7,551 research outputs found
Discussion of “An analysis of global warming in the Alpine region based on nonlinear nonstationary time series models” by F. Battaglia and M. K. Protopapas
The annual temperatures recorded for the last two centuries in fifteen european stations around the Alps are analyzed. They show a global warming whose growth rate is not however constant in time. An analysis based on linear Arima models does not provide accurate results. Thus, we propose threshold nonlinear nonstationary models based on several regimes both in time and in levels. Such models fit all series satisfactorily, allow a closer description of the temperature changes evolution, and help to discover the essential differences in the behavior of the different stations
Interpolation of nonstationary high frequency spatial-temporal temperature data
The Atmospheric Radiation Measurement program is a U.S. Department of Energy
project that collects meteorological observations at several locations around
the world in order to study how weather processes affect global climate change.
As one of its initiatives, it operates a set of fixed but irregularly-spaced
monitoring facilities in the Southern Great Plains region of the U.S. We
describe methods for interpolating temperature records from these fixed
facilities to locations at which no observations were made, which can be useful
when values are required on a spatial grid. We interpolate by conditionally
simulating from a fitted nonstationary Gaussian process model that accounts for
the time-varying statistical characteristics of the temperatures, as well as
the dependence on solar radiation. The model is fit by maximizing an
approximate likelihood, and the conditional simulations result in
well-calibrated confidence intervals for the predicted temperatures. We also
describe methods for handling spatial-temporal jumps in the data to interpolate
a slow-moving cold front.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS633 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A specification test for nonlinear nonstationary models
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 test framework allows for linear and nonlinear models
with endogenous 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 is useful in other
applications. Simulations examine the finite sample performance of the test.Comment: Published in at http://dx.doi.org/10.1214/12-AOS975 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
On efficient simulation in dynamic models
Ways of improving the efficiency of Monte-Carlo (MC) techniques are studied for dynamic models. Such models cause the conventional Antithetic Variate (AV) technique to fail, and will be proved to reduce the benefit from using Control Variates with nearly nonstationary series. This paper suggests modifications of the two conventional variance reduction techniques to enhance their efficiency. New classes of AVs are also proposed. Methods of reordering innovations are found to do less well than others which rely on changing some signs in the spirit of the traditional AV. Numerical and analytical calculations are given to investigate the features of the proposed techniques. JEL classification code: C15 Key words: Dynamic models, Monte-Carlo (MC), Variance Reduction Technique (VRT), Antithetic Variate (AV), Control Variate (CV), Efficiency Gain (EG), Response Surface (RS).
Laws and Limits of Econometrics
We start by discussing some general weaknesses and limitations of the econometric approach. A template from sociology is used to formulate six laws that characterize mainstream activities of econometrics and the scientific limits of those activities, we discuss some proximity theorems that quantify by means of explicit bounds how close we can get to the generating mechanism of the data and the optimal forecasts of next period observations using a finite number of observations. The magnitude of the bound depends on the characteristics of the model and the trajectory of the observed data. The results show that trends are more elusive to model than stationary processes in the sense that the proximity bounds are larger. By contrast, the bounds are of smaller order for models that are unidentified or nearly unidentified, so that lack or near lack of identification may not be as fatal to the use of a model in practice as some recent results on inference suggest, we look at one possible future of econometrics that involves the use of advanced econometric methods interactively by way of a web browser. With these methods users may access a suite of econometric methods and data sets online. They may also upload data to remote servers and by simple web browser selections initiate the implementation of advanced econometric software algorithms, returning the results online and by file and graphics downloads.Activities and limitations of econometrics, automated modeling, nearly unidentified models, nonstationarity, online econometrics, policy analysis, prediction, quantitative bounds, trends, unit roots, weak instruments
Asymptotic theory of least squares estimators for nearly unstable processes under strong dependence
This paper considers the effect of least squares procedures for nearly
unstable linear time series with strongly dependent innovations. Under a
general framework and appropriate scaling, it is shown that ordinary least
squares procedures converge to functionals of fractional Ornstein--Uhlenbeck
processes. We use fractional integrated noise as an example to illustrate the
important ideas. In this case, the functionals bear only formal analogy to
those in the classical framework with uncorrelated innovations, with Wiener
processes being replaced by fractional Brownian motions. It is also shown that
limit theorems for the functionals involve nonstandard scaling and nonstandard
limiting distributions. Results of this paper shed light on the asymptotic
behavior of nearly unstable long-memory processes.Comment: Published in at http://dx.doi.org/10.1214/009053607000000136 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Real interest rate persistence: evidence and implications
The real interest rate plays a central role in many important financial and macroeconomic models, including the consumption-based asset pricing model, neoclassical growth model, and models of the monetary transmission mechanism. We selectively survey the empirical literature that examines the time-series properties of real interest rates. A key stylized fact is that postwar real interest rates exhibit substantial persistence, shown by extended periods of time where the real interest rate is substantially above or below the sample mean. The finding of persistence in real interest rates is pervasive, appearing in a variety of guises in the literature. We discuss the implications of persistence for theoretical models, illustrate existing findings with updated data, and highlight areas for future research.Interest rates
Multi-regime models for nonlinear nonstationary time series
Nonlinear nonstationary models for time series are considered, where the series is generated from an autoregressive equation whose coe±cients change both according to time and the delayed values of the series itself, switching between several regimes. The transition from one regime to the next one may be discontinuous (self-exciting threshold model), smooth (smooth transition model) or continuous linear (piecewise linear threshold model). A genetic algorithm for identifying and estimating such models is proposed, and its behavior is evaluated through a simulation study and application to temperature data and a financial index.
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