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on Econometrics |
| By: | Meitz, Mika (Dept. of Economic Statistics, Stockholm School of Economics); Saikkonen, Pentti (Dept. of Statistics, University of Helsinki) |
| Abstract: | This paper studies a class of Markov models which consist of two components. Typically, one of the components is observable and the other is unobservable or 'hidden'. Conditions under which (a form of) geometric ergodicity of the unobservable component is inherited by the joint process formed of the two components are given. This immediately implies the existence of initial values such that the joint process is strictly stationary and beta-mixing. In addition to this, conditions for beta-mixing and existence of moments for the joint process are also provided in the case of (possibly) nonstationary initial values. All these results are applied to a general model which includes as special cases various first order generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive conditional duration (ACD) models with possibly complicated nonlinear structures. |
| Keywords: | - |
| JEL: | C22 |
| Date: | 2004–10–07 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:hastef:0573&r=ecm |
| By: | Mototsugu Shintani (Department of Economics, Vanderbilt University) |
| Abstract: | This paper extends the diffusion index (DI) forecast approach of Stock and Watson (1998, 2002) to the case of possibly nonlinear dynamic factor models. When the number of series is large, a two-step procedure based on the principal components method is useful since it allows the wide variety of the nonlinearity in the factors. The factors extracted from a large Japanese data suggest some evidence of nonlinear structure. Furthermore, both the linear and nonlinear DI forecasts in Japan outperform traditional time series forecasts, while the linear DI forecast, in most cases, performs as well as the nonlinear DI forecast. |
| Keywords: | Diffusion Index, Dynamic Factor Model, Nonlinearity, Prediction |
| JEL: | F31 F41 |
| Date: | 2003–10 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:0322&r=ecm |
| By: | OLE E. BARNDORFF-NIELSEN; PETER REINHARD HANSEN; ASGER LUNDE; NEIL SHEPHARD |
| Abstract: | We consider kernel-based estimators of integrated variances in the presence of independent market microstructure effects. We derive the bias and variance properties for all regular kernel-based estimators and derive a lower bound for their asymptotic variance. Further we show that the subsample-based estimator is closely related to a Bartlett-type kernel estimator. The small difference between the two estimators due to end effects, turns out to be key for the consistency of the subsampling estimator. This observation leads us to a modified class of kernel-based estimators, which are also consistent. We study the efficiency of our new kernel-based procedure. We show that optimal modified kernel-based estimator converges to the integrated variance at the optimal rate, m^1/4, where m is the number of intraday returns. |
| JEL: | C13 C22 |
| Date: | 2004 |
| URL: | http://d.repec.org/n?u=RePEc:sbs:wpsefe:2004fe20&r=ecm |
| By: | Ole E. Barndorff-Nielsen; Neil Shephard |
| Abstract: | In this brief note we review some of our recent results on the use of high frequency financial data to estimate objects like integrated variance in stochastic volatility models. Interesting issues include multipower variation, jumps and market microstructure effects. |
| Date: | 2004 |
| URL: | http://d.repec.org/n?u=RePEc:sbs:wpsefe:2004fe22&r=ecm |
| By: | Ole BARNDORFF--NIELSEN; Svend Erik GRAVERSEN; Jean JACOD; Mark PODOLSKIJ; Neil SHEPHARD |
| Abstract: | Consider a semimartingale of the form Y_{t}=Y_0+\int _0^{t}a_{s}ds+\int _0^{t}_{s-} dW_{s}, where a is a locally bounded predictable process and (the "volatility") is an adapted right--continuous process with left limits and W is a Brownian motion. We define the realised bipower variation process V(Y;r,s)_{t}^n=n^{((r+s)/2)-1} \sum_{i=1}^{[nt]}|Y_{(i/n)}-Y_{((i-1)/n)}|^{r}|Y_{((i+1)/n)}-Y_{(i/n)}|^{s}, where r and s are nonnegative reals with r+s>0. We prove that V(Y;r,s)_{t}n converges locally uniformly in time, in probability, to a limiting process V(Y;r,s)_{t} (the "bipower variation process"). If further is a possibly discontinuous semimartingale driven by a Brownian motion which may be correlated with W and by a Poisson random measure, we prove a central limit theorem, in the sense that \sqrt(n) (V(Y;r,s)^n-V(Y;r,s)) converges in law to a process which is the stochastic integral with respect to some other Brownian motion W', which is independent of the driving terms of Y and \sigma. We also provide a multivariate version of these results. |
