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on Econometric Time Series |
| By: | Zhongfang He (University of Toronto (Canada)); John M. Maheu (University of Toronto (Canada); Rimini Centre for Economic Analysis, Rimini, Italy); |
| Abstract: | A sequential Monte Carlo method for estimating GARCH models subject to an unknown number of structural breaks is proposed. Particle filtering techniques allow for fast and efficient updates of posterior quantities and forecasts in real-time. The method conveniently deals with the path dependence problem that arises in these type of models. The performance of the method is shown to work well using simulated data. Applied to daily NASDAQ returns, the evidence favors a partial structural break specification in which only the intercept of the conditional variance equation has breaks compared to the full structural break specification in which all parameters are subject to change. The empirical application underscores the importance of model assumptions when investigating breaks. A model with normal return innovations result in strong evidence of breaks; while more flexible return distributions such as t-innovations or a GARCH-jump mixture model still favor breaks but indicate much more uncertainty regarding the time and impact of them. |
| Keywords: | particle filter, GARCH model, change point, sequential Monte Carlo |
| Date: | 2009–01 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:11-09&r=ets |
| By: | Carlos Llano (Universidad Autonoma de Madrid, Spain The Rimini Centre for Economic Analysis, Rimini, Italy); Wolfgang Polasek (Institute for Advanced Studies, Vienna, Austria and The Rimini Centre for Economic Analysis, Italy); Richard Sellner (Institute for Advanced Studies, Vienna, Austria) |
| Abstract: | Completing data sets that are collected in heterogeneous units is a quite frequent problem. Chow and Lin (1971) were the rst to develop a unied framework for the three problems (interpolation, extrapolation and distribution) of predicting times series by related series (the `indicators'). This paper develops a spatial Chow-Lin procedure for cross-sectional and panel data and compares the classical and Bayesian estimation methods. We outline the error covariance structure in a spatial context and derive the BLUE for the ML and Bayesian MCMC estimation. Finally, we apply the procedure to Spanish regional GDP data between 2000-2004. We assume that only NUTS-2 GDP is known and predict GDP at NUTS-3 level by using socio-economic and spatial information available at NUTS-3. The spatial neighborhood is dened by either km distance, travel time, contiguity and trade relationships. After running some sensitivity analysis, we present the forecast accuracy criteria comparing the predicted values with the observed ones. |
| Keywords: | Interpolation, Spatial panel econometrics, MCMC, Spatial |
| Date: | 2009–01 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:05-09&r=ets |
| By: | Alexander Subbotin (Centre d'Economie de la Sorbonne et Higher School of Economics); Thierry Chauveau (Centre d'Economie de la Sorbonne); Kateryna Shapovalova (Centre d'Economie de la Sorbonne) |
| Abstract: | We overview different methods of modeling volatility of stock prices and exchange rates, focusing on their ability to reproduce the empirical properties in the corresponding time series. The properties of price fluctuations vary across the time scales of observation. The adequacy of different models for describing price dynamics at several time horizons simultaneously is the central topic of this study. We propose a detailed survey of recent volatility models, accounting for multiple horizons. These models are based on different and sometimes competing theoretical concepts. They belong either to GARCH or stochastic volatility model families and often borrow methodological tools from statistical physics. We compare their properties and comment on their pratical usefulness and perspectives. |
| Keywords: | Volatility modeling, GARCH, stochastic volatility, volatility cascade, multiple horizons in volatility. |
| JEL: | G10 C13 |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:09036&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Liangjun Su (School of Economics, Singapore Management University) |
| Abstract: | Recent work by Wang and Phillips (2009b, c) has shown that ill posed inverse problems do not arise in nonstationary nonparametric regression and there is no need for nonparametric instrumental variable estimation. Instead, simple Nadaraya Watson nonparametric estimation of a (possibly nonlinear) cointegrating regression equation is consistent with a limiting (mixed) normal distribution irrespective of the endogeneity in the regressor, near integration as well as integration in the regressor, and serial dependence in the regression equation. The present paper shows that some closely related results apply in the case of structural nonparametric regression with independent data when there are continuous location shifts in the regressor. In such cases, location shifts serve as an instrumental variable in tracing out the regression line similar to the random wandering nature of the regressor in a cointegrating regression. Asymptotic theory is given for local level and local linear nonparametric estimators, links with nonstationary cointegrating regression theory and nonparametric IV regression are explored, and extensions to the stationary strong mixing case are given. In contrast to standard nonparametric limit theory, local level and local linear estimators have identical limit distributions, so the local linear approach has no apparent advantage in the present context. Some interesting cases are discovered, which appear to be new in the literature, where nonparametric estimation is consistent whereas parametric regression is inconsistent even when the true (parametric) regression function is known. The methods are further applied to establish a limit theory for nonparametric estimation of structural panel data models with endogenous regressors and individual effects. Some simulation evidence is reported. |
| Keywords: | Fixed effects, Kernel regression, Location shift, Mixing, Nonparametric IV, Nonstationarity, Panel model, Structural estimation |
| JEL: | C13 C14 |
| Date: | 2009–06 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1702&r=ets |
