事实上，梅纳德(1988)曾质疑，现货统计特性的差异率和远期溢价是否是造成偏差的唯一因素。为了规避计量经济学的相关问题，他们采用了三种方法进行估计(Chiang, 1988)。这些测试包括基于协方差的测试、精确有限样本符号的测试和最优条件的测试。由此可见，虽然偏差有所减小，但“k”仍然短于基于统一的理论值(Maynard, 2003)。跟踪基于偏差的混合证据来源;梅纳德(2000)的结论是，单独的统计性质的方法不太可能解决这个谜题。
Kellard et al.(1990)最终提供了证据，证明拼图相关的经济和统计解释需要合作。CAPM的使用为合理化预期提供了一个框架，它描述了真实的风险溢价更长的记忆以及即期汇率条件方差，为远期溢价谜题中时间序列的类似行为提供了解释(Chinn et al.， 2004)。而正向溢价诱导的长记忆导致长尾自然分布，有助于产生负向的“贝塔k”主要系数。
This puzzle has been the key essential puzzle within the macroeconomics internationally. After 2 decades, there still is no particular solution of accepted nature.
As a matter of fact, it has been questioned by Maynard (1988), on whether the differenced rates of spot statistical properties as well as the forward premium are the only contributor’s towards biasness. They employed 3 methods for estimation aiming at circumventing the relevant problems of econometrics (Chiang, 1988). These included test based on covariance, the test for exact finite sample signs and a test for optimal conditioning. It was seen that even though some bias are decreased, but still “beta k” is shorter of unity based theoretical value (Maynard, 2003). Following a source of bias based mixed evidence; Maynard (2000) concluded that methods of statistical nature individually have no unlikeliness of resolving the puzzle.
Kellard et al. (1990), finally provided evidence that puzzle related economic and statistics explanation needs to be collaborated. Applying a framework for rationalized expectations, it is seen that CAPM consumption depicts that true risk premium longer memory along with the spot rate conditional variance provide explanation to analogous behaviour of time series within the puzzle of forward premium (Chinn et al., 2004). Then the forward premium induced long memory results in distributions of long tail nature helping in production of major coefficients of” beta k” with negativity.