| Date: | 2004 |
| URL: | http://d.repec.org/n?u=RePEc:sbs:wpsefe:2004fe21&r=ecm |
| By: | Peter X.-K. Song (Department of Mathematics and Statistics, York University; Toronto, ON); Yanqin Fan (Department of Economics, Vanderbilt University); John D. Kalbfleisch (Department of Biostatistics, University of Michigan School of Public Health) |
| Abstract: | This paper presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest. The method circumvents the need to compute second order derivatives of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log likelihood from a simply analyzed model and the second part is used to update estimates from the first. Convergence properties of this fixed point algorithm are examined and asymptotics are derived for estimators obtained by using only a finite number of steps. Illustrative examples considered in the paper include bivariate and multivariate Gaussian copula models, nonnormal random effects and state space models. Properties of the algorithm and of estimators are evaluated in simulation studies on a bivariate copula model and a nonnormal linear random effects model. |
| Keywords: | Copula models, fixed-point algorithm, information dominance, iterative algorithm, nonnormal random effects, score equation, state space models |
| JEL: | C13 C61 C63 |
| Date: | 2003–09 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:0319&r=ecm |
| By: | Mototsugu Shintani (Department of Economics, Vanderbilt University); Oliver Linton (Department of Economics, London School of Economics) |
| Abstract: | This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for testing the chaotic hypothesis based on the estimated Lyapunov exponents and a consistent variance estimator. A simulation study to evaluate small sample performance is reported. We also apply our procedures to daily stock return data. In most cases, the hypothesis of chaos in the stock return series is rejected at the 1% level with an exception in some higher power transformed absolute returns. |
| Keywords: | Artificial neural networks, nonlinear dynamics, nonlinear time series, nonparametric regression, sieve estimation |
| JEL: | C14 C22 |
| Date: | 2003–05 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:0309&r=ecm |
| By: | Joshua D. Angrist; Guido M. Kuersteiner |
| Abstract: | Time series data are widely used to explore causal relationships, typically in a regression framework with lagged dependent variables. Regression-based causality tests rely on an array of functional form and distributional assumptions for valid causal inference. This paper develops a semi-parametric test for causality in models linking a binary treatment or policy variable with unobserved potential outcomes. The procedure is semiparametric in the sense that we model the process determining treatment -- the policy propensity score -- but leave the model for outcomes unspecified. This general approach is motivated by the notion that we typically have better prior information about the policy determination process than about the macro-economy. A conceptual innovation is that we adapt the cross-sectional potential outcomes framework to a time series setting. This leads to a generalized definition of Sims (1980) causality. We also develop a test for full conditional independence, in contrast with the usual focus on mean independence. Our approach is illustrated using data from the Romer and Romer (1989) study of the relationship between the Federal reserve's monetary policy and output. |
| JEL: | C14 C22 E52 |
| Date: | 2004–12 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:10975&r=ecm |
| By: | González Gómez, Andrés (Dept. of Economic Statistics, Stockholm School of Economics) |
| Abstract: | In this paper we introduce the Smooth Permanent Surge [SPS] model. The model is an integrated non lineal moving average process with possibly unit roots in the moving average coefficients. The process nests the Stochastic Permanent Break [STOPBREAK] process by Engle and Smith (1999) and in a limiting case it converges to Threshold Integrated Moving Average [TIMA] models by Gonzalo and Martinez (2003). A test of SPS against STOPBREAK process is presented. Additionally, we introduce a new test for testing SPS process against the random walk. The small sample properties of these tests are <p> investigated by Monte Carlo experiments. An application to the stock markets is presented. |
