Abstract
Some tests for an epidemic type change in a first order nearly nonstationary autoregressive process are investigated. Limit distributions of the tests are found under no change. Consistencyis examined under short epidemics in the mean of innovations.
Highlights
Consider random variables X1, X2, . . . , Xn with parameters of interest θ1, . . . , θn, n 2
Due to (4), we have the epidemic change model, where a sequence of dependent random variables satisfying the null hypothesis is shifted by a deterministic sequence
We study limit behavior of Tα,n for α = 0 (Levin and Kline statistic) and α ∈ (0, 1/2 − 1/p), p > 2, (Rackauskas and Suquet statistics) trying to see how the use of extra weighting improves the detection of short epidemics
Summary
Consider random variables X1, X2, . . . , Xn with parameters of interest θ1, . . . , θn, n 2. Yao [3] have studied various test statistics in order to detect an epidemic change in the mean values of a sequence of independent normally distributed random variables. For the model Xi = θi + i, i 1, where ( i, i 1) is a sequence of independent identically distributed mean zero random variables, Rackauskas and Suquet [12] have shown that, for any 0 < α < 1/2, statistics Tα,n(X1, . Due to (4), we have the epidemic change model, where a sequence of dependent random variables satisfying the null hypothesis is shifted by a deterministic sequence. This is the reason why statistics (2) seems very natural in this situation.
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