables that account for the evolution of the underlying level, slope, seasonality and trading days. Variable selection is performed by estimating the posterior model probabilities using a suitable Gibbs sampling scheme. The paper conducts an extensive empirical application on a large and representative set of monthly time series concerning industrial production and retail turnover. We find strong support for the presence of stochastic trends in the series, either in the form of a time-varying level, or, less frequently, of a stochastic slope, or both. Seasonality is a more stable component: only in 70% of the cases we were able to select at least one stochastic trigonometric cycle out of the six possible cycles. Most frequently the time variation is found in correspondence with the fundamental and the first harmonic cycles. An interesting and intuitively plausible finding is that the probability of estimating time-varying components increases with the sample size available. However, even for very large sample sizes we were unable to find stochastically varying calendar effects. |
| Keywords: | Nonstationarity. Variable selection. Linear Mixed Models. |
| JEL: | E32 E37 C53 |
| Date: | 2011–09 |
| URL: | http://d.repec.org/n?u=RePEc:syb:wpbsba:07/2011&r=ets |
| By: | Smeekes Stephan; Urbain Jean-Pierre (METEOR) |
| Abstract: | In this paper we investigate the validity of the univariate autoregressive sieve bootstrap appliedto time series panels characterized by general forms of cross-sectional dependence, including butnot restricted to cointegration. Using the final equations approach we show that while it ispossible to write such a panel as a collection of infinite order autoregressive equations, theinnovations of these equations are not vector white noise. This causes the univariateautoregressive sieve bootstrap to be invalid in such panels. We illustrate this result with asmall numerical example using a simple bivariate system for which the sieve bootstrap is invalid,and show that the extent of the invalidity depends on the value of specific parameters. We alsoshow that Monte Carlo simulations in small samples can be misleading about the validity of theunivariate autoregressive sieve bootstrap. The results in this paper serve as a warning about thepractical use of the autoregressive sieve bootstrap in panels where cross-sectional dependence ofgeneral from may be present. |
| Keywords: | econometrics; |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2011055&r=ets |
| By: | Di Iorio, Francesca; Fachin, Stefano |
| Abstract: | We address the issue of estimation and inference in dependent non-stationary panels of small cross-section dimensions. The main conclusion is that the best results are obtained applying bootstrap inference to single-equation estimators, such as FM-OLS and DOLS. SUR estimators perform badly, or are even unfeasible, when the time dimension is not very large compared to the cross-section dimension. -- |
| Keywords: | Panel cointegration,FM-OLS,FM-SUR,DOLS,DSUR |
| JEL: | C15 C23 C33 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:ifwedp:20121&r=ets |
| By: | M. Hashem Pesaran; Alexander Chudik |
| Abstract: | This paper investigates the problem of aggregation in the case of large linear dynamic panels, where each micro unit is potentially related to all other micro units, and where micro innovations are allowed to be cross sectionally dependent. Following Pesaran (2003), an optimal aggregate function is derived and used (i) to establish conditions under which Granger's (1980) conjecture regarding the long memory properties of aggregate variables from "a very large scale dynamic, econometric model" holds, and (ii) to show which distributional features of micro parameters can be identified from the aggregate model. ; The paper also derives impulse response functions for the aggregate variables, distinguishing between the effects of macro and aggregated idiosyncratic shocks. Some of the findings of the paper are illustrated by Monte Carlo experiments. The paper also contains an empirical application to consumer price inflation in Germany, France and Italy, and re-examines the extent to which "observed" inflation persistence at the aggregate level is due to aggregation and/or common unobserved factors. Our findings suggest that dynamic heterogeneity as well as persistent common factors are needed for explaining the observed persistence of the aggregate inflation. |
| Keywords: | Index numbers (Economics) ; Price levels |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:fip:feddgw:101&r=ets |
| By: | Domenico Giannone; Michèle Lenza; Giorgio E. Primiceri |
| Abstract: | Vector autoregressions (VARs) are flexible time series models that can capture complex dynamic interrelationships among macroeconomic variables. However, their dense parameterization leads to unstable inference and inaccurate out-of- sample forecasts, particularly for models with many variables. A potential solution to this problem is to use informative priors, in order to shrink the richly parameterized unrestricted model towards a parsimonious naïve benchmark, and thus reduce estimation uncertainty. This paper studies the optimal choice of the informativeness of these priors, which we treat as additional parameters, in the spirit of hierarchical modeling. This approach is theoretically grounded, easy to implement, and greatly reduces the number and importance of subjective choices in the setting of the prior. Moreover, it performs very well both in terms of out-of-sample forecasting, and accuracy in the estimation of impulse response functions. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/106648&r=ets |
