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Full-Text Articles in Economics
Boosting The Hp Filter For Trending Time Series With Long Range Dependence, Eva Biswas, Farzad Sabzikar, Peter C. B. Phillips
Boosting The Hp Filter For Trending Time Series With Long Range Dependence, Eva Biswas, Farzad Sabzikar, Peter C. B. Phillips
Cowles Foundation Discussion Papers
This paper extends recent asymptotic theory developed for the Hodrick Prescott (HP) filter and boosted HP (bHP) filter to long range dependent time series that have fractional Brownian motion (fBM) limit processes after suitable standardization. Under general conditions it is shown that the asymptotic form of the HP filter is a smooth curve, analogous to the finding in Phillips and Jin (2021) for integrated time series and series with deterministic drifts. Boosting the filter using the iterative procedure suggested in Phillips and Shi (2021) leads under well defined rate conditions to a consistent estimate of the fBM limit process or …
Bootstrapping I(1) Data, Peter C.B. Phillips
Bootstrapping I(1) Data, Peter C.B. Phillips
Cowles Foundation Discussion Papers
A functional law for an I(1) sample data version of the continuous-path block bootstrap of Paparoditis and Politis (2001) is given. The results provide an alternative demonstration that continuous-path block bootstrap unit root tests are consistent under the null.
Local Limit Theory And Spurious Nonparametric Regression, Peter C.B. Phillips
Local Limit Theory And Spurious Nonparametric Regression, Peter C.B. Phillips
Cowles Foundation Discussion Papers
A local limit theorem is proved for sample covariances of nonstationary time series and integrable functions of such time series that involve a bandwidth sequence. The resulting theory enables an asymptotic development of nonparametric regression with integrated or fractionally integrated processes that includes the important practical case of spurious regressions. Some local regression diagnostics are suggested for forensic analysis of such regresssions, including a local R² and a local Durbin Watson (DW) ratio, and their asymptotic behavior is investigated. The most immediate findings extend the earlier work on linear spurious regression (Phillips, 1986), showing that the key behavioral characteristics of …
Optimal Electoral Timing: Exercise Wisely And You May Live Longer, Jussi Keppo, Lones Smith, Dmitry Davydov
Optimal Electoral Timing: Exercise Wisely And You May Live Longer, Jussi Keppo, Lones Smith, Dmitry Davydov
Cowles Foundation Discussion Papers
In many democratic countries, the timing of elections is flexible. We explore this potentially valuable option using insights from option pricing in finance. The paper offers three main contributions on this problem. First, we derive a rationally-based mean-reverting political support process for the parties, assuming that politically heterogeneous voters continuously learn over time about evolving party fortunes. We solve for the long-run density for this process and derive the polling process from it by adding polling noise. Second, we explore optimal timing using the political support process. The incumbent sees its poll support, and must call an election within five …
Nonstationary Discrete Choice: A Corrigendum And Addendum, Peter C.B. Phillips, Sainan Jin, Ling Hu
Nonstationary Discrete Choice: A Corrigendum And Addendum, Peter C.B. Phillips, Sainan Jin, Ling Hu
Cowles Foundation Discussion Papers
We correct the limit theory presented in an earlier paper by Hu and Phillips (Journal of Econometrics, 2004) for nonstationary time series discrete choice models with multiple choices and thresholds. The new limit theory shows that, in contrast to the binary choice model with nonstationary regressors and a zero threshold where there are dual rates of convergence ( n 1 /4 and n 3 /4 ), all parameters including the thresholds converge at the rate n 3 /4 . The presence of non-zero thresholds therefore materially affects rates of convergence. Dual rates of convergence reappear when stationary variables are present …
Regression Asymptotics Using Martingale Convergence Methods, Rustam Ibragimov, Peter C.B. Phillips
Regression Asymptotics Using Martingale Convergence Methods, Rustam Ibragimov, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Weak convergence of partial sums and multilinear forms in independent random variables and linear processes to stochastic integrals now plays a major role in nonstationary time series and has been central to the development of unit root econometrics. The present paper develops a new and conceptually simple method for obtaining such forms of convergence. The method relies on the fact that the econometric quantities of interest involve discrete time martingales or semimartingales and shows how in the limit these quantities become continuous martingales and semimartingales. The limit theory itself uses very general convergence results for semimartingales that were obtained in …
Fractional Brownian Motion As A Differentiable Generalized Gaussian Process, Victoria Zinde-Walsh, Peter C.B. Phillips
Fractional Brownian Motion As A Differentiable Generalized Gaussian Process, Victoria Zinde-Walsh, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Brownian motion can be characterized as a generalized random process and, as such, has a generalized derivative whose covariance functional is the delta function. In a similar fashion, fractional Brownian motion can be interpreted as a generalized random process and shown to possess a generalized derivative. The resulting process is a generalized Gaussian process with mean functional zero and covariance functional that can be interpreted as a fractional integral or fractional derivative of the delta-function.