| Keywords: | Linearity test; Monte Carlo testing; Smooth transitions; Moving Averages Models; Permanent Shock; Transitory Shocks. |
| JEL: | C12 C15 C22 C51 C52 |
| Date: | 2004–12–07 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:hastef:0572&r=ecm |
| By: | Clifford Hurvich (New York University USA); Eric Moulines (ENST, Paris, France); Philippe Soulier (Universite Paris X, France) |
| Abstract: | We consider semiparametric estimation of the memory parameter in a model which includes as special cases both the long-memory stochastic volatility (LMSV) and fractionally integrated exponential GARCH (FIEGARCH) models. Under our general model the logarithms of the squared returns can be decomposed into the sum of a long-memory signal and a white noise. We consider periodogram-based estimators using a local Whittle criterion function. We allow the optional inclusion of an additional term to account for possible correlation between the signal and noise processes, as would occur in the FIEGARCH model. We also allow for potential nonstationarity in volatility, by allowing the signal process to have a memory parameter d^* >= 1/2. We show that the local Whittle estimator is considtent for d^* in (0,1). We also show that the local Whittle estimator is asymptotically normal for d^* in (0,3/4) and asymptotically recovers the optimal semiparametric rate of convergence for this problem. In particular, if the spectral density of the short memory component of the signal is sufficiently smooth, a convergence rate of n^{2/5-\delta} for d^* in (0,3/4) can be attained, where n is the sample size and \delta > 0 is arbitrarily small. This represents a strong improvement over the performance of existing semiparametric estimators of persistence in volatility. We also prove that the standard Gaussian semiparametric estimator is asymptotically normal if d^*=0. This yields a test for long memory in volatility. |
| Keywords: | LMSV, FIEGARCH |
| JEL: | C1 C2 C3 C4 C5 C8 |
| Date: | 2004–12–14 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpem:0412006&r=ecm |
| By: | Phillip Gould; Anne B. Koehler; Farshid Vahid-Araghi; Ralph D. Snyder; J. Keith Ord; Rob J. Hyndman |
| Abstract: | A new approach to forecasting seasonal data is proposed where seasonal terms can be updated using the most recent relevant information. It was developed to handle features encountered in hourly electricity load data and daily hospital admissions data. The associated state space model is estimated with methods adapted from exponential smoothing, although the Kalman filter may also be used. It nests existing seasonal models and outperforms them over a range of prediction horizons on the data. The approach is likely to be useful in a wide range of applications involving both high and low frequency data. |
| Keywords: | Exponential smoothing; Holt-Winters; Seasonality; Structural time series model |
| JEL: | C22 |
| Date: | 2004–12 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2004-28&r=ecm |
| By: | Mengchen Hsieh (New York University); Clifford Hurvich (New York University); Philippe Soulier (Universite Paris X) |
| Abstract: | We consider processes with second order long range dependence resulting from heavy tailed durations. We refer to this phenomenon as duration- driven long range dependence (DDLRD), as opposed to the more widely studied linear long range dependence based on fractional differencing of an $iid$ process. We consider in detail two specific processes having DDLRD, originally presented in Taqqu and Levy (1986), and Parke (1999). For these processes, we obtain the limiting distribution of suitably standardized discrete Fourier transforms (DFTs) and sample autocovariances. At low frequencies, the standardized DFTs converge to a stable law, as do the standardized autocovariances at fixed lags. Finite collections of standardized autocovariances at a fixed set of lags converge to a degenerate distribution. The standardized DFTs at high frequencies converge to a Gaussian law. Our asymptotic results are strikingly similar for the two DDLRD processes studied. We calibrate our asymptotic results with a simulation study which also investigates the properties of the semiparametric log periodogram regression estimator of the memory parameter. |
