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.

REGIME-SWITCHING AUTOREGRESSIVE COEFFICIENTS AND THE ASYMPTOTICS FOR UNIT ROOT TESTS

2008 ◽  
Vol 24 (4) ◽  
pp. 1137-1148
Author(s):  
Giuseppe Cavaliere ◽  
Iliyan Georgiev
Keyword(s):  
Sample Size ◽  
Unit Root ◽  
Regime Switching ◽  
Asymptotic Theory ◽  
Unit Roots ◽  
Stationary Regime ◽  
Unit Root Tests ◽  
Asymptotic Results ◽  
Switching Models ◽  
Root Model

Most of the asymptotic results for Markov regime-switching models with possible unit roots are based on specifications implying that the number of regime switches grows to infinity as the sample size increases. Conversely, in this note we derive some new asymptotic results for the case of Markov regime switches that are infrequent in the sense that their number is bounded in probability, even asymptotically. This is achieved by (inversely) relating the probability of regime switching to the sample size. The proposed asymptotic theory is applied to a well-known stochastic unit root model, where the dynamics of the observed variable switches between a unit root regime and a stationary regime.

An approximation to the distribution of the sample correlation coefficient

Biometrika ◽  
1978 ◽  
Vol 65 (3) ◽  
pp. 654-656 ◽  
Author(s):  
SADANORI KONISHI
Keyword(s):  
Correlation Coefficient ◽  
Sample Correlation

Using Incidence Sampling to Estimate Covariances

1979 ◽  
Vol 4 (1) ◽  
pp. 41-58 ◽  
Author(s):  
Thomas R. Knapp
Keyword(s):  
Missing Data ◽  
Correlation Coefficient ◽  
Sample Covariance ◽  
Sample Correlation

This paper is an attempt to illustrate the generality of incidence sampling for estimating a parameter whose estimator preserves the unbiasedness of generalized symmetric means, a property which the sample covariance possesses but which the sample correlation coefficient does not. The problem of missing data is also addressed.

On the Distribution of the Sample Correlation Coefficient

1992 ◽  
pp. 466-469
Author(s):  
N. N. Mikhail ◽  
F. A. Chimenti ◽  
J. D. Kidder
Keyword(s):  
Correlation Coefficient ◽  
Sample Correlation

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.

scholarly journals UNIFORM ASYMPTOTIC NORMALITY IN STATIONARY AND UNIT ROOT AUTOREGRESSION

2011 ◽  
Vol 27 (6) ◽  
pp. 1117-1151 ◽  
Author(s):  
Chirok Han ◽  
Peter C. B. Phillips ◽  
Donggyu Sul
Keyword(s):  
Normal Distribution ◽  
Rate Of Convergence ◽  
Unit Root ◽  
Asymptotic Theory ◽  
Signal Strength ◽  
Rates Of Convergence ◽  
Moment Conditions ◽  
First Order ◽  
The Cost ◽  
Artificial Shrinkage

While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly mechanism for preserving information and signal strength in autoregressions with some very desirable properties. In first order autoregression, a partially aggregated estimator based on moment conditions in differences is shown to have a limiting normal distribution that holds uniformly in the autoregressive coefficient ρ, including stationary and unit root cases. The rate of convergence is $\root \of n $ when $\left| \rho \right| < 1$ and the limit distribution is the same as the Gaussian maximum likelihood estimator (MLE), but when ρ = 1 the rate of convergence to the normal distribution is within a slowly varying factor of n. A fully aggregated estimator (FAE) is shown to have the same limit behavior in the stationary case and to have nonstandard limit distributions in unit root and near integrated cases, which reduce both the bias and the variance of the MLE. This result shows that it is possible to improve on the asymptotic behavior of the MLE without using an artificial shrinkage technique or otherwise accelerating convergence at unity at the cost of performance in the neighborhood of unity. Confidence intervals constructed from the FAE using local asymptotic theory around unity also lead to improvements over the MLE.

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