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on Econometric Time Series |
| By: | Matthieu Garcin (Centre d'Economie de la Sorbonne & Natixis Asset Management); Clément Goulet (Centre d'Economie de la Sorbonne) |
| Abstract: | In this paper we propose a new model for estimating returns and volatility. Our approach is based both on the wavelet denoising technique and on the variational theory. We assess that the volatility can be expressed as a non-parametric functional form of past returns. Therefore, we are able to forecast both returns and volatility and to build confidence intervals for predicted returns. Our technique outperforms classical time series theory. Our model does not require the stationarity of the observed log-returns, it preserves the volatility stylised facts and it is based on a fully non-parametric form. This non-parametric form is obtained thanks to the multiplicative noise theory. To our knowledge, this is the first time that such a method is used for financial modelling. We propose an application to intraday and daily financial data |
| Keywords: | Volatility modeling; non variational calculus; wavelet theory; trading strategy |
| JEL: | C14 C51 C53 C58 |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:15086&r=ets |
| By: | YAMAMOTO, Yohei |
| Abstract: | Financial and macroeconomic time-series data often exhibit infrequent but large jumps. Such jumps may be considered as outliers that are independent of the underlying data-generating processes and contaminate inferences on their model. In this study, we investigate the effects of such jumps on asymptotic inference for large-dimensional common factor models. We first derive the upper bound of jump magnitudes with which the standard asymptotic inference goes through. Second, we propose a jump-correction method based on a series-by-series outlier detection algorithm without accounting for the factor structure. This method gains standard asymptotic normality for the factor model unless outliers occur at common dates. Finally, we propose a test to investigate whether the jumps at a common date are independent outliers or are of factors. A Monte Carlo experiment confirms that the proposed jump-correction method retrieves good finite sample properties. The proposed test shows good size and power. Two small empirical applications illustrate usefulness of the proposed methods. |
| Keywords: | outliers, large-dimensional common factor models, principal components, jumps |
| JEL: | C12 C38 |
| Date: | 2015–07–02 |
| URL: | http://d.repec.org/n?u=RePEc:hit:hiasdp:hias-e-4&r=ets |
| By: | Andreas Basse-O'Connor (Department of Mathematics); Raphaël Lachièze-Rey (Heidelberg University - Department of Mathematics); Mark Podolskij (Department of Mathematics and CREATES) |
| Abstract: | In this paper we present some new limit theorems for power variation of k-th order increments of stationary increments Lévy driven moving averages. In this infill sampling setting, the asymptotic theory gives very surprising results, which (partially) have no counterpart in the theory of discrete moving averages. More specifically, we will show that the first order limit theorems and the mode of convergence strongly depend on the interplay between the given order of the increments, the considered power p, the Blumenthal-Getoor index of the driving pure jump Lévy process L and the behaviour of the kernel function g at 0. First order asymptotic theory essentially comprise three cases: stable convergence towards a certain infinitely divisible distribution, an ergodic type limit theorem and convergence in probability towards an integrated random process. We also prove the second order limit theorem connected to the ergodic type result. When the driving Lévy process L is a symmetric stable process we obtain two different limits: a central limit theorem and convergence in distribution towards a stable random variable. |
| Keywords: | Power variation, limit theorems, moving averages, fractional processes, stable convergence, high frequency data |
| JEL: | C10 C13 C14 |
| Date: | 2015–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2015-56&r=ets |
| By: | Niels Haldrup (Aarhus University and CREATES); J. Eduardo Vera-Valdés (Aarhus University and CREATES) |
| Abstract: | It is commonly argued that observed long memory in time series variables can result from cross-sectional aggregation of dynamic heterogeneous micro units. For instance, Granger (1980) demonstrated that aggregation of AR(1) processes with a Beta distributed AR coefficient can exhibit long memory under certain conditions and that the aggregated series will have an autocorrelation function that exhibits hyperbolic decay. In this paper, we further analyze this phenomenon. We demonstrate that the aggregation argument leading to long memory is consistent with a wide range of definitions of long memory. In a simulation study we seek to quantify Granger's result and find that indeed both the time series and cross-sectional dimensions have to be rather significant to