| Keywords: | Long Memory; Structural Change |
| JEL: | C1 C2 C3 C4 C5 C8 |
| Date: | 2004–12–15 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpem:0412009&r=ecm |
| By: | Willa Chen (Texas A&M University); Clifford Hurvich (New York University) |
| Abstract: | We consider a common components model for multivariate fractional cointegration, in which the s>=1 components have different memory parameters. The cointegrating rank is allowed to exceed 1. The true cointegrating vectors can be decomposed into orthogonal fractional cointegrating subspaces such that vectors from distinct subspaces yield cointegrating errors with distinct memory parameters, denoted by d_k for k=1,...,s. We estimate each cointegrating subsspace separately using appropriate sets of eigenvectors of an averaged periodogram matrix of tapered, differenced observations. The averaging uses the first m Fourier frequencies, with m fixed. We will show that any vector in the k'th estimated coingetraging subspace is, with high probability, close to the k'th true cointegrating subspace, in the sense that the angle between the estimated cointegrating vector and the true cointegrating subspace converges in probability to zero. The angle is O_p(n^{- \alpha_k}), where n is the sample size and \alpha_k is the shortest distance between the memory parameters corresponding to the given and adjacent subspaces. We show that the cointegrating residuals corresponding to an estimated cointegrating vector can be used to obtain a consistent and asymptotically normal estimate of the memory parameter for the given cointegrating subspace, using a univariate Gaussian semiparametric estimator with a bandwidth that tends to \infty more slowly than n. We also show how these memory parameter estimates can be used to test for fractional cointegration and to consistently identify the cointegrating subspaces. |
| Keywords: | Fractional Cointegration; Long Memory; Tapering; Periodogram |
| JEL: | C1 C2 C3 C4 C5 C8 |
| Date: | 2004–12–15 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpem:0412007&r=ecm |
| By: | Yakov Amihud (New York University); Clifford Hurvich (New York University); Yi Wang (New York University) |
| Abstract: | We propose a new hypothesis testing method for multi-predictor regressions with finite samples, where the dependent variable is regressed on lagged variables that are autoregressive. It is based on the augmented regressiom method (ARM; Amihud and Hurvich (2004)), which produces reduced-bias coefficients and is easy to implement. The method's usefulness is demonstrated by simulations and by an empirical example, where stock returns are predicted by dividend yield and by bond yield spread. For single-predictor regressions, we show that the ARM outperforms bootstrapping and that the ARM performs better than Lewellen's (2003) method in many situations. |
| Keywords: | Augmented Regression Method (ARM); Bootstrapping; Hypothesis Testing |
| JEL: | G |
| Date: | 2004–12–15 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpfi:0412022&r=ecm |
| By: | Yakov Amihud (New York University); Clifford Hurvich (New York University) |
| Abstract: | Standard predictive regressions produce biased coefficient estimates in small samples when the regressors are Gaussian first-order autoregressive with errors that are correlated with the error series of the dependent variable; see Stambaugh (1999) for the single-regressor model. This paper proposes a direct and convenient method to obtain reduced-bias estimators for single and multiple regressor models by employing an augmented regression, adding a proxy for the errors in the autoregressive model. We derive bias expressions for both the ordinary least squares and our reduced-bias estimated coefficients. For the standard errors of the estimated predictive coefficients we develop a heuristic estimator which performs well in simulations, for both the single-predictor model and an important specification of the multiple- predictor model. The effectiveness of our method is demonstrated by simulations and by empirical estimates of common predictive models in finance. Our empirical results show that some of the predictive variables that were significant under ordinary least squares become insignificant under our estimation procedure. |
| Keywords: | Stock Returns; Dividend Yields; Autoregressive Models |
| JEL: | C1 C2 C3 C4 C5 C8 |
| Date: | 2004–12–15 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpem:0412008&r=ecm |