| By: | Nayoung Lee; Hyungsik Roger Moon; Martin Weidner (Institute for Fiscal Studies and UCL) |
| Abstract: | <p>This paper studies a simple dynamic panel linear regression model with interactive fixed effects in which the variable of interest is measured with error. To estimate the dynamic coefficient, we consider the least-squares minimum distance (LS-MD) estimation method. </p><p></p> |
| Date: | 2011–12 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:37/11&r=ets |
| By: | Vygintas Gontis; Aleksejus Kononovicius; Stefan Reimann |
| Abstract: | We investigate large changes, bursts, of the continuous stochastic signals, when the exponent of multiplicativity is higher than one. Earlier we have proposed a general nonlinear stochastic model which can be transformed into Bessel process with known first hitting (first passage) time statistics. Using these results we derive PDF of burst duration for the proposed model. We confirm analytical expressions by numerical evaluation and discuss bursty behavior of return in financial markets in the framework of modeling by nonlinear SDE. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1201.3083&r=ets |
| By: | Ladislav Kristoufek |
| Abstract: | In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlations detection - classical and modified rescaled range analyses. A focus is put on an effect of different distributional properties on an ability of the methods to efficiently distinguish between short and long-term memory. To do so, we analyze the behavior of the estimators for independent, short-range dependent, and long-range dependent processes with innovations from 8 different distributions. We find that apart from a combination of very high levels of kurtosis and skewness, both estimators are quite robust to distributional properties. Importantly, we show that R/S is biased upwards (yet not strongly) for short-range dependent processes, while M-R/S is strongly biased downwards for long-range dependent processes regardless of the distribution of innovations. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1201.3511&r=ets |
| By: | Hao Meng (ECUST); Fei Ren (ECUST); Gao-Feng Gu (ECUST); Xiong Xiong (TJU); Yong-Jie Zhang (TJU); Wei-Xing Zhou (ECUST); Wei Zhang (TJU) |
| Abstract: | Understanding the statistical properties of recurrence intervals of extreme events is crucial to risk assessment and management of complex systems. The probability distributions and correlations of recurrence intervals for many systems have been extensively investigated. However, the impacts of microscopic rules of a complex system on the macroscopic properties of its recurrence intervals are less studied. In this Letter, we adopt an order-driven stock market model to address this issue for stock returns. We find that the distributions of the scaled recurrence intervals of simulated returns have a power law scaling with stretched exponential cutoff and the intervals possess multifractal nature, which are consistent with empirical results. We further investigate the effects of long memory in the directions (or signs) and relative prices of the order flow on the characteristic quantities of these properties. It is found that the long memory in the order directions (Hurst index $H_s$) has a negligible effect on the interval distributions and the multifractal nature. In contrast, the power-law exponent of the interval distribution increases linearly with respect to the Hurst index $H_x$ of the relative prices, and the singularity width of the multifractal nature fluctuates around a constant value when $H_x<0.7$ and then increases with $H_x$. No evident effects of $H_s$ and $H_x$ are found on the long memory of the recurrence intervals. Our results indicate that the nontrivial properties of the recurrence intervals of returns are mainly caused by traders' behaviors of persistently placing new orders around the best bid and ask prices. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1201.2825&r=ets |
| By: | Matteo Marsili |
| Abstract: | For fat tailed distributions (i.e. those that decay slower than an exponential), large deviations not only become relatively likely, but the way in which they are realized changes dramatically: A finite fraction of the whole sample deviation is concentrated on a single variable: large deviations are not the accumulation of many small deviations, but rather they are dominated to a single large fluctuation. The regime of large deviations is separated from the regime of typical fluctuations by a phase transition where the symmetry between the points in the sample is {\em spontaneously broken}. This phenomenon has been discussed in the context of mass transport models in physics, where it takes the form of a condensation phase transition. Yet, the phenomenon is way more general. For example, in risk management of large portfolios, it suggests that one should expect losses to concentrate on a single asset: when extremely bad things happen, it is likely that there is a single factor on which bad luck concentrates. Along similar lines, one should expect that bubbles in financial markets do not gradually deflate, but rather burst abruptly and that in the most rainy day of a year, precipitation concentrate on a given spot. Analogously, when applied to biological evolution, we're lead to infer that, if fitness changes for individual mutations have a broad distribution, those large deviations that lead to better fit species are not likely to result from the accumulation of small positive mutations. Rather they are likely to arise from large rare jumps. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1201.2817&r=ets |