由於收集或測量變數的成本因素, 經濟資料會在不同的頻率下取樣, 因此研究一般都是取得不同頻率的資料。本文將藉由 Miller (2014) 提 出之共積混合資料樣本模型建立共積變異數檢定, 用以擴展 Yang et al. (2014) 在相同頻率下的共積變異數檢定, 使該檢定可以使用不同頻率的
資料。
納入 CoMIDAS 模型, 以多項式權重函數將模型變為非線性模型, 解 決高頻率資料導致的參數增殖, 保留更多資料的資訊。本文藉由 Kiefer et al.(2000) 的方法推導的檢定統計式最後收斂至一布朗運動函數分配, 與 Yang et al.(2014) 所推導的相同。由於放寬使用混合頻率資料, 保留
更多的資訊會使得檢定更為強健。
蒙地卡羅模擬的結果與分析一致, 相同頻率下以及本文混合頻率下 之檢定大小的表現差不多, 檢定力則是本文較相同頻率下的更為優秀。 在高頻率期數還不大時, 檢定力表現差異不大, 期數越大, 則檢定力的表
現即差距越大。模擬結果得到本文的檢定性質更優秀。

Economic data are sampled at different frequencies because of the cost of collecting or measuring variables. In this paper, the cointegration variance test is established by using cointegrating mixed data sampling (CoMIDAS) model introduced by Miller(2014),which is used to extend the cointegration
variance test of Yang et al.(2014) at matched sample frequency.
CoMIDAS model was included, and the model was changed into a nonlinear model by polynomial weight function, so as to solve the parameter proliferation caused by high frequency data and retain more information of data. In this paper, the test statistics derived by the method of Kiefer et al. (2000) converges to a
brownian-motion function distribution, which is the same as that derived by Yang et al.(2014). By liberalizing the use of mixed frequency data, retaining more information makes test more robust.
The results of Monte Carlo simulation are consistent with the analysis, and the test size is similar at the matched frequency and the mixed frequency, and the power is better than that at the matched frequency. When the number of high frequency periods is not large, there is little difference in the performance of power. The larger the number of periods, the greater the difference is in the performance of power.The simulation results show that the model we presented in this paper can obtain better test properties.

論文審定書. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... i
摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
圖次. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
表次. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
第1 章緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
第1.1 節研究背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
第1.2 節研究動機與目的. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
第1.3 節研究架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
第2 章文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第2.1 節回顧相同頻率下的共積變異數檢定. . . . . . . . . . . . . . . . . 4
第2.2 節回顧CoMIDAS 模型. . . . . . . . . . . . . . . . . . . . . . . . . . 5
第2.2.1 節MIDAS 模型. . . . . . . . . . . . . . . . . . . . . . . . . . . 6
第2.2.2 節CoMIDAS 模型. . . . . . . . . . . . . . . . . . . . . . . . . 7
第3 章研究方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
第3.1 節模型設定與假設. . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
第3.2 節NLS 估計的共積均衡誤差平方的漸進分配. . . . . . . . . . . . . 15
第3.3 節運用KVB 法的檢定統計式. . . . . . . . . . . . . . . . . . . . . . 24
第4 章蒙地卡羅(Monte Carlo) 模擬. . . . . . . . . . . . . . . . . . . . . . . . . 27
第5 章結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Anderou, E., Ghysels, E., Kourtellos, A., 2010. Regression models with mixed sampling
frequency. Journal of Econometrics 158, 246–261.
Armesto, M. T., Engemann, K. M., Owyang, M. T., 2010. Forecasting with mixed frequencies.
Journal of Financial Econometrics 92 (6), 521–536.
Chang, Y., Joon, Y. P., Phillips, P. C. B., 2001. Nonlinear econometric models with cointegrated
and deterministically trending regressors. Econometrics Journal 4, 1–36.
Clements, M. P., Beatriz, G., 2009. Forecasting us output growth using leading indicators:
an appraisal using midas models. Journal of Applied Econometrics 24, 1187–1206.
Davidson, J., 1994. Stochastic limit theory:a introduction for econometricians. Oxford
University Press, USA.
Engle, R., Granger, C., 1987. Co-integration and error correction:representation, estimation,
and testing. Econometrica 55 (2), 251–276.
Foroni, C., Marcellino, M., 2013. A survey of econometric methods for mixed frequency
data. Working paper.
Ghysels, E., Santa-Clara, P., Valkanov, R., 2006. Predicting volatility: Geting the most out
of return data sampled at different frequencies. Journal of Econometrics 131, 59–95.
Ghysels, E., Santa-Clara, P., Volkanov, R., 2004. The midas touch: Mixed data sampling
regression models. CIRANO Working Paper, 2004s-20.
Ghysels, E., Santa-Clara, P., Volkanov, R., 2005. There is a risk-return trade-off after all.
Journal of Financial Economics 76, 509–548.
Ghysels, E., Sinko, A., Valkanov, R., 2007. Midas regressions: Further results and new
directions. Econometric Reviews 26 (1), 53–90.
Granger, C. W. J., 1990. Aggregation of time series variables: A survey. Disaggregation
in Econometric Modelling, 17–34.
Johansen, S., 1988. Statistical analysis of cointegration vectors. Journal of Economic Dynamics
and Control 12, 231–254.
Kiefer, N., Vogelsang, T., Bunzel, H., 2000. Simple robust testing of regression hypothesis.
Econometrica 68 (3), 695–714.
Lee, C., 2017. A residual-based test for equal cointegration variance in a mixed frequency
sample. Working paper, Institute of Economics, National Sun Yat-sen University.
Lee, C., Shie, F. S., Chang, C., 2012. How close a relationship does a capital market have
with other such markets? Pacific-Basin Finance Journal 20 (3), 349–362.
Miller, J. I., 2014. Mixed-frequency cointegrating regressions with parsimonious distributed
lag structures. Journal of Financial Econometrics 12 (3), 584–614.
Phillips, P. C. B., Solo, V., 1992. Asymptotics for linear processes. The Annals of Statistics
20 (2), 971–1001.
Stock, J. H., 1987. Temporal aggregation and structural inference in macroeconomics
comment. Carnegie-Rochester Conference Series of Public Policy 26, 131–139.
Wooldridge, J., 1994. Estimation and inference for dependent precesses. Handbook of
Econometrics 4, 2639–2738.
Yang, L., Lee, C., Shie, F. S., 2014. How close a relationship does a capital market have
with other markets? a reexamination based on the equal variance test. Pacific-Basin
Finance Journal 26, 198–226.