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on Econometric Time Series |
| By: | Afonso Gonçalves da Silva; Afonso Gonçalves da Silva; Peter M Robinson; Peter M Robinson |
| Abstract: | Asset returns are frequently assumed to be determined by one or more commonfactors. We consider a bivariate factor model, where the unobservable commonfactor and idiosyncratic errors are stationary and serially uncorrelated, but havestrong dependence in higher moments. Stochastic volatility models for the latentvariables are employed, in view of their direct application to asset pricing models.Assuming the underlying persistence is higher in the factor than in the errors, afractional cointegrating relationship can be recovered by suitable transformation ofthe data. We propose a narrow band semiparametric estimate of the factorloadings, which is shown to be consistent with a rate of convergence, and its finitesample properties are investigated in a Monte Carlo experiment. |
| Keywords: | Fractional cointegration, stochastic volatility, narrow band leastsquares, semiparametric analysis. |
| JEL: | C22 |
| Date: | 2007–05 |
| URL: | http://d.repec.org/n?u=RePEc:cep:stiecm:/2007/519&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Chang Sik Kim (School of Economics, Sungkyunkwan University) |
| Abstract: | An asymptotic expansion is given for the autocovariance matrix of a vector of stationary long-memory processes with memory parameters d satisfying 0 < d < 1/2. The theory is then applied to deliver formulae for the long run covariance matrices of multivariate time series with long memory. |
| Keywords: | Asymptotic expansion, Autocovariance function, Fourier integral, Long memory, Long run variance, Spectral density |
| JEL: | C22 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1611&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Ke-Li Xu (Dept. of Mathematics, Yale University) |
| Abstract: | This paper proposes a novel positive nonparametric estimator of the conditional variance function without relying on a logarithmic transformation. The basic idea is to apply the re-weighted Nadaraya-Watson regression estimator of Hall and Presnell (1999, Journal of the Royal Statistical Society B, 61, 143--158) to squared residuals. The new conditional variance estimator is asymptotically equivalent to the local linear estimator and is restricted to be positive in finite samples. A small simulation is performed to compare the new methodology with Ziegelmann's (2002) local exponential and Yu and Jones's (2004) local likelihood-based estimators of the conditional variance. |
| Keywords: | Conditional variance function, Empirical likelihood, Heteroskedasticity, Local linear estimator, Nadaraya-Watson estimator, Nonlinear time series; Nonparametric regression, Volatility |
| JEL: | C22 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1612&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Tassos Magdalinos (University of Nottingham, UK) |
| Abstract: | A limit theory is developed for multivariate regression in an explosive cointegrated system. The asymptotic behavior of the least squares estimator of the cointegrating coefficients is found to depend upon the precise relationship between the explosive regressors. When the eigenvalues of the autoregressive matrix are distinct, the centered least squares estimator has an exponential rate of convergence and a mixed normal limit distribution. No central limit theory is applicable here and Gaussian innovations are assumed. On the other hand, when some regressors exhibit common explosive behavior, a different mixed normal limiting distribution is derived with rate of convergence reduced to n^0.5. In the latter case, mixed normality applies without any distributional assumptions on the innovation errors by virtue of a Lindeberg type central limit theorem. Conventional statistical inference procedures are valid in this case, the stationary convergence rate dominating the behavior of the least squares estimator. |
| Keywords: | Central limit theory, Exposive cointegration, Explosive process, Mixed normality |
| JEL: | C22 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1614&r=ets |
| By: | Michael J. Dueker; Zacharias Psaradakis; Martin Sola; Fabio Spagnolo |
| Abstract: | In this paper we propose a contemporaneous threshold multivariate smooth transition autoregressive (C-MSTAR) model in which the regime weights depend on the ex ante probabilities that latent regime-specific variables exceed certain threshold values. The model is a multivariate generalization of the contemporaneous threshold autoregressive model introduced by Dueker et al. (2007). A key feature of the model is that the transition function depends on all the parameters of the model as well as on the data. The stability and distributional properties of the proposed model are investigated. The C-MSTAR model is also used to examine the relationship between US stock prices and interest rates. |
