
on Econometric Time Series 
By:  Morten Ørregaard Nielsen (School of Economics and Management, University of Aarhus, Denmark) 
Abstract:  This paper presents a family of simple nonparametric unit root tests indexed by one parameter, d, and containing Breitung’s (2002) test as the special case d = 1. It is shown that (i) each member of the family with d > 0 is consistent, (ii) the asymptotic distribution depends on d, and thus reflects the parameter chosen to implement the test, and (iii) since the asymptotic distribution depends on d and the test remains consistent for all d > 0, it is possible to analyze the power of the test for different values of d. The usual PhillipsPerron or DickeyFuller type tests are indexed by bandwidth, lag length, etc., but have none of these three properties. It is shown that members of the family with d < 1 have higher asymptotic local power than the Breitung (2002) test, and when d is small the asymptotic local power of the proposed nonparametric test is relatively close to the parametric power envelope, particularly in the case with a linear timetrend. Furthermore, GLS detrending is shown to improve power when d is small, which is not the case for Breitung’s (2002) test. Simulations demonstrate that when applying a sieve bootstrap procedure, the proposed variance ratio test has very good size properties, with finite sample power that is higher than that of Breitung’s (2002) test and even rivals the (nearly) optimal parametric GLS detrended augmented DickeyFuller test with lag length chosen by an information criterion. 
Keywords:  Augmented DickeyFuller test, fractional integration, GLS detrending, nonparametric, nuisance parameter, tuning parameter, power envelope, unit root test, variance ratio 
JEL:  C22 
Date:  2008–06–30 
URL:  http://d.repec.org/n?u=RePEc:aah:create:200836&r=ets 
By:  Dennis Kristensen (School of Economics and Management, University of Aarhus, Denmark) 
Abstract:  The main uniform convergence results of Hansen (2008) are generalized in two directions: Data is allowed to (i) be heterogenously dependent and (ii) depend on a (possibly unbounded) parameter. These results are useful in semiparametric estimation problems involving timeinhomogenous models and/or sampling of continuoustime processes. The usefulness of these results are demonstrated by two applications: Kernel regression estimation of a timevarying AR(1) model , and the kernel density estimation of a Markov chain that has not been intialized at its stationary distribution. 
Keywords:  Nonparametric estimation; uniform consistency; kernel estimation; density estimation; heterogeneous time series 
JEL:  C14 C32 
Date:  2008–07–01 
URL:  http://d.repec.org/n?u=RePEc:aah:create:200837&r=ets 
By:  D.S.G. Pollock 
Abstract:  An account is given of various filtering procedures that have been implemented in a computer program, which can be used in analysing econometric time series. The program provides some new filtering procedures that operate primarily in the frequency domain. Their advantage is that they are able to achieve clear separations of components of the data that reside in adjacent frequency bands in a way that the conventional timedomain methods cannot. Several procedures that operate exclusively within the time domain have also been implemented in the program. Amongst these are the bandpass filters of Baxter and King and of Christiano and Fitzgerald, which have been used in estimating business cycles. The Henderson filter, the Butterworth filter and the Leser or Hodrick–Prescott filter are also implemented. These are also described in this paper. Econometric filtering procedures must be able to cope with the trends that are typical of economic time series. If a trended data sequence has been reduced to stationarity by differencing prior to its filtering, then the filtered sequence will need to be reinflated. This can be achieved within the time domain via the summation operator, which is the inverse of the difference operator. The effects of the differencing can also be reversed within the frequency domain by recourse to the frequencyresponse function of the summation operator. 
Date:  2008–06 
URL:  http://d.repec.org/n?u=RePEc:lec:leecon:08/21&r=ets 
By:  James D. Hamilton 
Abstract:  Although ARCHrelated models have proven quite popular in finance, they are less frequently used in macroeconomic applications. In part this may be because macroeconomists are usually more concerned about characterizing the conditional mean rather than the conditional variance of a time series. This paper argues that even if one's interest is in the conditional mean, correctly modeling the conditional variance can still be quite important, for two reasons. First, OLS standard errors can be quite misleading, with a "spurious regression" possibility in which a true null hypothesis is asymptotically rejected with probability one. Second, the inference about the conditional mean can be inappropriately influenced by outliers and highvariance episodes if one has not incorporated the conditional variance directly into the estimation of the mean, and infinite relative efficiency gains may be possible. The practical relevance of these concerns is illustrated with two empirical examples from the macroeconomics literature, the first looking at market expectations of future changes in Federal Reserve policy, and the second looking at changes over time in the Fed's adherence to a Taylor Rule. 
JEL:  E52 
Date:  2008–06 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:14151&r=ets 
By:  Masayuki Hirukawa (Department of Economics, Northern Illinois University); Nikolay Gospodinov (Department of Economics, Concordia University and CIREQ) 
Abstract:  This paper considers a nonstandard kernel regression for strongly mixing processes when the regressor is nonnegative. The nonparametric regression is implemented using asymmetric kernels [Gamma (Chen, 2000b), Inverse Gaussian and Reciprocal Inverse Gaussian (Scaillet, 2004) kernels] that possess some appealing properties such as lack of boundary bias and adaptability in the amount of smoothing. The paper investigates the asymptotic and finitesample properties of the asymmetric kernel NadarayaWatson, local linear, and reweighted NadarayaWatson estimators. Pointwise weak consistency, rates of convergence and asymptotic normality are established for each of these estimators. As an important economic application of asymmetric kernel regression estimators, we reexamine the problem of estimating scalar diffusion processes. 
Date:  2008–06 
URL:  http://d.repec.org/n?u=RePEc:tky:fseres:2008cf573&r=ets 
By:  Wolfgang Härdle; Nikolaus Hautsch; Uta Pigorsch 
Abstract:  Measuring and modeling financial volatility is the key to derivative pricing, asset allocation and risk management. The recent availability of highfrequency data allows for refined methods in this field. In particular, more precise measures for the daily or lower frequency volatility can be obtained by summing over squared highfrequency returns. In turn, this socalled realized volatility can be used for more accurate model evaluation and description of the dynamic and distributional structure of volatility. Moreover, nonparametric measures of systematic risk are attainable, that can straightforwardly be used to model the commonly observed timevariation in the betas. The discussion of these new measures and methods is accompanied by an empirical illustration using highfrequency data of the IBM incorporation and of the DJIA index. 
Keywords:  Realized Volatility, Realized Betas, Volatility Modeling 
JEL:  C13 C14 C22 C52 C53 
Date:  2008–06 
URL:  http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2008045&r=ets 