reflect the theoretical asymptotic results. Long memory can result even for moderate T,N dimensions but can vary considerably from the theoretical degree of memory. Also, Granger's result is most precise in samples with a relatively high degree of memory. Finally, we show that even though the aggregated process will behave as generalized fractional process and thus converge to a fractional Brownian motion asymptotically, the fractionally differenced series does not behave according to an ARMA process. In particular, despite the autocorrelation function is summable and hence the fractionally differenced process satisfy the conditions for being I(0), it still exhibits hyperbolic decay. This may have consequences for the validity of ARFIMA time series modeling of long memory processes when the source of memory is due to aggregation. |
| Keywords: | Long memory, Fractional Integration, Aggregation |
| JEL: | C2 C22 |
| Date: | 2015–12–12 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2015-59&r=ets |
| By: | Marco Valerio Geraci; Jean-Yves Gnabo |
| Keywords: | financial interconnectedness; time-varying parameter; granger casuality |
| JEL: | G10 G18 C32 G32 C51 C63 |
| Date: | 2015–12 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/222092&r=ets |
| By: | Allen, D.E.; McAleer, M.J.; Peiris, S.; Singh, A.K. |
| Abstract: | This paper features an analysis of major currency exchange rate movements in relation to the US dollar, as constituted in US dollar terms. Euro, British pound, Chinese yuan, and Japanese yen are modelled using a variety of non- linear models, including smooth transition regression models, logistic smooth transition regressions models, threshold autoregressive models, nonlinear autoregressive models, and additive nonlinear autoregressive models, plus Neural Network models. The results suggest that there is no dominating class of time series models, and the different currency pairs relationships with the US dollar are captured best by neural net regression models, over the ten year sample of daily exchange rate returns data, from August 2005 to August 2015. |
| Keywords: | non linear models, time series, non-parametric, smooth-transition regression models, neural networks, GMDH shell |
| JEL: | C45 C53 F3 G15 |
| Date: | 2015–11–01 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureir:79217&r=ets |
| By: | Kaddour Hadri; Eiji Kurozumi; Yao Rao |
| Abstract: | In this paper, we propose new cointegration tests for single equations and panels. In both cases, the asymptotic distributions of the tests, which are derived with N fixed and T -> infinity, are shown to be standard normals. The effects of serial correlation and cross-sectional dependence are mopped out via long-run variances. An effective bias correction is derived which is shown to work well in finite samples; particularly when N is smaller than T. Our panel tests are robust to possible cointegration across units. |
| Keywords: | Cointegration, Panel cointegration, Cross-section dependence, Bias correction, DOLS, FCLT |
| JEL: | C12 C15 C22 C23 |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:qub:wpaper:1402&r=ets |
| By: | Andreas Basse-O'Connor (Department of Mathematics); Mark Podolskij (Department of Mathematics and CREATES) |
| Abstract: | In this paper we present some limit theorems for power variation of stationary increments Lévy driven moving averages in the setting of critical regimes. In [5] the authors derived first and second order asymptotic results for k-th order increments of stationary increments Lévy driven moving averages. The limit theory heavily depends on the interplay between the given order of the increments, the considered power, the Blumenthal-Getoor index of the driving pure jump Lévy process L and the behavior of the kernel function g at 0. In this work we will study the critical cases, which were not covered in the original work [5]. |
| Keywords: | Power variation, limit theorems, moving averages, fractional processes, stable convergence, high frequency data |
| JEL: | C10 C13 C14 |
| Date: | 2015–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2015-57&r=ets |
| By: | Matthieu Garcin (Centre d'Economie de la Sorbonne & Natixis Asset Management); Dominique Guegan (Centre d'Economie de la Sorbonne) |
| Abstract: | By filtering wavelet coefficients, it is possible to construct a good estimate of a pure signal from noisy data. Especially, for a simple linear noise influence, Donoho and Johnstone (1994) have already defined an optimal filter design in the sense of a good reconstruction of the pure signal. We set here a different framework where the influence of the noise is non-linear. In particular, we propose an optimal method to filter the wavelet coefficients of a discrete dynamical system disrupted by a weak noise, in order to construct good estimates of the pure signal, including Bayes' estimate, minimax estimate, oracular estimate or thresholding estimate. We present the example of a simple chaotic dynamical system as well as an adaptation of our technique in order to show empirically the robustness of the thresholding method in presence of leptokurtic noise. Moreover, we test both the hard and the soft thresholding and also another kind of smoother thresholding which seems to have almost the same reconstruction power as the hard thresholding |