| Keywords: | Time-series analysis ; Capital assets pricing model |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedlwp:2007-019&r=ets |
| By: | Rob J. Hyndman; Yeasmin Khandakar |
| Abstract: | Automatic forecasts of large numbers of univariate time series are often needed in business and other contexts. We describe two automatic forecasting algorithms that have been implemented in the forecast package for R. The first is based on innovations state space models that underly exponential smoothing methods. The second is a step-wise algorithm for forecasting with ARIMA models. The algorithms are applicable to both seasonal and non-seasonal data, and are compared and illustrated using four real time series. We also briefly describe some of the other functionality available in the forecast package. |
| Keywords: | ARIMA models; automatic forecasting; exponential smoothing; prediction intervals; state space models; time series, R. |
| JEL: | C53 C22 C52 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2007-6&r=ets |
| By: | Pim Ouwehand; Rob J. Hyndman; Ton G. de Kok; Karel H. van Donselaar |
| Abstract: | We present an approach to improve forecast accuracy by simultaneously forecasting a group of products that exhibit similar seasonal demand patterns. Better seasonality estimates can be made by using information on all products in a group, and using these improved estimates when forecasting at the individual product level. This approach is called the group seasonal indices (GSI) approach, and is a generalization of the classical Holt-Winters procedure. This article describes an underlying state space model for this method and presents simulation results that show when it yields more accurate forecasts than Holt-Winters. |
| Keywords: | Common seasonality; demand forecasting; exponential smoothing; Holt-Winters; state space model. |
| JEL: | C53 C22 C52 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2007-7&r=ets |
| By: | Gunky Kim; Mervyn J. Silvapulle; Paramsothy Silvapulle |
| Abstract: | A semiparametric method is studied for estimating the dependence parameter and the joint distribution of the error term in a class of multivariate time series models when the marginal distributions of the errors are unknown. This method is a natural extension of Genest et al. (1995a) for independent and identically distributed observations. The proposed method first obtains √n-consistent estimates of the parameters of each univariate marginal time-series, and computes the corresponding residuals. These are then used to estimate the joint distribution of the multivariate error terms, which is specified using a copula. Our developments and proofs make use of, and build upon, recent elegant results of Koul and Ling (2006) and Koul (2002) for these models. The rigorous proofs provided here also lay the foundation and collect together the technical arguments that would be useful for other potential extensions of this semiparametric approach. It is shown that the proposed estimator of the dependence parameter of the multivariate error term is asymptotically normal, and a consistent estimator of its large sample variance is also given so that confidence intervals may be constructed. A large scale simulation study was carried out to compare the estimators particularly when the error distributions are unknown, which is almost always the case in practice. In this simulation study, our proposed semiparametric method performed better than the well-known parametric methods. An example on exchange rates is used to illustrate the method. |
| Keywords: | Association; Copula; Estimating Equation; Pseudolikelihood; Semiparametric. |
| JEL: | C13 C14 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2007-8&r=ets |
| By: | Tatsuyoshi Junji Shimada (School of Management, Aoyama Gakuin University); Yoshihiko Tsukuda (Graduate School of Economics, Tohoku University); Tatsuyoshi Miyakoshi (Graduate School of Economics and Osaka School of International Public Policy (OSIPP), Osaka University) |
