本文採用Götz et al. (2014) 的混合頻率誤差修正模型(Mixed Frequency Error Correction Model, MF-ECM) 為架構，對中國國內生產毛額(Gross Domestic Product, GDP) 進行預測。
混合頻率誤差修正模型最大的優點是能夠改善誤差修正模型(Error Correction Model, ECM) 透過加總或平均將不同頻率的數據轉變成相同頻率而造成的資訊流失，此模型將動態混合頻率共整合關係項加進具有混合頻率數據採樣的分布滯後模型，寫成誤差修正模型的形式，以期能提高預測精準度。
本文使用的樣本資料為中國國內生產毛額1995 年第一季到2016 年第四季及中國進、出口1995 年1 月至2016 年12 月，運用混合頻率誤差修正模型和誤差修正模型，以中國進、出口資料對中國國內生產毛額進行樣本內預測，比較兩個模型的預測力指標，發現混合頻率誤差修正模型的預測精準度比誤差修正模型高，最後我們提供2017 年第一季中國國內生產毛額的樣本外預測值作為參考。

In this paper, we use the mixed frequency error correction model of Götz et al. (2014)
as a framework for forecasting the gross domestic product (GDP) of China. The biggest
advantage of the mixed frequency error correction model is its ability to improve the error
correction model (ECM).
The loss of information is caused by converting the data of different frequencies into
the same frequency by adding or averaging. This model adds the dynamic mixing frequency
co-integration relation term to the autorgressive distributed lag model with mixed
frequency data sampling and writes the form of error correction model in order to improve
prediction accuracy.
The sample data used in this paper are gross domestic product in China from the first
quarter of 1995 to the fourth quarter of 2016, and the national import and export from January
1995 to December 2016. Using the mixed frequency error correction model and the
error correction model, the prediction indicators of both models were compared by conducting
intra-sample predictions on China’s gross domestic product and import-export
data. It was discovered that the prediction accuracy of the mixed frequency error correction
model was higher than that of the error correction model.
Finally, we provided a sample prediction for the gross domestic product (GDP) for the
first quarter of 2017 as reference.

論文審定書i
謝辭ii
摘要iii
Abstract iv
目錄v
圖次vii
表次viii
1 緒論1
1.1 研究動機及目的. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 文獻回顧3
2.1 計量文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 理論文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 實證文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 研究方法9
3.1 ADF 單根檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 共整合檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2.1 共整合關係. . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2.2 Engle - Granger 兩階段共整合檢定. . . . . . . . . . . . . . . . 11
3.2.3 Johansen 共整合檢定. . . . . . . . . . . . . . . . . . . . . . . 11
3.2.4 最適落後期數選擇. . . . . . . . . . . . . . . . . . . . . . . . 15
3.3 混合頻率誤差修正模型. . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.3.1 以誤差修正模型表現的混合頻率自迴歸分佈滯後模型. . . . 15
3.3.2 預測模型: 不受限制的短期動態. . . . . . . . . . . . . . . . . 17
3.3.3 進入動態混合頻率共整合關係的高頻觀察值選擇. . . . . . . 18
3.4 預測力指標. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.5 Diebold - Mariano 檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 實證分析與結果21
4.1 資料處理與來源. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2 落後期數選擇. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.3 共整合檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.4 估計混合頻率共整合項. . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.5 估計混合頻率誤差修正模型. . . . . . . . . . . . . . . . . . . . . . . 24
4.6 估計誤差修正模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.7 樣本內預測. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.8 樣本外預測. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5 結論30
參考文獻32

