CLT for largest eigenvalues and unit root testing for high-dimensional nonstationary time series

This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To simultaneously handle these two types of time-varying features, a two-step approach is proposed: multiple change point locations are first identified on the basis of comparing the difference between the localized averages on sample covariance matrices, and then graph supports are recovered on the basis of a kernelized time-varying constrained L 1 -minimization for inverse matrix estimation (CLIME) estimator on each segment. We derive the rates of convergence for estimating the change points and precision matrices under mild moment and dependence conditions. In particular, we show that this two-step approach is consistent in estimating the change points and the piecewise smooth precision matrix function, under a certain high-dimensional scaling limit. The method is applied to the analysis of network structure of the S&P 500 index between 2003 and 2008.

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An Empirical Study on Efficient Market Hypothesis: The Case of Indian Capital Markets

MUDRA Journal of Finance and Accounting ◽

10.17492/mudra.v1i2.2467 ◽

2014 ◽

Vol 1 (2) ◽

Author(s):

Anjala Kalsie

Keyword(s):

Time Series ◽

Empirical Study ◽

Time Series Analysis ◽

Unit Root ◽

Weak Form ◽

Efficient Market Hypothesis ◽

Efficient Markets ◽

Test Unit ◽

Unit Root Testing ◽

Univariate Time Series

The objective of this paper is to study the efficiency of Indian stock markets during the period 2001-2011. The weak form of efficient markets is extensively tested using NIFTY and 6 major NSE sectoral indices Pharma, IT, MNC, Bank, FMCG and Nifty Junior. Univariate time series analysis of indices returns is carried using tests for randomness / non-stationarity - runs test, unit root testing. ACF, correlograms and other relevant statistical methods. The study concludes that Indian markets are inefficient in its weak form for the study period.

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Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power

Econometric Theory ◽

10.1017/s0266466600009993 ◽

1995 ◽

Vol 11 (5) ◽

pp. 1148-1171 ◽

Cited By ~ 176

Author(s):

Bruce E. Hansen

Keyword(s):

Time Series ◽

Asymptotic Distribution ◽

Unit Root ◽

Convex Combination ◽

Ordinary Least Squares ◽

Power Functions ◽

Large Power ◽

Unit Root Testing ◽

Local Asymptotic Power ◽

Fuller Distribution

In the context of testing for a unit root in a univariate time series, the convention is to ignore information in related time series. This paper shows that this convention is quite costly, as large power gains can be achieved by including correlated stationary covariates in the regression equation.The paper derives the asymptotic distribution of ordinary least-squares estimates of the largest autoregressive root and its t-statistic. The asymptotic distribution is not the conventional Dickey-Fuller distribution, but a convex combination of the Dickey-Fuller distribution and the standard normal, the mixture depending on the correlation between the equation error and the regression covariates. The local asymptotic power functions associated with these test statistics suggest enormous gains over the conventional unit root tests. A simulation study and empirical application illustrate the potential of the new approach.

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