In this study, we introduce three distinct testing methods for testing alpha in high dimensional linear factor pricing model that deals with dependent data. The first method is a sum-type test procedure, which exhibits high performance when dealing with dense alternatives. The second method is a max-type test procedure, which is particularly effective for sparse alternatives. For a broader range of alternatives, we suggest a Cauchy combination test procedure. This is predicated on the asymptotic independence of the sum-type and max-type test statistics. Both simulation studies and practical data application demonstrate the effectiveness of our proposed methods when handling dependent observations.

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