2010 | 11 | 3 | 158-168
Article title

Distribution Approximations for Cusum and Cusumsq Statistics

Title variants
Languages of publication
The cumulative sum (cusum) is an important statistics in testing for a change point. This paper is concerned with the distribution approximations to the cusum statistic under the null and alternative hypotheses. We also consider distribution approximations for the cumulative sum of squares (cusumsq) test statistics. Finally, a discussion section is given.
Physical description
  • Central Bank of Iran
  • CHERNOFF, H. and ZACKS, S. (1964). Estimating the current mean of a normal distribution which is subjected to changes in time. Ann. Math. Statist. 35, 999–1018.
  • CONNIFFE, D. and SPENCER, J. E. (2000). Approximating the distribution of the maximum partial sum of normal deviates. Journal of Statistical Planning and Inference, 88, 19–27.
  • CSORGO, M., and HORVATH, L., (1997). Limit Theorems in Change Point Analysis, Wiley. UK.
  • GENZ, A. (1992). Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics, 1, 141–150
  • HABIBI, R., SADOOGHI-ALVANDI, S. M. and NEMATOLLAHI, A. R. (2005). Change point detection in a general class of distributions. Communications in Statistics, Theory and Methods 34, 1935–1938.
  • HALUNGA, A. G., OSBORN, D. R. and M. SENSIER (2009). Changes in the order of integration of US and UK infation. Economics Letters 102, 30–32.
  • HILLEBRAND, E. and SCHNABL, G. (2003). The effects of Japanese foreign exchange intervention: GARCH estimation and change point detection. Discussion Paper No.6. Japan Bank for International Cooperation (JBIC).
  • HINKLEY, D., (1970). Inference about the change-point in a sequence of random variables. Biometrika 57, 1–17.
  • HSU, D.A., (1979). Detecting shifts of parameter in gamma sequences, with applications to stock price and air traffic flow analysis. J. Amer. Statist. Assoc. 74, 31–40.
  • INCLAN, C. and TIAO, G. C. (1994). Use of cumulative sums of squares for retrospective detection of changes of variances. J. Amer. Statist. Assoc. 89, 913–923.
  • KIM S., S. CHO and S. LEE (2000), On the cusum test for parameter changes in GARCH(1,1) models, Communications in Statistics, Theory and Methods 29, 445–462.
  • MIKOSCH, T. and STARICA, C. (2003). Change of structure in financial time series, long range dependence and the GARCH modeld. Review of Economics and Statistics, forthcoming.
  • PAGE, E. S. (1954). Continuous inspection schemes. Biometrika 41, 100–115.
  • PLOBERGER, W. and KRAMER, W. (1992). The cusum test with ols residuals. Econometrica 60, 271–285.
  • SANSO, A., ARAGO, V. and CARRION, J. L. (2004). Testing for changes in the unconditional variance of financial time series, University of Barcelona Working Paper.
  • WORSLEY, K. J. (1986). Confidence regions and test for a change point in a sequence of exponential family random variables. Biometrika 73, 91–104.
Document Type
Publication order reference
YADDA identifier
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.