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Articles 1 - 10 of 10
Full-Text Articles in Social and Behavioral Sciences
Specification Tests For Nonlinear Dynamic Models, Igor Kheifets
Specification Tests For Nonlinear Dynamic Models, Igor Kheifets
Cowles Foundation Discussion Papers
We propose a new adequacy test and a graphical evaluation tool for nonlinear dynamic models. The proposed techniques can be applied in any setup where parametric conditional distribution of the data is specified, in particular to models involving conditional volatility, conditional higher moments, conditional quantiles, asymmetry, Value at Risk models, duration models, diffusion models, etc. Compared to other tests, the new test properly controls the nonlinear dynamic behavior in conditional distribution and does not rely on smoothing techniques which require a choice of several tuning parameters. The test is based on a new kind of multivariate empirical process of contemporaneous …
Specification Testing For Nonlinear Cointegrating Regression, Qiying Wang, Peter C.B. Phillips
Specification Testing For Nonlinear Cointegrating Regression, Qiying Wang, Peter C.B. Phillips
Cowles Foundation Discussion Papers
We provide a limit theory for a general class of kernel smoothed U statistics that may be used for specification testing in time series regression with nonstationary data. The framework allows for linear and nonlinear models of cointegration and regressors that have autoregressive unit roots or near unit roots. The limit theory for the specification test depends on the self intersection local time of a Gaussian process. A new weak convergence result is developed for certain partial sums of functions involving nonstationary time series that converges to the intersection local time process. This result is of independent interest and useful …
Optimal Estimation Under Nonstandard Conditions, Werner Ploberger, Peter C.B. Phillips
Optimal Estimation Under Nonstandard Conditions, Werner Ploberger, Peter C.B. Phillips
Cowles Foundation Discussion Papers
We analyze optimality properties of maximum likelihood (ML) and other estimators when the problem does not necessarily fall within the locally asymptotically normal (LAN) class, therefore covering cases that are excluded from conventional LAN theory such as unit root nonstationary time series. The classical Hájek-Le Cam optimality theory is adapted to cover this situation. We show that the expectation of certain monotone “bowl-shaped” functions of the squared estimation error are minimized by the ML estimator in locally asymptotically quadratic situations, which often occur in nonstationary time series analysis when the LAN property fails. Moreover, we demonstrate a direct connection between …
Lad Asymptotics Under Conditional Heteroskedasticity With Possibly Infinite Error Densities, Jin Seo Cho, Chirok Han, Peter C.B. Phillips
Lad Asymptotics Under Conditional Heteroskedasticity With Possibly Infinite Error Densities, Jin Seo Cho, Chirok Han, Peter C.B. Phillips
Cowles Foundation Discussion Papers
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.
Further Evidence On The Great Crash, The Oil Price Shock, And The Unit Root Hypothesis, Eric Zivot, Donald W.K. Andrews
Further Evidence On The Great Crash, The Oil Price Shock, And The Unit Root Hypothesis, Eric Zivot, Donald W.K. Andrews
Cowles Foundation Discussion Papers
Recently Perron (1989) has carried out tests of the unit root hypothesis against the alternative hypothesis of trend stationarity with a break in the trend occurring at the Great Crash of 1929 or at the 1973 oil price shock. His analysis covers the Nelson-Plosser macroeconomic data series as well as a post-war quarter real GNP series. His tests reject the unit root null hypothesis for most of the series. This paper takes issue with the assumption used by Perron that the Great Crash and the oil price shock can be treated as exogenous events. A variation of Perron’s test is …
Asymptotics For Semiparametric Econometric Models: I. Estimation, Donald W.K. Andrews
Asymptotics For Semiparametric Econometric Models: I. Estimation, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper provides a general framework for proving the square root of T consistency and asymptotic normality of a wide variety of semiparametric estimators. The results apply in time series and cross-sectional modeling contexts. The class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator. The criterion function need not be differentiable. The method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes. This paper also considers tests …
Multiple Regression With Integrated Time Series, Peter C.B. Phillips
Multiple Regression With Integrated Time Series, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Recent work on the theory of regression with integrated process is reviewed. This work is particularly relevant in economics where many financial series and macroeconomic time series exhibit nonstationary characteristics and are often well modeled individually as simple ARIMA processes. The theory makes extensive use of weak convergence methods and allows for integrated processes that are driven by quite general weakly dependent and possibly heterogeneously distributed innovations. The theory also includes near integrated time series, which have roots near unity, and cointegrated series, which move together over time but are individually nonstationary. A general framework for asymptotic analysis is given …
Weak Convergence Of Sample Covariance Matrices To Stochastic Integrals Via Martingale Approximations, Peter C.B. Phillips
Weak Convergence Of Sample Covariance Matrices To Stochastic Integrals Via Martingale Approximations, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Under general conditions the sample covariance matrix of a vector martingale and its differences converges weakly to the matrix stochastic integral from zero to one of ∫ 0 1 BdB ’, where B is vector Brownian motion. For strictly stationary and ergodic sequences, rather than martingale differences, a similar result obtains. In this case, the limit is ∫ 0 1 BdB ’ + Λ and involves a constant matrix Λ, of bias terms whose magnitude depends on the serial correlation properties of the sequence. This note gives a simple proof of the result using martingale approximations.
Weak Convergence To The Matrix Stochastic Integral Bdb, Peter C.B. Phillips
Weak Convergence To The Matrix Stochastic Integral Bdb, Peter C.B. Phillips
Cowles Foundation Discussion Papers
The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form ∫ 0 1 WdW , where W ( r ) is standard Brownian motion. In multiple regressions and vector autoregressions with vector ARIMA processes the theory involves weak convergence to matrix stochastic integrals of the form ∫ 0 1 BdB ’, where B ( r ) is vector Brownian motion with non scalar covariance matrix. This paper studies the weak convergence of sample covariance matrices to ∫ 0 1 BdB ’ under quite general conditions. The theory is …
Testing For A Unit Root In Time Series Regression, Peter C.B. Phillips, Pierre Perron
Testing For A Unit Root In Time Series Regression, Peter C.B. Phillips, Pierre Perron
Cowles Foundation Discussion Papers
This paper proposes some new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory …