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on Econometric Time Series |
| By: | Kim Christensen (Aarhus University and CREATES); Roel Oomen (Deutsche Bank, London); Mark Podolskij (University of Heidelberg and CREATES) |
| Abstract: | In this paper, we demonstrate that jumps in financial asset prices are not nearly as common as generally thought, and that they account for only a very small proportion of total return variation. We base our investigation on an extensive set of ultra high-frequency equity and foreign exchange rate data recorded at milli-second precision, allowing us to view the price evolution at a microscopic level. We show that both in theory and practice, traditional measures of jump variation based on low-frequency tick data tend to spuriously attribute a burst of volatility to the jump component thereby severely overstating the true variation coming from jumps. Indeed, our estimates based on tick data suggest that the jump variation is an order of magnitude smaller. This finding has a number of important implications for asset pricing and risk management and we illustrate this with a delta hedging example of an option trader that is short gamma. Our econometric analysis is build around a pre-averaging theory that allows us to work at the highest available frequency, where the data are polluted bymicrostructure noise. We extend the theory in a number of directions important for jump estimation and testing. This also reveals that pre-averaging has a built-in robustness property to outliers in high-frequency data, and allows us to show that some of the few remaining jumps at tick frequency are in fact induced by data-cleaning routines aimed at removing the outliers. |
| Keywords: | jump variation, high-frequency data, market microstructure noise, pre-averaging, realised variation, outliers. |
| JEL: | C10 C80 |
| Date: | 2011–05–26 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2011-19&r=ets |
| By: | David F. Hendry |
| Abstract: | Unpredictability arises from intrinsic stochastic variation, unexpected instances of outliers, and unanticipated extrinsic shifts of distributions. We analyze their properties, relationships, and different effects on the three arenas in the title, which suggests considering three associated information sets. We note the implications of unanticipated shifts for forecasting, economic analyses of efficient markets, inter-temporal derivations, and general-to-specific model selection, tackling outliers and non-constancy by impulse-indicator saturation, and contrast the potential success in modeling breaks with the major difficulties confronting forecasting. |
| Keywords: | Unpredictability, 'Black Swans', distributional shfits, forecasing, model selection |
| JEL: | C51 C22 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:551&r=ets |
| By: | Mohamed Boutahar (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579); Rabeh Khalfaoui2 (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579) |
| Abstract: | In this paper we perform a Monte Carlo study based on three well-known semiparametric estimates for the long memory fractional parameter. We study the efficiency of Geweke and Porter-Hudak, Gaussian semiparametric and wavelet Ordinary Least-Square estimates in both stationary and non stationary models. We consider an adequate data tapers to compute non stationary estimates. The Monte Carlo simulation study is based on different sample size. We show that for d belonging to [1/4,1.25) the Haar estimate performs the others with respect to the mean squared error. The estimation methods are applied to energy data set for an empirical illustration. |
| Keywords: | wavelets; long memory; tapering; non-stationarity; volatility. |
| Date: | 2011–05–23 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-00595057&r=ets |
| By: | Liu, Philip (International Monetary Fund); Mumtaz, Haroon (Bank of England); Theophilopoulou, Angeliki (University of Westminister) |
| Abstract: | A growing literature has documented changes to the dynamics of key macroeconomic variables in industrialised countries and highlighted the possibility that these variables may react differently to structural shocks over time. However, existing empirical work on the international transmission of shocks largely abstracts from the possibility of changes to the international transmission mechanism across time. In addition, the literature has largely employed small-scale models with limited number of variables. This paper introduces an empirical model which allows the estimation of time-varying response of a large set of domestic variables to foreign money supply, demand and supply shocks. The key results show that a foreign monetary policy tightening resembles the classic beggar-thy-neighbour scenario for the United Kingdom in the period 1975-90. In more recent periods, the response is negative but largely insignificant. |
| Keywords: | Factor augmented VAR; Time-variation; Gibbs sampling. |
| Date: | 2011–05–27 |
| URL: | http://d.repec.org/n?u=RePEc:boe:boeewp:0425&r=ets |
| By: | Gian Piero Aielli (University of Padova); Massimiliano Caporin (University of Padova) |
| Abstract: | It is well-known that the estimated GARCH dynamics exhibit common patterns. Starting from this fact we extend the Dynamic Conditional Correlation (DCC) model by allowing for a cluster- ing structure of the univariate GARCH parameters. The model can be estimated in two steps, the first devoted to the clustering structure, and the second focusing on correlation parameters. Differently from the traditional two-step DCC estimation, we get large system feasibility of the joint estimation of the whole set of modelÕs parameters. We also present a new approach to the clustering of GARCH processes, which embeds the asymptotic properties of the univariate quasi-maximum-likelihood GARCH estimators into a Gaussian mixture clustering algorithm. Unlike other GARCH clustering techniques, our method logically leads to the selection of the optimal number of clusters. |