李慶男(2005。⟨ 時間序列講義⟩。國立中山大學經濟研究所。
易行健，李軍波，楊碧云(2004)。我國對外貿易與經濟增長之間的實證檢驗:1978-
2002。⟨ 石家庄經濟學院學報⟩ vol. 27 (4), pp. 428–431。
許和連，賴明勇(2002)。出口貿易帶動經濟增長假設在中國的進一步實驗。⟨ 湖南
大學學報: 自然科學版⟩ vol. 29 (3), pp. 124–128。
陳旭昇(2013)。⟨ 時間序列分析: 總體經濟與財務金融之應用⟩。二版，東華書局。
黃台心(2002)。出口與經濟成長的因果關係: 台灣的實證研究。⟨ 經濟論文叢刊⟩
vol. 30 (4), pp. 465–490。
楊奕農(2009)。⟨ 時間序列分析: 經濟與財務上之應用⟩。二版，雙葉書局。
劉桂珍，劉慧芳(2009)。對外貿易與經濟增長關係的實證分析。⟨ 全國商情(經濟
理論研究)⟩ vol. 11, pp. 040。
Ahmad, J., Kwan, A. C., (1991). Causality between exports and economic growth: empirical
evidence from africa. Economics Letters vol. 37 (3), pp. 243–248.
Akaike, H., (1974). A new look at the statistical model identification. IEEE transactions
on automatic control vol. 19 (6), pp. 716–723.
Awokuse, T. O., (2003). Is the export‐led growth hypothesis valid for canada?. Canadian
Journal of Economics vol. 30 (1), pp. 126–136.
Balassa, B., (1978). Exports and economic growth: further evidence. Journal of development
Economics vol. 5 (2), pp. 181–189.
Bhagwati, J., (1958). Immiserizing growth: a geometrical note. The Review of Economic
Studies vol. 25 (3), pp. 201–205.
Clements, M. P., Galvao, A. B., (2008). Macroeconomic forecasting with mixedfrequency
data: Forecasting output growth in the united states. Journal of Business
& Economic Statistics vol. 26 (4), pp. 546–554.
Dickey, D. A., Fuller, W. A., (1979). Distribution of the estimators for autoregressive time
series with a unit root. Journal of the American statistical association vol. 74 (366a),
pp. 427–431.
Diebold, F. X., Mariano, R. S., (1995). Comparing predictive accuracy. Journal of Business
& Economic Statistics, pp. 253–263.
Emery, R. F., (1967). The relation of exports and economic growth. Kyklos vol. 20 (4), pp.
470–486.
Engle, R. F., Granger, C. W., (1987). Co-integration and error correction: representation,
estimation, and testing. Econometrica: journal of the Econometric Society, pp. 251–
276.
Engle, R. F., Yoo, B. S., (1987). Forecasting and testing in co-integrated systems. Journal
of econometrics vol. 35 (1), pp. 143–159.
Feder, G., (1983). On exports and economic growth. Journal of development economics
vol. 12 (1-2), pp. 59–73.
Fountas, S., (2000). Some evidence on the export-led growth hypothesis for ireland. Applied
Economics Letters vol. 7, pp. 211–214.
Ghysels, E., Santa-Clara, P., Valkanov, R., (2004). The midas touch: Mixed data sampling
regression models. Finance.
Gourieroux, Christian, A. M., Renault, E., (1991). A general framework for factor models.
Institut National de la Statistique et des Etudes Economiques vol. 9107.
Granger, C. W., Newbold, P., (1974). Spurious regressions in econometrics. Journal of
econometrics vol. 2 (2), pp. 111–120.
Götz, T. B., Hecq, A., Urbain, J., (2014). Forecasting mixed‐frequency time series with
ecm‐midas models. Journal of Forecasting vol. 33 (3), pp. 198–213.
Johansen, S., (1988). Statistical analysis of cointegration vectors. Journal of economic
dynamics and control vol. 12 (2-3), pp. 231–254.
Johansen, S., Juselius, K., (1990). Maximum likelihood estimation and inference on cointegration—
with applications to the demand for money. Oxford Bulletin of Economics
and statistics vol. 52 (2), pp. 169–210.
Kravis, I. B., (1970). Trade as a handmaiden of growth: Similarities between the nineteenth
and twentieth centuries. The Economic Journal vol. 80 (320), pp. 850–872.
Krugman, P. R., (1979). Increasing returns, monopolistic competition, and international
trade. Journal of international Economics vol. 9 (4), pp. 469–479.
Kwan, A. C., Kwok, B., (1995). Exogeneity and the export-led growth hypothesis: the
case of china. Southern Economic Journal, pp. 1158–1166.
Miller, J. I., (2013). Mixed-frequency cointegrating regressions with parsimonious distributed
lag structures. Journal of Financial Econometrics vol. 12 (3), pp. 584–614.
Osterwald‐Lenum, M., (1992). A note with quantiles of the asymptotic distribution of the
maximum likelihood cointegration rank test statistics1. Oxford bulletin of economics
and statistics vol. 54 (3), pp. 461–472.
Phillips, P. C., Ouliaris, S., (1990). Asymptotic properties of residual based tests for cointegration.
Econometrica: Journal of the Econometric Society, pp. 165–193.
Prebisch, R., (1962). The economic development of latin america and its principal problems.
Economic Bulletin for Latin America.
Ricardo, D., (1817)a. On foreign trade. Principles of political economy and taxation.
Ricardo, D., (1817)b. Principles of political economy and taxation.
Said, S. E., Dickey, D. A., (1984). Testing for unit roots in autoregressive-moving average
models of unknown order. Biometrika vol. 71 (3), pp. 599–607.
Schwarz, G., (1978). Estimating the dimension of a model. The annals of statistics vol.
6 (2), pp. 461–464.