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Autocorrelated Regression Model Used in Seasonal Fractionally Integrated Processes

Year 2007, Volume: 5 Issue: 1, 75 - 83, 13.07.2007

Abstract

In the literature, there are a few studies for seasonal fractionally integrated processes in recent years. Semi-parametric methods based on logarithmic periodogram were proposed to estimate seasonal fractionally differencing parameter. The methods based on logarithmic periodogram can be used as a spectral density function of seasonal fractionally integrated processes. Also autocorrelation function instead of spectral density function can be used to seasonal fractionally integrated processes. In this study, a new parameter estimation method based on autocorrelation function is proposed for seasonal fractionally integrated process. This new method is compared classical methods in the literature by a simulation studies.

References

  • Arteche, J., Robinson, P.M., 2000. Semiparametric Inference in Seasonal and Cyclical Long Memory Processes. Journal of Time Series Analysis, 21(1), 1-25.
  • Arteche, J., 2002. Semiparametric Robust Tests on Seasonal or Cyclical Long Memory Time Series. Journal of Time Series Analysis, 23(3), 251-285.
  • Baillie, R.T., 1996. Long Memory Processes and Fractional Integration in Econometrics. Journal of Econometrics, 73, 5-59.
  • Brietzke, E.H.M., Lopes S.R.C., Bisognin C., 2005. A Closed Formula for the Durbin-Levinson’s Algorithm in Seasonal Fractionally Integrated Processes. Mathematical and Computer Modeling, 42, 1191-1206.
  • Candelon, B., Gil-Alana, L.A., 2004. Seasonal and Long-run Fractional Integration in the Industrial Production Indeces of Some Latin American Countries. Journal of Policy Modeling, 26,301-313.
  • Chung, C.F., Baillie, R.T., 1993. Small Sample Bias in Conditional Sum of Squares Estimators of Fractionally Integrated ARMA Models. Empirical Economics, 18, 791-806.
  • Chung, C.F., Ching-Fan, 1996. A Generalized Fractionally Integrated Autoregressive Moving Average Processes. Journal of Time Series Analysis, 17(2), 111-140.
  • Darne, O., Guiraud V., Terraza M., 2004. Forecasts of the Seasonal Fractional Integrated Series. Journal of Forecasting, 23,1-17.
  • Eğrioğlu E., Günay S., 2005. Uzun Dönem Bağımlı Normal Akgürültü Sürecinde Otokorelasyon Regresyonu ile Parametre Tahmini. Anadolu Üniversitesi Bilim ve Teknoloji Dergisi, 6, 61-66.
  • Gil-Alana L.A., Robinson P.M., 2001. Testing of Seasonal Fractional Integration in UK and Japanese Consumption and Income. Journal of Applied Econometrics, 16, 95-114.
  • Gil-Alana L.A., 2002. Seasonal Long Memory in the Aggregate Output. Economics Letters, 74,333-337.
  • Gil-Alana L.A., 2003a. Seasonal Misspecification in the Context of Fractionally Integrated Univariate Time Series. Computational Economics, 22, 65-74.
  • Gil-Alana L.A., 2003b. Modelling Seasonality with Fractionally Integrated Processes, Technical Report.
  • Giraitis L., Leipus R., 1995. A Generalized Fractionally Differencing Approach in Long Memory Modeling. Lithuanian Mathematical Journal, 35, 53-65.
  • Giraitis L, Hidalgo J., Robinson P.M., 2001. Gaussian Estimation of Parametric Spectral Density with Unknown Pole. Ann. Statist., 29(4), 987-1023.
  • Hassler U., Wolters J., 1994. On the Power of Unit Root Tests Against Fractional Alternatives. Economics Letters, 45, 1-5.
  • Hassler U., Wolters J., 1995. Long Memory in Inflation Rates: International Evidence. Journal of Business & Economic Statistics, 13(1), 37-45.
  • Hosking, J.R.M., 1984. Modeling Persistence in Hydrological Time Series Using Fractionally Differencing. Water Resources Research, 20-12, pp. 1898-1908.
  • Montanari A., Rosso R., Taqqu M.S., 2000. A Seasonal Fractional ARIMA Model Applied to Nile River Monthly Flows at Aswan. Water Resour. Res., 36(5), 1249-1259.
  • Ooms M., Hassler U., 1997. On the Effect of Seasonal Adjustment on the Log-Periodogram Regression. Economics Letters, 56, 135-141.
  • Ould H., 2002. Asymptotic Behavior of the Empirical Process for Seasonal Long-Memory Data. European Series in Applied and Industrial Mathematics, 6, 293-309.
  • Palma W., Chan N.H., 2005. Efficient Estimation of Seasonal Long-Range Dependent Processes. Journal of Time Series Analysis, 26(6), 863-892.
  • Porter-Hudak S., 1990. An Application of the Seasonal Fractionally Differenced Model to the Monetary Aggregates. Journal of American Statistical Association, 85 (410), 338-344.
  • Ray B.K., 1993. Long-Range Forecasting of IBM Product Revenues Using a Seasonal Fractionally Differenced ARMA Model. International Journal of Forecasting, 9, 255-269.
  • Reinsen V.A., Rodrigues A.L., Palma W., 2006a. Estimating Seasonal Long-Memory Processes: A Monte Carlo Study. Journal of Statistical Computation and Simulations, 76(4),305-316.
  • Reinsen V.A., Rodrigues A.L., Palma W., 2006b. Estimation of Seasonal Fractionally Integrated Processes. Computational Statistics and Data Analysis, 50, 568-582.
  • Valesco C., Robinson P.M., 2000. Whittle Pseudo-Maximum Likelihood Estimation of Nonstationary Time Series. J. Amer. Statis. Assoc., 95(452), 1229-1243

