L09_S08_OverlappingNonOverlap

L09_S08_OverlappingNonOverlap - OVERLAPPING VS....

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Time Series: Data sequentially collected over time. AR(1): X i = λX i-1 +Y i . The Y i ’s are from a uniform [-1, 1] distribution and λ is a constant. For this AR(1) process, X 1 = λX 0 +Y 1 , X 49 0 0 = = i i i Y λ and the Yi's are from a uniform [-1, 1] distribution. By the use of the Central Limit Theorem, the X 0 's are approximately normally distributed with a mean of 0 and a variance of ) 1 ( 3 1 2 100 - - . Use three different values of lambda: λ = 0.5, λ = 0.35 and λ = -0.5 Measure of accuracy: The Average Relative Error formula is used as a measure of accuracy: | | 200 1 ARE 200 1 , n = = - i i n n n B V V , where V n is the sample variance of the Monte Carlo 1000 sample medians of sample size n and B n,i is the bootstrap sample variance of the bootstrap sample medians. 200 is the number of bootstrap subsamples. The details Non-Overlapping Moving Block Bootstrap, aka: Disjoint Block Bootstrap. 11
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L09_S08_OverlappingNonOverlap - OVERLAPPING VS....

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