| Keywords: | wavelets; dynamical systems; chaos; Gaussian noise; Cauchy noise; thresholding; nonequispaced design; non-linear noise impact |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:15085&r=ets |
| By: | Claudio, Morana |
| Abstract: | The paper introduces a new simple semiparametric estimator of the conditional variance covariance and correlation matrix (SP-DCC). While sharing a similar sequential approach to existing dynamic conditional correlation (DCC) methods, SP-DCC has the advantage of not requiring the direct parameterization of the conditional covariance or correlation processes, therefore also avoiding any assumption on their long-run target. In the proposed framework, conditional variances are estimated by univariate GARCH models, for actual and suitably transformed series, in the first step; the latter are then nonlinearly combined in the second step, according to basic properties of the covariance and correlation operator, to yield nonparametric estimates of the various conditional covariances and correlations. Moreover, in contrast to available DCC methods, SP-DCC allows for straightforward estimation also for the non-symultaneous case, i.e., for the estimation of conditional cross-covariances and correlations, displaced at any time horizon of interest. A simple ex-post procedure, to ensure well behaved conditional covariance and correlation matrices, grounded on nonlinear shrinkage, is finally proposed. Due to its sequential implementation and scant computational burden, SP-DCC is very simple to apply and suitable for the modeling of vast sets of conditionally heteroskedastic time series. |
| Keywords: | Multivariate GARCH model, dynamic conditional correlation, semiparametric estimation |
| JEL: | C30 C51 |
| Date: | 2015–12–10 |
| URL: | http://d.repec.org/n?u=RePEc:mib:wpaper:317&r=ets |
| By: | Damiano Brigo; Camilla Pisani; Francesco Rapisarda |
| Abstract: | The Multi Variate Mixture Dynamics model is a tractable, dynamical, arbitrage-free multivariate model characterized by transparency on the dependence structure, since closed form formulae for terminal correlations, average correlations and copula function are available. It also allows for complete decorrelation between assets and instantaneous variances. Each single asset is modelled according to a lognormal mixture dynamics model, and this univariate version is widely used in the industry due to its flexibility and accuracy. The same property holds for the multivariate process of all assets, whose density is a mixture of multivariate basic densities. This allows for consistency of single asset and index/portfolio smile. In this paper, we generalize the MVMD model by introducing shifted dynamics and we propose a definition of implied correlation under this model. We investigate whether the model is able to consistently reproduce the implied volatility of FX cross rates, once the single components are calibrated to univariate shifted lognormal mixture dynamics models. We compare the performance of the shifted MVMD model in terms of implied correlation with those of the shifted Simply Correlated Mixture Dynamics model where the dynamics of the single assets are connected naively by introducing correlation among their Brownian motions. Finally, we introduce a model with uncertain volatilities and correlation. The Markovian projection of this model is a generalization of the shifted MVMD model. |
| Date: | 2015–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1512.04741&r=ets |
| By: | Kim, Jae; Choi, In |
| Abstract: | This paper re-evaluates the key past results of unit root test, emphasizing that the use of a conventional level of significance is not in general optimal due to the test having low power. The optimal levels for popular unit root tests, chosen using the line of enlightened judgement under a symmetric loss function, are found to be much higher than conventional ones. We also propose simple calibration rules for the optimal level of significance for a range of unit root tests based on asymptotic local power. At the optimal levels, many time series in the extended Nelson-Plosser data set are judged to be trend-stationary, including real income variables, employment variables and money stock. We also find nearly all real exchange rates covered in the Elliott-Pesavento study to be stationary at the optimal levels, which lends strong support for the purchasing power parity. Additionally, most of the real interest rates covered in the Rapach-Weber study are found to be stationary. |
| Keywords: | Expected Loss; Optimal Level of Significance; Power of the Test; Response Surface |
| JEL: | C12 E30 F30 |
| Date: | 2015–12–17 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:68411&r=ets |