Mevsimsel Kesirli Bütünleşik Akgürültü Sürecinde Otokorelasyonlu Regresyon Yöntemi

Year 2007, Volume: 5 Issue: 1, 75 - 83, 13.07.2007

Abstract

Mevsimsel kesirli bütünleşik zaman serileri için son yıllarda az sayıda çalışma literatürde yer almaktadır. Mevsimsel kesirli bütünleşik zaman serilerinde fark parametresinin tahmini için logaritmik periodograma dayalı bazı yarı parametrik tahmin yöntemleri önerilmiştir. Logaritmik periodograma dayalı yöntemler, genellikle mevsimsel kesirli bütünleşik serilerin spektral yoğunluk fonksiyonunun özelliklerinden esinlenmektedir. Spektral yoğunluk fonksiyonu yerine, bu fonksiyonla aynı bilgiyi taşıyan otokorelasyon fonksiyonundan yararlanmak da mümkündür. Bu çalışmada mevsimsel kesirli bütünleşik akgürültü sürecinde örneklem otokorelasyon katsayılarına dayalı yeni bir tahmin yöntemi önerilmiştir. Önerilen yöntem bir benzetim çalışması yardımıyla daha önceki yöntemler ile karşılaştırılarak, üstün yönleri belirlenmiştir.