| Keywords: | dynamic conditional correlations, time series clustering, multivariate GARCH, composite likelihood. |
| JEL: | C32 C53 C51 C52 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:pad:wpaper:0133&r=ets |
| By: | Antonio García Ferrer; Ester González Prieto; Daniel Peña |
| Abstract: | In this paper, we apply independent component analysis (ICA) for prediction and signal extraction in multivariate time series data. We compare the performance of three different ICA procedures, JADE, SOBI, and FOTBI that estimate the components exploiting either the non-Gaussianity, or the temporal structure of the data, or combining both, non-Gaussianity as well as temporal dependence. Some Monte Carlo simulation experiments are carried out to investigate the performance of these algorithms in order to extract components such as trend, cycle, and seasonal components. Moreover, we empirically test the performance of those three ICA procedures on capturing the dynamic relationships among the industrial production index (IPI) time series of four European countries. We also compare the accuracy of the IPI time series forecasts using a few JADE, SOBI, and FOTBI components, at different time horizons. According to the results, FOTBI seems to be a good starting point for automatic time series signal extraction procedures, and it also provides quite accurate forecasts for the IPIs. |
| Keywords: | ICA, Signal extraction, Multivariate time series, Forecasting |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws111611&r=ets |
| By: | Gianni Amisano (DG-Research, European Central Bank, Kaiserstrasse 29, D-60311, Frankfurt am Main, Germany and Department of Economics University of Brescia.); Oreste Tristani (DG-Research, European Central Bank, Kaiserstrasse 29, D-60311, Frankfurt am Main, Germany.) |
| Abstract: | Phenomena such as the Great Moderation have increased the attention of macro-economists towards models where shock processes are not (log-)normal. This paper studies a class of discrete-time rational expectations models where the variance of exogenous innovations is subject to stochastic regime shifts. We first show that, up to a second-order approximation using perturbation methods, regime switching in the variances has an impact only on the intercept coefficients of the decision rules. We then demonstrate how to derive the exact model likelihood for the second-order approximation of the solution when there are as many shocks as observable variables. We illustrate the applicability of the proposed solution and estimation methods in the case of a small DSGE model. JEL Classification: E0, C63. |
| Keywords: | DSGE models, second-order approximation, regime switching, time-varying volatility. |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20111341&r=ets |
| By: | Stelios Bekiros |
| Abstract: | This study explores the direction and nature of causal linkages among six currencies denoted relative to United States dollar (USD), namely Euro (EUR), Great Britain Pound (GBP), Japanese Yen (JPY), Swiss Frank (CHF), Australian Dollar (AUD) and Canadian Dollar (CAD). These are the most liquid and widely traded currency pairs in the world and make up about 90% of total Forex trading worldwide. The data covers the period 3/20/1987-11/14/2007, including the Asian crisis, the dot-com bubble and the period just before the outbreak of the US subprime crisis. The objective of the paper is to test for the existence of both linear and nonlinear causal relationships among these currency markets. The modified Baek-Brock test for nonlinear non-causality is applied on the currency return time series as well as the linear Granger test. Further to the classical pairwise analysis causality testing is conducted in a multivariate formulation, to correct for the effects of the other variables. A new stepwise multivariate filtering approach is implemented. To check if any of the observed causality is strictly nonlinear, the nonlinear causal relationships of VAR/VECM filtered residuals are also examined. Finally, the hypothesis of nonlinear non-causality is investigated after controlling for conditional heteroskedasticity in the data using GARCH-BEKK, CCC-GARCH and DCC-GARCH models. Significant nonlinear causal linkages persisted even after multivariate GARCH filtering. This indicates that if nonlinear effects are accounted for, neither FX market leads or lags the other consistently and currency returns may exhibit statistically significant higher-order moments and asymmetries. |
| Keywords: | nonparametric Granger causality; filtering; multivariate GARCH models; spillovers |
| JEL: | C14 C51 F31 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2011/22&r=ets |
| By: | Stelios Bekiros |
| Abstract: | The present study builds upon the seminal work of Engel and West [2005, Journal of Political Economy 113, 485-517] and in particular on the relationship between exchange rates and fundamentals. The paper discusses the well-known puzzle that fundamental variables such as money supplies, interest rates, outputs etc. provide help in predicting changes in floating exchange rates. It also tests the theoretical result of Engel and West (2005) that in a rational expectations present-value model, the asset price manifests near-random walk behaviour if the fundamentals are I(1) and the factor for discounting future fundamentals is near one. The study explores the direction and nature of causal interdependencies and cross-correlations among the most widely traded currencies in the world, their country-specific fundamentals and their US-differentials. A new VAR/VECM-GARCH multivariate filtering approach is implemented, whilst linear and nonlinear non-causality is tested on the time series. In addition to pairwise causality testing, several different groupings of variables are explored. The methodology is extensively tested and validated on simulated and empirical data. The implication is that although exchange rates and fundamentals appear to be linked in a way that is broadly consistent with asset-pricing models, there is no indication of a prevailing causal behaviour from fundamentals to exchange rates or vice-versa. When nonlinear effects are accounted for, the evidence implies that the pattern of leads and lags changes over time. These results may influence the greater predictability of currency markets. Overall, fundamentals may be important determinants of FX rates, however there may be some other unobservable variables driving the currency rates that current asset-pricing models have not yet captured. |