| Abstract: | This paper investigates whether the upturns and downturns of the U.S. market exert asymmetric influence on the conditional mean and volatility of the Japanese market using the daily returns on stock price indices. Using both the EGARCH and SV models, which simultaneously allow two kinds of asymmetric international transmissions across the markets, the result reconfirms the symmetric transmission in the conditional mean obtained by Bahng and Shin (2003) and the asymmetric transmission in the conditional volatility obtained by Koutmos and Booth (1995) although each of them analyzed the only one spillover effect separately. Although the EGARCH and SV models lead to similar results about the spillover effects, the SV model is preferred to the EGARCH model in terms of the Lagrange Multiplier test of the EGARCH against the SV models. The shock to volatility in the U.S. market with the SV model is asymmetrically transmitted to the volatility in the Japanese market. |
| Keywords: | Economic growth; asymmetric transmission; conditional mean and volatility; Japan and the U.S. stock markets; EGARCH and SV models; |
| JEL: | G14 G15 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:osk:wpaper:0723&r=ets |
| By: | Ralf Becker; Adam Clements |
| Abstract: | Forecasting volatility has received a great deal of research attention. Many articles have considered the relative performance of econometric model based and option implied volatility forecasts. While many studies have found that implied volatility is the preferred approach, a number of issues remain unresolved. One issue being the relative merit of combination forecasts. By utilising recent econometric advances, this paper considers whether combination forecasts of S&P 500 volatility are statistically superior to a wide range of model based forecasts and implied volatility. It is found that combination forecasts are the dominant approach, indicating that the VIX cannot simply be viewed as a combination of various model based forecasts. |
| Keywords: | Implied volatility, volatility forecasts, volatility models, realized volatility, combination forecasts. |
| JEL: | C12 C22 G00 |
| Date: | 2007–06–14 |
| URL: | http://d.repec.org/n?u=RePEc:qut:auncer:2007-92&r=ets |
| By: | Ralf Becker; Adam Clements |
| Abstract: | This paper presents a GARCH type volatility model with a time-varying unconditional volatility which is a function of macroeconomic information. It is an extension of the SPLINE GARCH model proposed by Engle and Rangel (2005). The advantage of the model proposed in this paper is that the macroeconomic information available (and/or forecasts)is used in the parameter estimation process. Based on an application of this model to S&P500 share index returns, it is demonstrated that forecasts of macroeconomic variables can be easily incorporated into volatility forecasts for share index returns. It transpires that the model proposed here can lead to significantly improved volatility forecasts compared to traditional GARCH type volatility models. |
| Keywords: | Volatility, macroeconomic data, forecast, spline, GARCH. |
| JEL: | C12 C22 G00 |
| Date: | 2007–06–14 |
| URL: | http://d.repec.org/n?u=RePEc:qut:auncer:2007-93&r=ets |
| By: | Rao, B. Bhaskara |
| Abstract: | Applied economists working with time series data face a dilemma in selecting between models with deterministic and stochastic trends. While models with deterministic trends are widely used, models with stochastic trends are not so well known. In an influential paper Harvey (1997) strongly advocates a structural time series approach with stochastic trends in place of the widely used autoregressive models based on unit root tests and cointegration techniques. Therefore, it is important to understand their relative merits. This paper suggests that both methodologies are useful and they may perform differently in different models. This paper provides a few guidelines to the applied economists to understand these alternative methods. |
| Keywords: | Stochastic and Deterministic Trends; Bai-Perron Tests; STAMP; Structural Time Series Models. |
| JEL: | C10 C22 C13 C00 C20 |
| Date: | 2007–06–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:3580&r=ets |
| By: | David Hendry (Department of Economics, University of Oxford); Carlos Santos (Faculdade de Economia e Gestão, Universidade Católica Portuguesa (Porto)) |
| Abstract: | We develop a new automatically-computable test for super exogeneity, using a variant of general-to-specific modelling. Based on the recent developments in impulse saturation applied to marginal models under the null that no impulses matter, we select the significant impulses for testing in the conditional. The approximate analytical non-centrality of the test is derived for a failure of invariance and for a failure of weak exogeneity when there is a shift in the marginal model. Monte Carlo simulations confirm the nominal significance levels under the null, and power against the two alternatives. |
| Keywords: | super exogeneity, general-to-specific, test power, indicators, cobreaking |
| JEL: | C51 C22 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:cap:wpaper:112007&r=ets |