References

  • Arteche, J., Robinson, P.M., 2000. Semiparametric Inference in Seasonal and Cyclical Long Memory Processes. Journal of Time Series Analysis, 21(1), 1-25.
  • Arteche, J., 2002. Semiparametric Robust Tests on Seasonal or Cyclical Long Memory Time Series. Journal of Time Series Analysis, 23(3), 251-285.
  • Baillie, R.T., 1996. Long Memory Processes and Fractional Integration in Econometrics. Journal of Econometrics, 73, 5-59.
  • Brietzke, E.H.M., Lopes S.R.C., Bisognin C., 2005. A Closed Formula for the Durbin-Levinson’s Algorithm in Seasonal Fractionally Integrated Processes. Mathematical and Computer Modeling, 42, 1191-1206.
  • Candelon, B., Gil-Alana, L.A., 2004. Seasonal and Long-run Fractional Integration in the Industrial Production Indeces of Some Latin American Countries. Journal of Policy Modeling, 26,301-313.
  • Chung, C.F., Baillie, R.T., 1993. Small Sample Bias in Conditional Sum of Squares Estimators of Fractionally Integrated ARMA Models. Empirical Economics, 18, 791-806.
  • Chung, C.F., Ching-Fan, 1996. A Generalized Fractionally Integrated Autoregressive Moving Average Processes. Journal of Time Series Analysis, 17(2), 111-140.
  • Darne, O., Guiraud V., Terraza M., 2004. Forecasts of the Seasonal Fractional Integrated Series. Journal of Forecasting, 23,1-17.
  • Eğrioğlu E., Günay S., 2005. Uzun Dönem Bağımlı Normal Akgürültü Sürecinde Otokorelasyon Regresyonu ile Parametre Tahmini. Anadolu Üniversitesi Bilim ve Teknoloji Dergisi, 6, 61-66.
  • Gil-Alana L.A., Robinson P.M., 2001. Testing of Seasonal Fractional Integration in UK and Japanese Consumption and Income. Journal of Applied Econometrics, 16, 95-114.
  • Gil-Alana L.A., 2002. Seasonal Long Memory in the Aggregate Output. Economics Letters, 74,333-337.
  • Gil-Alana L.A., 2003a. Seasonal Misspecification in the Context of Fractionally Integrated Univariate Time Series. Computational Economics, 22, 65-74.
  • Gil-Alana L.A., 2003b. Modelling Seasonality with Fractionally Integrated Processes, Technical Report.
  • Giraitis L., Leipus R., 1995. A Generalized Fractionally Differencing Approach in Long Memory Modeling. Lithuanian Mathematical Journal, 35, 53-65.
  • Giraitis L, Hidalgo J., Robinson P.M., 2001. Gaussian Estimation of Parametric Spectral Density with Unknown Pole. Ann. Statist., 29(4), 987-1023.
  • Hassler U., Wolters J., 1994. On the Power of Unit Root Tests Against Fractional Alternatives. Economics Letters, 45, 1-5.
  • Hassler U., Wolters J., 1995. Long Memory in Inflation Rates: International Evidence. Journal of Business & Economic Statistics, 13(1), 37-45.
  • Hosking, J.R.M., 1984. Modeling Persistence in Hydrological Time Series Using Fractionally Differencing. Water Resources Research, 20-12, pp. 1898-1908.
  • Montanari A., Rosso R., Taqqu M.S., 2000. A Seasonal Fractional ARIMA Model Applied to Nile River Monthly Flows at Aswan. Water Resour. Res., 36(5), 1249-1259.
  • Ooms M., Hassler U., 1997. On the Effect of Seasonal Adjustment on the Log-Periodogram Regression. Economics Letters, 56, 135-141.
  • Ould H., 2002. Asymptotic Behavior of the Empirical Process for Seasonal Long-Memory Data. European Series in Applied and Industrial Mathematics, 6, 293-309.
  • Palma W., Chan N.H., 2005. Efficient Estimation of Seasonal Long-Range Dependent Processes. Journal of Time Series Analysis, 26(6), 863-892.
  • Porter-Hudak S., 1990. An Application of the Seasonal Fractionally Differenced Model to the Monetary Aggregates. Journal of American Statistical Association, 85 (410), 338-344.
  • Ray B.K., 1993. Long-Range Forecasting of IBM Product Revenues Using a Seasonal Fractionally Differenced ARMA Model. International Journal of Forecasting, 9, 255-269.
  • Reinsen V.A., Rodrigues A.L., Palma W., 2006a. Estimating Seasonal Long-Memory Processes: A Monte Carlo Study. Journal of Statistical Computation and Simulations, 76(4),305-316.
  • Reinsen V.A., Rodrigues A.L., Palma W., 2006b. Estimation of Seasonal Fractionally Integrated Processes. Computational Statistics and Data Analysis, 50, 568-582.
  • Valesco C., Robinson P.M., 2000. Whittle Pseudo-Maximum Likelihood Estimation of Nonstationary Time Series. J. Amer. Statis. Assoc., 95(452), 1229-1243
There are 27 citations in total.

Details

Primary Language Turkish
Subjects Statistics
Journal Section Research Articles
Authors

Erol Eğrioğlu

Süleyman Günay This is me

Publication Date July 13, 2007
Published in Issue Year 2007 Volume: 5 Issue: 1

Cite

APA Eğrioğlu, E., & Günay, S. (2007). Mevsimsel Kesirli Bütünleşik Akgürültü Sürecinde Otokorelasyonlu Regresyon Yöntemi. İstatistik Araştırma Dergisi, 5(1), 75-83.