| Keywords: | simulation-based inference; causality; random walk; filtering; nonlinearity; asset-pricing |
| JEL: | F31 F37 C52 C53 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2011/21&r=ets |
| By: | Stelios Bekiros; Massimiliano Marcellino |
| Abstract: | This paper relies on wavelet multiresolution analysis to capture the dependence structure of currency markets and reveal the complex dynamics across different timescales. It investigates the nature and direction of causal relationships among the most widely traded currencies denoted relative to the United States Dollar (USD), namely Euro (EUR), Great Britain Pound (GBP) and Japanese Yen (JPY). The timescale analysis involves the estimation of linear vis-à-vis nonlinear and spectral causality of wavelet components and aggregate series as well as the detection of short- vs. long-run linkages and cross-scale correlations. Moreover, this study attempts to probe into the micro-foundations of across-scale heterogeneity in the causality pattern on the basis of trader behavior with different time horizons. New stylized properties emerge in the volatility structure and the implications for the flow of information across scales are inferred. The examined period starts from the introduction of the Euro and covers the dot-com bubble, the financial crisis of 2007-2010 and the Eurozone debt crisis. Technically, this paper presents an invariant discrete wavelet transform that deals efficiently with phase shifts, dyadic-length and boundary effects. It also proposes a new entropy-based methodology for the determination of the optimal decomposition level. Overall, there is no indication of a global causal behavior that dominates at all timescales. When the nonlinear effects are accounted for, the evidence of dynamical bidirectional causality implies that the pattern of leads and lags changes over time. These results may prove useful to quantify the process of integration as well as influence the greater predictability of currency markets. |
| Keywords: | exchange rates; wavelets; timescale analysis; causality; entropy |
| JEL: | C14 C32 C51 F31 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2011/23&r=ets |
| By: | Pesaran, M.H.; Chudik, A. |
| Abstract: | This paper considers 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 the limiting behavior of the aggregation error is investigated as N (the number of cross section units) increases. Certain distributional features of micro parameters are also identified from the aggregate function. The paper then establishes Granger's (1980) conjecture regarding the long memory properties of aggregate variables from 'a very large scale dynamic, econometric model', and considers the time profiles of the effects of macro and micro shocks on the aggregate and disaggregate variables. Some of these findings are illustrated in Monte Carlo experiments, where we also study the estimation of the aggregate effects of micro and macro shocks. The paper concludes with 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. |
| JEL: | C43 E31 |
| Date: | 2011–01–31 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1118&r=ets |
| By: | Francesco Carravetta; Marco M. Sorge |
| Abstract: | This paper describes a method for solving a class of forward-looking Markov-switching Rational Expectations models under noisy measurement, by specifying the unobservable expectations component as a general-measurable function of the observable states of the system, to be determined optimally via stochastic control and filtering theory. Solution existence is proved by setting this function to the regime-dependent feedback control minimizing the mean-square deviation of the equilibrium path from the corresponding perfect-foresight autoregressive Markov jump state motion. As the exact expression of the conditional (rational) expectations term is derived both in finite and infinite horizon model formulations, no (asymptotic) stationarity assumptions are needed to solve forward the system, for only initial values knowledge is required. A simple sufficient condition for the mean-square stability of the obtained rational expectations equilibrium is also provided. |
| Keywords: | Rational Expectations, Markov-switching dynamic systems, Dynamic programming, Time-varying Kalman filter |
| JEL: | C5 C61 C62 C63 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:bon:bonedp:bgse05_2011&r=ets |
| By: | Pagliarani, Stefano; Pascucci, Andrea |
| Abstract: | We present a simplified approach to the analytical approximation of the transition density related to a general local volatility model. The methodology is sufficiently flexible to be extended to time-dependent coefficients, multi-dimensional stochastic volatility models, degenerate parabolic PDEs related to Asian options and also to include jumps. |
| Keywords: | option pricing; analytical approximation; local volatility |
| JEL: | G12 |
| Date: | 2011–05–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:31107&r=ets |