Abstract
The Markov order is a crucial measure of the memory of a process and its information is essential for appropriate simulation of aspects of the process. In this paper we suggest a robust and straightforward exact significance test based on generating surrogate data to assess the Markov order of a time series. This method is valid for any sample size and certifies a uniform sampling from the set of sequences that definitely have the nth order characteristics of the observed data. The Markov property and order of IEEE802.11a errors are investigated using this test.
Highlights
An evolution in time of a random phenomenon is a process which can be described by a stochastic process
A Markov chain satisfies the Markov property, which means that future behavior is independent of past behavior when the present is known
The Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) are two wellknown order estimators according to the Maximum Likelihood (Ding J.,Tarokh V.,Yang Y., 2017) (Katz, 1981)
Summary
An evolution in time of a random phenomenon is a process which can be described by a stochastic process. The Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) are two wellknown order estimators according to the Maximum Likelihood (Ding J.,Tarokh V.,Yang Y., 2017) (Katz, 1981) These methods are only valid in the limit of large samples and their efficiency can not be assured in small sample cases. The exact significance test is employed for any sample size According to this method, the test statistic distribution is explored by sampling from the set of sequences (named as surrogates) that corresponds exactly to the nth order characteristics of the observed time series. The exact significance test is explained according to surrogate data generation and Whittle's formula for any sample size This exact significance test is applied for the error data of IEEE802.11a based OFDM system to test the Markov property and find the order of the Markov model
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