| By: | Jin Seo Cho (Dept. of Economics, Korea University); Chirok Han (Dept. of Economics, Korea University); Peter C.B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | Least absolute deviations (LAD) estimation of linear time-series models is considered under conditional heteroskedasticity and serial correlation. The limit theory of the LAD estimator is obtained without assuming the finite density condition for the errors that is required in standard LAD asymptotics. The results are particularly useful in application of LAD estimation to financial time series data. |
| Keywords: | Asymptotic leptokurtosis, Convex function, Infinite density, Least absolute deviations, Median, Weak convergence |
| JEL: | C12 G11 |
| Date: | 2009–06 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1703&r=ets |
| By: | Ioannis Kasparis (University of Cyprus); Peter C.B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The requisite limit theory involves sample covariances of integrable transformations of non-stationary sequences and time translated sequences, allowing for the presence of a bandwidth parameter so as to accommodate kernel regression. The theory is an extension of Wang and Phillips (2008) and is useful for the analysis of nonparametric regression models with a misspecified lag structure and in situations where temporal aggregation issues arise. The limit properties of the Nadaraya-Watson (NW) estimator for cointegrating regression under misspecified lag structure are derived, showing the NW estimator to be inconsistent with a "pseudo-true function" limit that is a local average of the true regression function. In this respect nonlinear cointegrating regression differs importantly from conventional linear cointegration which is invariant to time translation. When centred on the pseudo-function and appropriately scaled, the NW estimator still has a mixed Gaussian limit distribution. The convergence rates are the same as those obtained under correct specification but the variance of the limit distribution is larger. Some applications of the limit theory to non-linear distributed lag cointegrating regression are given and the practical import of the results for index models, functional regression models, and temporal aggregation are discussed. |
| Keywords: | Dynamic misspecification, Functional regression, Integrable function, Integrated process, Local time, Misspecification, Mixed normality, Nonlinear cointegration, Nonparametric regression |
| JEL: | C22 C32 |
| Date: | 2009–06 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1700&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Liangjun Su (School of Economics, Singapore Management University) |
| Abstract: | This paper explores a paradox discovered in recent work by Phillips and Su (2009). That paper gave an example in which nonparametric regression is consistent whereas parametric regression is inconsistent even when the true regression functional form is known and used in regression. This appears to be a paradox, as knowing the true functional form should not in general be detrimental in regression. In the present case, local regression methods turn out to have a distinct advantage because of endogeneity in the regressor. The paradox arises because additional correct information is not necessarily advantageous when information is incomplete. In the present case, endogeneity in the regressor introduces bias when the true functional form is known, but interestingly does not do so in local nonparametric regression. We examine this example in detail and propose two new consistent estimators for the parametric regression, which address the endogeneity in the regressor by means of spatial bounding and bias correction using nonparametric estimation. Some simulations are reported illustrating the paradox and the new procedures. |
| Keywords: | Bias-correction, Endogeneity, Kernel regression, L_{2} regression, Location shift, Nonparametric IV, Nonstationarity, Paradox, Spatial regression, Structural Estimation |
| JEL: | C13 C14 |
| Date: | 2009–06 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1704&r=ets |
| By: | Chirok Han (Dept. of Economics, Korea University); Jin Seo Cho (Dept. of Economics, Korea University); Peter C.B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | Statistics are developed to test for the presence of an asymptotic discontinuity (or infinite density or peakedness) in a probability density at the median. The approach makes use of work by Knight (1998) on L_1 estimation asymptotics in conjunction with non-parametric kernel density estimation methods. The size and power of the tests are assessed, and conditions under which the tests have good performance are explored in simulations. The new methods are applied to stock returns of leading companies across major U.S. industry groups. The results confirm the presence of infinite density at the median as a new significant empirical evidence for stock return distributions. |
| Keywords: | Asymptotic leptokurtosis, Infinite density at the median, Least absolute deviations, Kernel density estimation, Stock returns, Stylized facts |
| JEL: | C12 G11 |
| Date: | 2009–06 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1701&r=ets |
| By: | Proietti, Tommaso; Luati, Alessandra |
| Abstract: | The paper concerns the design of nonparametric low-pass filters that have the property of reproducing a polynomial of a given degree. Two approaches are considered. The first is locally weighted polynomial regression (LWPR), which leads to linear filters depending on three parameters: the bandwidth, the order of the fitting polynomial, and the kernel. We find a remarkable linear (hyperbolic) relationship between the cutoff period (frequency) and the bandwidth, conditional on the choices of the order and the kernel, upon which we build the design of a low-pass filter. The second hinges on a generalization of the maximum concentration approach, leading to filters related to discrete prolate spheroidal sequences (DPSS). In particular, we propose a new class of lowpass filters that maximize the concentration over a specified frequency range, subject to polynomial reproducing constraints. The design of generalized DPSS filters depends on three parameters: the bandwidth, the polynomial order, and the concentration frequency. We discuss the properties of the corresponding filters in relation to the LWPR filters, and illustrate their use for the design of low-pass filters by investigating how the three parameters are related to the cutoff frequency. |
| Keywords: | Trend filters; Kernels; Concentration; Filter Design. |
| JEL: | E32 C14 C22 |
| Date: | 2009–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:15510&r=ets |