An Alternative Approach to the Asymptotic Theory of Spurious Regression, Cointegration, and Near Cointegration

1993 ◽  
Vol 9 (1) ◽  
pp. 36-61 ◽  
Author(s):  
Katsuto Tanaka
Keyword(s):  
Asymptotic Theory ◽  
Distribution Functions ◽  
Present Approach ◽  
Local Power ◽  
Limiting Distributions ◽  
Spurious Regression ◽  
Alternative Approach

An alternative approach is taken to the asymptotic theory of cointegration. The present approach gives a different expression for the limiting distributions of statistics associated with cointegration, which enables us to compute accurately the distribution functions. Alternative interpretations of cointegration are given and a notion of near cointegration is introduced. We then devise tests which take cointegration as the null and discuss the limiting local power under the alternative of near cointegration.

LSTUR regression theory and the instability of the sample correlation coefficient between financial return indices

2020 ◽  
Author(s):  
Tim Ginker ◽  
Offer Lieberman
Keyword(s):  
Correlation Coefficient ◽  
Unit Root ◽  
Asymptotic Theory ◽  
Financial Return ◽  
Spurious Regression ◽  
Root Model ◽  
Sampling Window ◽  
Sample Correlation ◽  
Underlying Processes ◽  
Regression Theory

Summary It is well known that the sample correlation coefficient between many financial return indices exhibits substantial variation on any reasonable sampling window. This stylised fact contradicts a unit root model for the underlying processes in levels, as the statistic converges in probability to a constant under this modeling scheme. In this paper, we establish asymptotic theory for regression in local stochastic unit root (LSTUR) variables. An empirical application reveals that the new theory explains very well the instability, in both sign and scale, of the sample correlation coefficient between gold, oil, and stock return price indices. In addition, we establish spurious regression theory for LSTUR variables, which generalises the results known hitherto, as well as a theory for balanced regression in this setting.

QUANTILE-BASED STUDY OF (DYNAMIC) INACCURACY MEASURES

2019 ◽  
Vol 34 (2) ◽  
pp. 183-199
Author(s):  
Suchandan Kayal ◽  
Rajesh Moharana ◽  
S. M. Sunoj
Keyword(s):  
Distribution Function ◽  
Explicit Form ◽  
Statistical Models ◽  
Random Variables ◽  
Distribution Functions ◽  
Function Approach ◽  
Present Communication ◽  
Alternative Approach ◽  
Quantile Functions

AbstractIn the present communication, we introduce quantile-based (dynamic) inaccuracy measures and study their properties. Such measures provide an alternative approach to evaluate inaccuracy contained in the assumed statistical models. There are several models for which quantile functions are available in tractable form, though their distribution functions are not available in explicit form. In such cases, the traditional distribution function approach fails to compute inaccuracy between two random variables. Various examples are provided for illustration purpose. Some bounds are obtained. Effect of monotone transformations and characterizations are provided.

scholarly journals Asymptotic Theory for Cointegration Analysis When the Cointegration Rank Is Deficient

Econometrics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 6 ◽  
Author(s):  
David Bernstein ◽  
Bent Nielsen
Keyword(s):  
Recent Work ◽  
Asymptotic Theory ◽  
Cointegration Analysis ◽  
Finite Sample ◽  
Sample Analysis ◽  
Limiting Distributions ◽  
Cointegration Tests

We consider cointegration tests in the situation where the cointegration rank is deficient. This situation is of interest in finite sample analysis and in relation to recent work on identification robust cointegration inference. We derive asymptotic theory for tests for cointegration rank and for hypotheses on the cointegrating vectors. The limiting distributions are tabulated. An application to US treasury yields series is given.

scholarly journals ASYMPTOTIC THEORY FOR LOCAL TIME DENSITY ESTIMATION AND NONPARAMETRIC COINTEGRATING REGRESSION

2009 ◽  
Vol 25 (3) ◽  
pp. 710-738 ◽  
Author(s):  
Qiying Wang ◽  
Peter C.B. Phillips
Keyword(s):  
Density Estimation ◽  
Local Time ◽  
Asymptotic Theory ◽  
Time Estimation ◽  
Fourier Integral ◽  
Limit Theory ◽  
Integral Methods ◽  
Alternative Approach ◽  
Integrated Time Series ◽  
Time Density

Asymptotic theory is developed for local time density estimation for a general class of functionals of integrated and fractionally integrated time series. The main result provides a convenient basis for developing a limit theory for nonparametric cointegrating regression and nonstationary autoregression. The treatment directly involves local time estimation and the density function of the processes under consideration, providing an alternative approach to the Markov chain and Fourier integral methods that have been used in other recent work on these problems.

Effect of Variations in Calibrated Wave Parameters on Wave Crest and Height Distributions

2010 ◽  
Author(s):  
Janou Hennig ◽  
Jule Scharnke
Keyword(s):  
Power Spectra ◽  
Distribution Functions ◽  
Wave Crest ◽  
Wave Power ◽  
Wave Group ◽  
Wave Measurements ◽  
Initial Wave ◽  
Alternative Approach ◽  
Wave Basin ◽  
Wave Trains

In common model test practice, wave power spectra are calibrated prior to the actual model tests. The resulting wave crest and height distributions can be determined from the measured wave time traces at different reference location in the basin but they are not calibrated purposely. The corresponding wave group spectra follow from the wave power spectra together with arbitrarily chosen wave seeds applied to the wave trains. As an alternative approach, the seeds which give the highest and lowest wave group spectra can be applied in the tests. In this paper, results of wave measurements in MARIN’s Shallow Water Basin are presented which include a variation in water depth, wave seed (group spectrum) and location of measurement for the same initial wave power spectrum. The resulting wave crest and height distributions at different wave basin locations are analyzed and compared to theoretical distribution functions. A discussion of possible reasons for differences between theory and measurement concludes the investigation.

scholarly journals Limiting Distributions for the Minimum-Maximum Models

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 719
Author(s):  
Ling Peng ◽  
Lei Gao
Keyword(s):  
Convergence Analysis ◽  
Numerical Experiments ◽  
Random Sequence ◽  
Extreme Value ◽  
Distribution Functions ◽  
Extreme Value Distributions ◽  
Limiting Distributions ◽  
Theoretical Results ◽  
Independent And Identically Distributed

We consider the extreme value problem of the minimum-maximum models for the independent and identically distributed random sequence and stationary random sequence, respectively. By invoking some probability formulas and Taylor’s expansions of the distribution functions, the limiting distributions for these two kinds of sequences are obtained. Moreover, convergence analysis is carried out for those extreme value distributions. Several numerical experiments are conducted to validate our theoretical results.

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