Variance Change Point Research Articles

Wavelet Packet Methods for the Analysis of Variance of Time Series With Application to Crack Widths on the Brunelleschi Dome

In this article we extend the definition of wavelet variance to wavelet packets. We also adapt to wavelet packets an iterated cumulative sum of squares algorithm for the location of variance change points. Wavelet packets have greater decorrelation properties than standard wavelets in that they induce a finer partitioning of the frequency domain of the process generating the data. This allows our procedure to be applied to a wide class of processes. We show this on simulated data and on a benchmark time series. Our initial interest in wavelet variance change points location was motivated by an application to time series of crack widths on the Brunelleschi dome of the Santa Maria del Fiore cathedral in Florence. The structure of the dome includes an internal thick dome and an external thin one. In an effort to understand the dynamics of the crack widths we apply wavelet packet variance analysis to measurements from instruments located in the different parts of the outer and inner domes, highlighting different features and seasonal behavior. Our findings agree well with the structural functions of the different elements of the dome and also reveal some interesting aspects regarding the dynamics of crack evolution.

On Testing for a Change-Point in Variance of Normal Distribution

This paper addresses the problem of testing for a change about the variance of sequence of normal random variables with unknown means. It compares the power performance of five tests, namely: L-test based on LEHMANN'S (1951) U-statistic, B-test based on bayesian method, R-test derived from likelihood method, C-test based on BROWN et al.'s (1975) CUSUM of squares method and finally, the LM-test based on NYBLOM'S (1989) and HANSEN'S (1991) Lagrange multiplier method. An empirical power comparison of the five tests suggests that none of the tests power lead to another. However, it is observed that when change-point is between the beginning and the mid portion, the L and R test are better and when the change-point is between the mid portion and the end, CUSUM of square and the B test are better as compared to the other tests.

Power comparison of some tests for testing change point

This paper considers the problem of testing for a change point in variance of the sequence of normal random variables with unknown means. We construct three tests, namely, L-test derived from Lehmann's (1951) U-statistic, B-test obtained from Bayesian method and R-test derived by using the maximum likelihood ratio technique. Simulation studies were carried out to calculate the approximate critical values and the power of these tests. An empirical power comparison of these tests suggest that the power of the B-test is generally better than its competitors, the other two tests.

Testing and Locating Variance Changepoints with Application to Stock Prices

Abstract This article explores testing and locating multiple variance changepoints in a sequence of independent Gaussian random variables (assuming known and common mean). This type of problem is very common in applied economics and finance. A binary procedure combined with the Schwarz information criterion (SIC) is used to search all of the possible variance changepoints existing in the sequence. The simulated power of the proposed procedure is compared to that of the CUSUM procedure used by Inclán and Tiao to cope with variance changepoints. The SIC and unbiased SIC for this problem are derived. To obtain the percentage points of the SIC criterion, the asymptotic null distribution of a function of the SIC is obtained, and then the approximate percentage points of the SIC are tabulated. Finally, the results are applied to the weekly stock prices. The unknown but common mean case is also outlined at the end.

Testing and Locating Variance Changepoints with Application to Stock Prices

This article explores testing and locating multiple variance changepoints in a sequence of independent Gaussian random variables (assuming known and common mean). This type of problem is very common in applied economics and finance. A binary procedure combined with the Schwarz information criterion (SIC) is used to search all of the possible variance changepoints existing in the sequence. The simulated power of the proposed procedure is compared to that of the CUSUM procedure used by Inclán and Tiao to cope with variance changepoints. The SIC and unbiased SIC for this problem are derived. To obtain the percentage points of the SIC criterion, the asymptotic null distribution of a function of the SIC is obtained, and then the approximate percentage points of the SIC are tabulated. Finally, the results are applied to the weekly stock prices. The unknown but common mean case is also outlined at the end.

Volatility Changes in the Indian Stock Market

Hsu (1982) also suggested a Bayesian robust inferential scheme to detect and estimate variance change points which assumes a symmetric heavy-tialed exponential power distribution and requires no data segmentation.