Nonstationary Discrete Choice, Ling Hu, Peter C.B. Phillips
Nonstationary Discrete Choice, Ling Hu, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops an asymptotic theory for time series discrete choice models with explanatory variables generated as integrated processes and with multiple choices and threshold parameters determining the choices. The theory extends recent work by Park and Phillips (2000) on binary choice models. As in this earlier work, the maximum likelihood (ML) estimator is consistent and has a limit theory with multiple rates of convergence ( n 3/4 and n 1 /4 ) and mixture normal distributions where the mixing variates depend on Brownian local time as well as Brownian motion. An extended arc sine limit law is given for …
Bootstrapping Spurious Regression, Peter C.B. Phillips
Bootstrapping Spurious Regression, Peter C.B. Phillips
Cowles Foundation Discussion Papers
The bootstrap is shown to be inconsistent in spurious regression. The failure of the bootstrap is spectacular in that the bootstrap effectively turns a spurious regression into a cointegrating regression. In particular, the serial correlation coefficient of the residuals in the bootstrap regression does not converge to unity, so the bootstrap is not even first order consistent. The block bootstrap serial correlation coefficient does converge to unity and is therefore first order consistent, but has a slower rate of convergence and a different limit distribution from that of the sample data serial correlation coefficient. The analysis covers spurious regressions involving …
Nonlinear Econometric Models With Cointegrated And Deterministically Trending Regressors, Yoosoon Chang, Joon Y. Park, Peter C.B. Phillips
Nonlinear Econometric Models With Cointegrated And Deterministically Trending Regressors, Yoosoon Chang, Joon Y. Park, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops an asymptotic theory for a general class of nonlinear nonstationary regressions, extending earlier work by Phillips and Hansen (1990) on linear cointegrating regressions. The model considered accommodates a linear time trend and stationary regressors, as well as multiple I(1) regressors. We establish consistency and derive the limit distribution of the nonlinear least squares estimator. The estimator is consistent under fairly general conditions but the convergence rate and the limiting distribution are critically dependent upon the type of the regression function. For integrable regression functions, the parameter estimates converge at a reduced n 1 /4 rate and have …
Nonstationary Binary Choice, Joon Y. Park, Peter C.B. Phillips
Nonstationary Binary Choice, Joon Y. Park, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops an asymptotic theory for time series binary choice models with nonstationary explanatory variables generated as integrated processes. Both logit and probit models are covered. The maximum likelihood (ML) estimator is consistent but a new phenomenon arises in its limit distribution theory. The estimator consists of a mixture of two components, one of which is parallel to and the other orthogonal to the direction of the true parameter vector, with the latter being the principal component. The ML estimator is shown to converge at a rate of n 3 /4 along its principal component but has the slower …
Nonlinear Regressions With Integrated Time Series, Joon Y. Park, Peter C.B. Phillips
Nonlinear Regressions With Integrated Time Series, Joon Y. Park, Peter C.B. Phillips
Cowles Foundation Discussion Papers
An asymptotic theory is developed for nonlinear regression with integrated processes. The models allow for nonlinear effects from unit root time series and therefore deal with the case of parametric nonlinear cointegration. The theory covers integrable, asymptotically homogeneous and explosive functions. Sufficient conditions for weak consistency are given and a limit distribution theory is provided. In general, the limit theory is mixed normal with mixing variates that depend on the sojourn time of the limiting Brownian motion of the integrated process. The rates of convergence depend on the properties of the nonlinear regression function, and are shown to be as …
Asymptotics For Nonlinear Transformations Of Integrated Time Series, Joon Y. Park, Peter C.B. Phillips
Asymptotics For Nonlinear Transformations Of Integrated Time Series, Joon Y. Park, Peter C.B. Phillips
Cowles Foundation Discussion Papers
An asymptotic theory for stochastic processes generated from nonlinear transformations of nonstationary integrated time series is developed. Various nonlinear functions of integrated series such as ARIMA time series are studied, and the asymptotic distributions of sample moments of such functions are obtained and analyzed. The transformations considered in the paper include a variety of functions that are used in practical nonlinear statistical analysis. It is shown that their asymptotic theory is quite different from that of integrated processes and stationary time series. When the transformation function is exponentially explosive, for instance, the convergence rate of sample functions is path-dependent. In …
Statistical Inference In Regressions With Integrated Processes: Part 1, Joon Y. Park, Peter C.B. Phillips
Statistical Inference In Regressions With Integrated Processes: Part 1, Joon Y. Park, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops a multivariate regression theory for integrated processes which simplifies and extends much earlier work. Our framework allows for both stochastic and certain deterministic regressors, vector autoregressions and regressors with drift. The main focus of the paper is statistical inference. The presence of nuisance parameters in the asymptotic distributions of regression F -tests is explored and new transformations are introduced to deal with these dependencies. Some specializations of our theory are considered in detail. In models with strictly exogenous regressors we demonstrate the validity of conventional asymptotic theory for appropriately constructed Wald tests. These tests provide a simple …
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 …
Towards A Unified Asymptotic Theory For Autoregression, Peter C.B. Phillips
Towards A Unified Asymptotic Theory For Autoregression, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops an asymptotic theory for a first order autoregression with a root near unity. Deviations from the unit root theory are measured through a noncentrality parameter. When this parameter is negative we have a local alternative that is stationary; when it is positive, the local alternative is explosive; and when it is zero we have the standard unit root theory. Our asymptotic theory accommodates these alternatives and helps to unify earlier theory in which the unit root case appears as a singularity of the asymptotics. The general theory is expressed in terms of functionals of a simple diffusion …
Regression Theory For Near-Integrated Time Series, Peter C.B. Phillips
Regression Theory For Near-Integrated Time Series, Peter C.B. Phillips
Cowles Foundation Discussion Papers
The concept of a near-integrated vector random process is introduced. Such processes help us to work towards a general asymptotic theory of regression for multiple time series in which some series may be integrated processes of the ARIMA type, others may be stable ARMA processes with near unit roots, and yet others may be mildly explosive. A limit theory for the sample moments of such time series is developed using weak convergence and is shown to involve a simple functionals of a vector diffusion. The results suggest finite sample approximations which in the stationary case correspond to conventional central limit …