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A martingale is a model in which the expectation for the next value is equal to the presently observed value, even given knowledge of prior values, ie

$E(X_{n+1} |X_1, X_2, ..,X_n)=X_n$

What tests for testing if a time series is a martingale are available? I am particularly interested in non-parametric tests. Is there any relation with conditional moments literature?

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