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Testing the Persistence of the Forward Premium: Structural Changes or Misspecification?

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Abstract

This study investigates whether the ignored structural break causes the forward premium non-stationary. This paper proposes to test for the presence of unit root with multiple structural breaks. We find that, as long as the dynamic lag structure is specified, the forward premium exhibits a non-stationary process even if structural breaks are accounted for and points to no evidence of moving toward stationarity. Given our findings, the structural change model seems less robust in explaining the forward premium puzzle.

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Notes

  1. As can be seen in Table 2.

  2. As seen in the Panel A of Table 8 where the lag order is selected by the MBIC, serial correlation still exists in the forward premium of Japanese yen and British pound. In order to further robustify our empirical evidence, this study also chooses the lag length by using the BIC criterion, with a preset of plausible maximum lag structure as 3. We then perform serial correlation testing to see if there is any remaining serial correlation with the optimal lag order chosen. If there is, we increase the lag order by one sequentially until serially uncorrelated residual vectors are obtained. The results based on such procedure are presented in the Panel B of Table 7, Panel B of Table 8, and Panels E though H of Table 10. Hereafter we name the above mentioned strategy as “the strategy based on the BIC.”

  3. For the purpose to strengthen our argument, given that Sakoulis et al. (2010) used the U.S. dollar as the reference currency, this study re-evaluates their work by using monthly mid-rate of spot and forward series of the same currencies during the same sample period. Results will be available upon request.

  4. Zivot and Andrews (1992)’s unit root tests on the forward premiums of our sample are provided in Table 12. Their test for allowing a structural break in level has the following form:

    y t  = a j  + φ 1 y t − 1 + δ 1 trend + ∑ p i = 1 γ 1i Δy t − i  + ε 1t , for t = T j−1 + 1,…,T j , where trend stands for a time trend. The other test regression for taking into account a breakpoint in both level and slope is as follows:

    \( {y}_t={a}_j+{\varphi}_2{y}_{t-1}+{\delta}_2 trend+{\chi}_{1j}{r}_{{}_{j,t-1}}+{\displaystyle {\sum}_{i=1}^p{\gamma}_{2i}\varDelta {y}_{t-i}+{\varepsilon}_{2t}}, \) for t = T j−1 + 1,…,T j , where r j,t−1 is the lagged variable where a structural change exists. Both forms are used to evaluate the unit root null hypothesis of φ 1 = 1 (φ 2 = 1) against the alternative hypothesis of φ 1 < 1 (φ 2 < 1).

  5. Elliott et al. (1996) argue, however, the standard DF unit root test only works when the series is an AR(1) process. In the case where the series is correlated at higher-order lags, the standard test may not be valid, because it violates the assumption of white noise (Diebold and Rudebusch 1991). The problem can be taken care of under the ADF unit root test; for it is a fact that the test carries a parametric correction for a higher-order correlation by assuming that the series follows an AR(p) process and by adding lagged difference terms of the dependent variable to the right-hand side of the test regression.

  6. We also plot the ACF of residuals for the six Euro forward premiums obtained from the AR(1) multiple structural break model. In consistent with the Ljung-Box statistics results, the ACF figures show that the autocorrelation at most lags is significant at the 5 % statistical significance, and thus residuals appear to be serially correlated. Results are available upon request.

  7. Table 6 presents estimates on the forward premium regression in AR(1) with a lag structure as follows: \( {y}_t=\tilde{a}+\tilde{b}{y}_{t-1}+{\displaystyle \sum_{i=1}^p{\tilde{\phi}}_i\varDelta {y}_{t-i}}+{\tilde{\upsilon}}_t. \)

  8. This study plots the autocorrelation of residuals for the six forward premiums, which are modelled as an AR(1) with a lag structure incorporated with multiple structural breaks. Based on the figure results, we reach the same conclusion with the Ljung-Box statistics results. The ACF results will be available upon request.

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Acknowledgments

The authors gratefully acknowledge specific comments by anonymous referees to improve the paper. All errors are the sole responsibility of the authors.

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Authors and Affiliations

  1. Department of Finance, Shih Hsin University, No. 1, Lane 17, Section 1, Mu-Cha Road, 11602, Taipei, Republic of China

    Tsung-Wu Ho

  2. Department of Finance, Chung Yuan Christian University, 200, Chung Pei Road, 32020, Chung Li, Republic of China

    Wan-Shin Mo

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  1. Tsung-Wu Ho
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Correspondence to Wan-Shin Mo.

Appendix 1

Appendix 1

Table 12 Zivot-Andrews unit root test
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Ho, TW., Mo, WS. Testing the Persistence of the Forward Premium: Structural Changes or Misspecification?. Open Econ Rev 27, 119–138 (2016). https://doi.org/10.1007/s11079-015-9365-9

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