Share This Article:

Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks

Abstract Full-Text HTML Download Download as PDF (Size:4246KB) PP. 292-312
DOI: 10.4236/ojs.2014.44030    3,047 Downloads   4,176 Views   Citations
Author(s)    Leave a comment

ABSTRACT

In the paper, a general framework for large scale modeling of macroeconomic and financial time series is introduced. The proposed approach is characterized by simplicity of implementation, performing well independently of persistence and heteroskedasticity properties, accounting for common deterministic and stochastic factors. Monte Carlo results strongly support the proposed methodology, validating its use also for relatively small cross-sectional and temporal samples.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Morana, C. (2014) Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks. Open Journal of Statistics, 4, 292-312. doi: 10.4236/ojs.2014.44030.

References

[1] Stock, J.H. and Watson, M.W. (2011) Dynamic Factor Models. In: Clements, M.P. and Hendry, D.F., Eds., Oxford Handbook of Economic Forecasting, Oxford University Press, Oxford, 35-60.
[2] Geweke, J. (1977) The Dynamic Factor Analysis of Economic Time Series. In: Aigner, D.J. and Goldberger, A.S., Eds., Latent Variables in Socio-Economic Models 1, North-Holland, Amsterdam.
[3] Dees, S., Pesaran, M.H., Smith, L.V. and Smith, R.P. (2010) Supply, Demand and Monetary Policy Shocks in a Multi-Country New Keynesian Model. ECB Working Paper Series, No. 1239.
[4] Bai, J. and Ng, S. (2004) A Panic Attack on Unit Roots and Cointegration. Econometrica, 72, 1127-1177.
[5] Bai, J.S. (2003) Inferential Theory for Factor Models of Large Dimensions. Econometrica, 71, 135-171.
http://dx.doi.org/10.1111/1468-0262.00392
[6] Bai, J.S. and Perron, P. (1998) Testing for and Estimation of Multiple Structural Changes. Econometrica, 66, 47-78.
http://dx.doi.org/10.2307/2998540
[7] Hamilton, J.D. (1989) A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica, 57, 357-384.
http://dx.doi.org/10.2307/1912559
[8] Enders, W. and Lee, J. (2012) The Flexible Fourier Form and Dickey-Fuller Type Unit Root Tests. Economics Letters, 117, 196-199.
http://dx.doi.org/10.1016/j.econlet.2012.04.081
[9] Baillie, R.T. and Morana, C. (2009) Modeling Long Memory and Structural Breaks in Conditional Variances: An Adaptive FIGARCH Approach. Journal of Economic Dynamics and Control, 33, 1577-1592.
http://dx.doi.org/10.1016/j.jedc.2009.02.009
[10] Baillie, R.T. and Morana, C. (2012) Adaptive ARFIMA Models with Applications to Inflation. Economic Modelling, 29, 2451-2459.
http://dx.doi.org/10.1016/j.econmod.2012.07.011
[11] González, A. and Teräsvirta, T. (2008) Modelling Autoregressive Processes with a Shifting Mean. Studies in Nonlinear Dynamics and Econometrics, 12, 1558-3708.
http://dx.doi.org/10.2202/1558-3708.1459
[12] Engle, R.F. and Rangel, J.C. (2008) The Spline-GARCH Model for Low Frequency Volatility and Its Global Macroeconomic Causes. Review of Financial Studies, 21, 1187-1222.
http://dx.doi.org/10.1093/rfs/hhn004
[13] Beran, J. and Weiershauser, A. (2011) On Spline Regression under Gaussian Subordination with Long Memory. Journal of Multivariate Analysis, 102, 315-335.
http://dx.doi.org/10.1016/j.jmva.2010.09.007
[14] Beran, J. and Feng, Y.H. (2002) SEMIFAR Models—A Semiparametric Approach to Modelling Trends, Long-Range Dependence and Nonstationarity. Computational Statistics and Data Analysis, 40, 393-419.
http://dx.doi.org/10.1016/S0167-9473(02)00007-5
[15] Engle, R.F. and Smith, A.D. (1999) Stochastic Permanent Breaks. The Review of Economics and Statistics, 81, 553-574.
http://dx.doi.org/10.1162/003465399558382
[16] Ray, B.K. and Tsay, R.S. (2002) Bayesian Methods for Change-Point Detection in Long-Range Dependent Processes. Journal of Time Series Analysis, 23, 687-705.
http://dx.doi.org/10.1111/1467-9892.00286
[17] Lu, Y. and Perron, P. (2010) Modeling and Forecasting Stock Return Volatility Using a Random Level Shift Model. Journal of Empirical Finance, 17, 138-156.
http://dx.doi.org/10.1016/j.jempfin.2009.10.001
[18] Perron, P. and Varsnekov, R.T. (2012) Combining Long Memory and Level Shifts in Modeling and Forecasting the Volatility of Asset Returns. Boston University, Boston.
[19] Chapman, D.A. and Ogaki, M. (1998) Cotrending and the Stationarity of the Real Interest Rate. Economics Letters, 42, 133-138.
http://dx.doi.org/10.1016/0165-1765(93)90050-M
[20] Bierens, H.J. (2000) Nonparametric Nonlinear Cotrending Analysis, with an Application to Interest and Inflation in the United States. Journal of Business and Economic Statistics, 18, 323-337.
http://dx.doi.org/10.2307/1392265
[21] Hendry, D.F. (1996) A Theory of Co-Breaking. Nuffield College, University of Oxford, Oxford.
[22] Hendry, D.F. and Massmann, M. (2007) Co-Breaking: Recent Advances and a Synopsis of the Literature. Journal of Business and Economic Statistics, 25, 33-51.
http://dx.doi.org/10.1198/073500106000000422
[23] Engle, R.F. and Kozicki, S. (1993) Testing for Common Features. Journal of Business & Economic Statistics, 11, 369-380.
http://dx.doi.org/10.1080/07350015.1993.10509966
[24] Engle, R.F. and Granger, C. (1987) Co-Integration and Error Correction: Representation, Estimation and Testing. Econometrica, 55, 251-276.
http://dx.doi.org/10.2307/1913236
[25] Bollerslev, T. (1990) Modelling the Coherence in Short-Run Nominal Exchange Rates: A Multivariate Generalized Arch Approach. Review of Economics and Statistics, 72, 489-505.
http://dx.doi.org/10.2307/2109358
[26] Baillie, R.T., Bollerslev, T. and Mikkelsen, H.O. (1996) Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 74, 3-30.
http://dx.doi.org/10.1016/S0304-4076(95)01749-6
[27] Conrad, C. and Haag, B.R. (2006) Inequality Constraints in the Fractionally Integrated GARCH Model. Journal of Financial Econometrics, 4, 413-449.
http://dx.doi.org/10.1093/jjfinec/nbj015
[28] Chan, N.H. and Palma, W. (1998) State Space Modeling of Long Memory Processes. Annals of Statistics, 26, 719-740. http://projecteuclid.org/euclid.aos/1028144856
http://dx.doi.org/10.1214/aos/1028144856
[29] Kilian, L. (2011) Structural Vector Autoregressions. CEPR Discussion Paper, No. 8515.
[30] Beran, J. and Feng, Y.H. (2001) Local Polynomial Estimation with a FARIMA-GARCH Error Process. Bernoulli, 7, 733-750.
http://dx.doi.org/10.2307/3318539
[31] Beran, J. and Feng, Y.H. (2002) Data Driven Bandwidth Choice for SEMIFAR Models. Journal of Computational and Graphical Statistics, 11, 690-713.
http://dx.doi.org/10.1198/106186002420
[32] Bordignon, S. and Raggi, D. (2010) Long Memory and Nonlinearities in Realized Volatility. University of Padova, Padova.
[33] Martens, M., van Dijk, D. and de Pooter, M. (2003) Modeling and Forecasting S&P500 Volatility: Long Memory, Structural Breaks and Nonlinearity. Erasmus University of Rotterdam, Rotterdam.
[34] Grassi, S. and de Magistris, P.S. (2011) When Long Memory Meets the Kalman Filter: A Comparative Study. Aarhus University, Aarhus.
[35] Lavielle, M. and Moulines, E. (2000) Least-Squares Estimation of an Unknown Number of Shifts in a Time Series. Journal of Time Series Analysis, 21, 33-59.
http://dx.doi.org/10.1111/1467-9892.00172
[36] Granger, C.W.J. and Hyung, N. (2004) Occasional Structural Breaks and Long Memory with an Application to the S&P500 Absolute Returns. Journal of Empirical Finance, 11, 399-421.
http://dx.doi.org/10.1016/j.jempfin.2003.03.001
[37] Morana, C. (2014) New Insights on the US OIS Spreads Term Structure during the Recent Financial Turmoil. Applied Financial Economics, 24, 291-317.
http://dx.doi.org/10.1080/09603107.2013.864034
[38] Bai, J.S. and Ng, S. (2013) Principal Components Estimation and Identification of Static Factors. Journal of Econometrics, 176, 18-29.
http://dx.doi.org/10.1016/j.jeconom.2013.03.007
[39] Robin, J.M. and Smith, R.J. (2000) Tests of Rank. Econometric Theory, 16, 151-175.
http://dx.doi.org/10.1017/S0266466600162012
[40] Peres-Neto, P.R., Jackson, D.A. and Somers, K.M. (2005) How Many Principal Components? Stopping Rules for Determining the Number of Non-Trivial Axes Revisited. Computational Statistics and Data Analysis, 49, 974-997.
http://dx.doi.org/10.1016/j.csda.2004.06.015
[41] Bai, J. and Ng, S. (2002) Determining the Number of Factors in Approximate Factor Models. Econometrica, 70, 191-221.
http://dx.doi.org/10.1111/1468-0262.00273
[42] Bai, J.S. and Ng, S. (2007) Determining the Number of Primitive Shocks in Factor Models. Journal of Business and Economic Statistics, 25, 52-60.
http://dx.doi.org/10.1198/073500106000000413
[43] Nielsen, M.O. and Frederiksen, P.H. (2005) Finite Sample Comparison of Parametric, Semiparametric and Wavelet Estimators of Fractional Integration. Econometric Reviews, 24, 405-443.
http://dx.doi.org/10.1080/07474930500405790
[44] Chan, N.H. and Palma, W. (2006) Estimation of Long-Memory Time Series Models: A Survey of Different Likelihood Based Approaches. In: Fomby, T.H. and Terrel, D., Eds., Econometric Analysis of Economic and Financial Time Series, Advances in Econometrics, Vol. 20, Emerald Group Publishing Limited, Bingley, 89-121.
[45] Robinson, P.M. (2006) Conditional-Sum-of-Squares Estimation of Models for Stationary Time Series with Long Memory. IMS Lecture Notes-Monograph Series, Time Series and Related Topics, 52, 130-137.
http://dx.doi.org/10.1214/074921706000000996
[46] Sowell, F. (1992) Maximum Likelihood Estimation of Stationary Univariate Fractionally Integrated Time Series Models. Journal of Econometrics, 53, 165-188.
http://dx.doi.org/10.1016/0304-4076(92)90084-5
[47] Martin, L.V. and Wilkins, N.P. (1999) Indirect Estimation of ARFIMA and VARFIMA Models. Journal of Econometrics, 93, 149-175.
http://dx.doi.org/10.1016/S0304-4076(99)00007-x
[48] Baillie, R. and Kapetanios, G. (2013) Inference for Impulse Response Functions from Multivariate Strongly Persistent Processes. Queen Mary University of London, London.
[49] Bai, J.S. and Ng, S. (2006) Confidence Intervals for Diffusion Index Forecasts and Inference with Factor-Augmented Regressions. Econometrica, 74, 1133-1150.
http://dx.doi.org/10.1111/j.1468-0262.2006.00696.x
[50] Bai, J.S. and Ng, S. (2008) Forecasting Economic Time Series Using Targeted Predictors. Journal of Econometrics, 146, 304-317.
http://dx.doi.org/10.1016/j.jeconom.2008.08.010
[51] Granger, C.W.J. and Jeon, Y. (2004) Thick Modeling. Economic Modelling, 21, 323-343.
[52] Alexander, C.O. (2002) Principal Component Models for Generating Large GARCH Covariance Matrices. Economic Notes, 31, 337-359.
http://dx.doi.org/10.1111/1468-0300.00089
[53] Amado, C. and Terasvirta, T. (2008) Modelling Conditional and Unconditional Heteroskedasticity with Smoothly Time-Varying Structure. CREATES Research Paper, No. 8.
[54] Hamilton, J.D. and Susmel, R. (1994) Autoregressive Conditional Heteroskedasticity and Changes in Regime. Journal of Econometrics, 64, 307-333.
http://dx.doi.org/10.1016/0304-4076(94)90067-1
[55] Engle, R.F. (2002) Dynamic Conditional Correlation—A Simple Class of Multivariate GARCH Models. Journal of Business and Economic Statistics, 20, 339-350.
http://dx.doi.org/10.1198/073500102288618487
[56] Engle, R.F. and Kelly, B.T. (2012) Dynamic Equicorrelation. Journal of Business and Economics Statistics, 30, 212-228.
[57] Quah, D. and Sargent, T.J. (1992) A Dinamic Index Model for Large Cross-Section. In: Stock, J. and Watson, M., Eds., Business Cycle, University of Chicago Press, Chicago.
[58] Watson, M. and Engle, R.F. (1983) Alternative Algorithms for the Estimation of Dynamic Factor, Mimic and Varying Coefficient Regression Models. Journal of Econometrics, 23, 385-400.
http://dx.doi.org/10.1016/0304-4076
[59] Doz, C., Giannone, D. and Reichlin, L. (2011) A Two-Step Estimator for Large Approximate Dynamic Factor Models Based on Kalman Filtering. Journal of Econometrics, 164, 188-205.
http://dx.doi.org/10.1016/j.jeconom.2011.02.012
[60] Doz, C., Giannone, D. and Reichlin, L. (2012) A Quasi Maximum Likelihood Approach for Large Approximate Dynamic Factor Models. Review of Economics and Statistics, 94, 1014-1024.
http://dx.doi.org/10.1162/REST_a_00225
[61] Bai, J.S. (2004) Estimating Cross-Section Common Stochastic Trends in Nonstationary Panel Data. Journal of Econometrics, 122, 137-138.
http://dx.doi.org/10.1016/j.jeconom.2003.10.022
[62] Castells, F., Laguna, P., Sornmo, L., Bollmann, A. and Millet-Roig, J. (2007) Principal Component Analysis in ECG Signa Processing. EURASIP Journal on Advances in Signal Processing, 1, 98-119.
http://dx.doi.org/10.1155/2007/74580
[63] Morana, C. (2007) Multivariate Modelling of Long Memory Processes with Common Components. Computational Statistics and Data Analysis, 52, 919-934.
http://dx.doi.org/10.1016/j.csda.2006.12.010
[64] Hatanka, M. and Yamada, H. (1994) Co-Trending: An Extended Version. University of Hiroshima, Hiroshima.
[65] Lansang, J.R.G. and Barrios, E.B. (2009) Principal Components Analysis of Nonstationary Time Series Data. Statistics and Computing, 19, 173-187.
http://dx.doi.org/10.1007/s11222-008-9082-y
[66] Morana, C. (2014) Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks. DEMS Working Paper Series, No. 273.
[67] Cassola, N. and Morana, C. (2012) Euro Money Market Spreads during the 2007-? Financial Crisis. Journal of Empirical Finance, 19, 548-557.
http://dx.doi.org/10.1016/j.jempfin.2012.04.003
[68] