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ZAMANSAL TOPLULAŞTIRMANIN BİRİM KÖK TESTLERİ ÜZERİNDEKİ ETKİSİ

Year 2019, Issue: 24, 233 - 258, 24.07.2019
https://doi.org/10.18092/ulikidince.498854

Abstract

Yüksek frekanslı serilerden düşük frekanslı seriler
elde edilmesine zamansal toplulaştırma denir. Bu çalışmada, zamansal
toplulaştırmanın iki farklı yaklaşımı olan sistematik örnek ve ortalama örnek
toplulaştırmaları kullanılarak, toplulaştırmanın standart birim kök testleri
üzerindeki etkisinin incelenmesi amaçlanmıştır. Bu amaçla çalışmada 1990-2015
dönemi itibari ile M1, fiyat, rezerv ve kur serileri kullanılmıştır. Logaritmik
dönüşüme tabi tutulmuş ve tutulmamış aylık frekanstaki serilerden her iki
toplulaştırma biçimine göre üçer aylık ve yıllık frekanslarda seriler elde
edilmiştir. Logaritmik dönüşüm yapılıp yapılmaması serilerin seviyelerinde
birim kök testleri bakımından pek bir farklılık yaratmazken, birinci
farklarında bazı farklı bulguların çıkmasına yol açmıştır. Aynı zamanda
toplulaştırma biçimi de birim kök testi sonuçlarını etkilemiştir.

References

  • Amemiya, T. ve Wu, Y. R. (1972). The Effect of Aggregation on Prediction in the Autoregressive Model. Journal of the American Statistical Association, 67(339), 628-632.
  • Brewer, K. R. W. (1973). Some Consequences of Temporal Aggregation and Systematic Sampling for ARMA and ARMAX Models. Journal of Econometrics, 1(2), 133-154.
  • Choi, I. (1992). Effects of Data Aggregation on the Power of Tests for a Unit Root: A Simulation Study. Economics Letters, 40(4), 397-401.
  • Dickey, D. A. ve Fuller, W. A. (1981). Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root. Econometrica, 49, 1057-1072.
  • Fujihara, R. A. ve Mougoue, M. (1994). Temporal Aggregation and Unit Roots in Nominal Foreign Exchange Rates. Review of Quantitative Finance and Accounting, 4(3), 291-303.
  • Granger, C. W. J. ve Siklos, P. L. (1995). Systematic Sampling, Temporal Aggregation, Seasonal Adjustment, and Cointegration Theory and Evidence. Journal of Econometrics, 66(1), 357-369.
  • Grunfeld, Y. ve Griliches, Z. (1960). Is Aggregation Necessarily Bad? The Review of Economics and Statistics, 42(1), 1-13.
  • Kwiatkowski, D., Phillips, P. C., Schmidt, P., Shin, Y. (1992). Testing the Null Hypothesis of Stationarity Against The Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?. Journal of Econometrics, 54(1-3), 159-178.
  • Leontief, W. (1947). Introduction to a Theory of the Internal Structure of Functional Relationships. Econometrica Journal of the Econometric Society, 15(4), 361-373.
  • Marcellino, M. (1999). Some Consequences of Temporal Aggregation in Empirical Analysis. Journal of Business & Economic Statistics, 17(1), 129-136.
  • Mundlak, Y. (1961). Aggregation over Time in Distributed Lag Models. International Economic Review, 2(2), 154-163.
  • Perron, P. (1989). The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis. Econometrica, 57(6), 1361-1401.
  • Perron, P. (1991). Test Consistency with Varying Sampling Frequency. Econometric Theory, 7(3), 341-368.
  • Phillips, C.B. P. ve Perron, P. (1988). Testing for A Unit Root in Time Series Regressions. Biometrika, 75(2), 335-346.
  • Pierse, R. ve Snell, A. (1995). Temporal Aggregation and the Power of Tests for A Unit Root. Journal of Econometrics, 65(2), 333-345.
  • Quenouille, M.H. (1958). Discrete Autoregressive Schemes with Varying Time-Intervals. Metrika, 1(1), 21-27.
  • Rossana, Robert J. ve John J. Seater (1992), “Aggregation, Unit Roots and the Time Series Structure of Manufacturing Real Wages”, International Economic Review, 159-179.
  • Shiller R. J. ve Perron, P. (1985). Testing the Random Walk Hypothesis: Power Versus Frequency of Observation. Economic Letters, 18(4), 381-386.
  • Telser, L. G. (1967). Discrete Samples and Moving Sums in Stationary Stochastic Processes. Journal of the American Statistical Association, 62(318), 484-499.
  • Theil, H. (1955). Linear Aggregation of Economic Relations. The American Economic Review, 45(4), 680-682.
  • Teles, P., Wei, W. W., Hodgess, E. M. (2008). Testing a Unit Root Based on Aggregate Time Series. Communications in Statistics-Theory and Methods, 37(4), 565-590.
  • Tiao, G. C. (1972). Asymptotic Behaviour of Temporal Aggregates of Time Series. Biometrika, 59(3), 525-531.
  • Yamak, R. ve Erdem, H. F. (2017). Uygulamalı Zaman Serisi Analizleri, 1. Baskı Trabzon: Celepler Matbaacılık.
  • Zellner, A. (1962). An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias. Journal of the American Statistical Association, 57(298), 348-368.
  • Zellner, A. ve Montmarquette, C. (1971). A Study of Some Aspects of Temporal Aggregation Problems in Econometric Analyses. The Review of Economics and Statistics, 53(4), 335-342.

EFFECT OF TEMPORAL AGGREGATION ON UNIT ROOT TESTS

Year 2019, Issue: 24, 233 - 258, 24.07.2019
https://doi.org/10.18092/ulikidince.498854

Abstract

The low-frequency
series obtained from high-frequency series is called temporal aggregation. The
aim of this study is to investigate the effect of aggregation on standard unit
root tests using systematic sampling and average sampling aggregations, which
are two different approaches of temporal aggregation. In this study, M1, price,
reserve and exchange rate series are used for the period 1990 to 2015. Both
quarterly and yearly frequencies are obtained by using both types of
aggregations with logarithmic and non-logarithmic monthly frequency series.
According to the 
results, logarithmic transform does not cause a significant
difference in terms of unit root tests at the levels of the series, it led some
different findings in the first differences of the series. Additionally, the
results of the unit root test are affected by the aggregation forms.

References

  • Amemiya, T. ve Wu, Y. R. (1972). The Effect of Aggregation on Prediction in the Autoregressive Model. Journal of the American Statistical Association, 67(339), 628-632.
  • Brewer, K. R. W. (1973). Some Consequences of Temporal Aggregation and Systematic Sampling for ARMA and ARMAX Models. Journal of Econometrics, 1(2), 133-154.
  • Choi, I. (1992). Effects of Data Aggregation on the Power of Tests for a Unit Root: A Simulation Study. Economics Letters, 40(4), 397-401.
  • Dickey, D. A. ve Fuller, W. A. (1981). Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root. Econometrica, 49, 1057-1072.
  • Fujihara, R. A. ve Mougoue, M. (1994). Temporal Aggregation and Unit Roots in Nominal Foreign Exchange Rates. Review of Quantitative Finance and Accounting, 4(3), 291-303.
  • Granger, C. W. J. ve Siklos, P. L. (1995). Systematic Sampling, Temporal Aggregation, Seasonal Adjustment, and Cointegration Theory and Evidence. Journal of Econometrics, 66(1), 357-369.
  • Grunfeld, Y. ve Griliches, Z. (1960). Is Aggregation Necessarily Bad? The Review of Economics and Statistics, 42(1), 1-13.
  • Kwiatkowski, D., Phillips, P. C., Schmidt, P., Shin, Y. (1992). Testing the Null Hypothesis of Stationarity Against The Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?. Journal of Econometrics, 54(1-3), 159-178.
  • Leontief, W. (1947). Introduction to a Theory of the Internal Structure of Functional Relationships. Econometrica Journal of the Econometric Society, 15(4), 361-373.
  • Marcellino, M. (1999). Some Consequences of Temporal Aggregation in Empirical Analysis. Journal of Business & Economic Statistics, 17(1), 129-136.
  • Mundlak, Y. (1961). Aggregation over Time in Distributed Lag Models. International Economic Review, 2(2), 154-163.
  • Perron, P. (1989). The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis. Econometrica, 57(6), 1361-1401.
  • Perron, P. (1991). Test Consistency with Varying Sampling Frequency. Econometric Theory, 7(3), 341-368.
  • Phillips, C.B. P. ve Perron, P. (1988). Testing for A Unit Root in Time Series Regressions. Biometrika, 75(2), 335-346.
  • Pierse, R. ve Snell, A. (1995). Temporal Aggregation and the Power of Tests for A Unit Root. Journal of Econometrics, 65(2), 333-345.
  • Quenouille, M.H. (1958). Discrete Autoregressive Schemes with Varying Time-Intervals. Metrika, 1(1), 21-27.
  • Rossana, Robert J. ve John J. Seater (1992), “Aggregation, Unit Roots and the Time Series Structure of Manufacturing Real Wages”, International Economic Review, 159-179.
  • Shiller R. J. ve Perron, P. (1985). Testing the Random Walk Hypothesis: Power Versus Frequency of Observation. Economic Letters, 18(4), 381-386.
  • Telser, L. G. (1967). Discrete Samples and Moving Sums in Stationary Stochastic Processes. Journal of the American Statistical Association, 62(318), 484-499.
  • Theil, H. (1955). Linear Aggregation of Economic Relations. The American Economic Review, 45(4), 680-682.
  • Teles, P., Wei, W. W., Hodgess, E. M. (2008). Testing a Unit Root Based on Aggregate Time Series. Communications in Statistics-Theory and Methods, 37(4), 565-590.
  • Tiao, G. C. (1972). Asymptotic Behaviour of Temporal Aggregates of Time Series. Biometrika, 59(3), 525-531.
  • Yamak, R. ve Erdem, H. F. (2017). Uygulamalı Zaman Serisi Analizleri, 1. Baskı Trabzon: Celepler Matbaacılık.
  • Zellner, A. (1962). An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias. Journal of the American Statistical Association, 57(298), 348-368.
  • Zellner, A. ve Montmarquette, C. (1971). A Study of Some Aspects of Temporal Aggregation Problems in Econometric Analyses. The Review of Economics and Statistics, 53(4), 335-342.
There are 25 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Sinem Eyüboğlu 0000-0002-3525-9173

Zehra Abdioğlu

Publication Date July 24, 2019
Published in Issue Year 2019 Issue: 24

Cite

APA Eyüboğlu, S., & Abdioğlu, Z. (2019). ZAMANSAL TOPLULAŞTIRMANIN BİRİM KÖK TESTLERİ ÜZERİNDEKİ ETKİSİ. Uluslararası İktisadi Ve İdari İncelemeler Dergisi(24), 233-258. https://doi.org/10.18092/ulikidince.498854

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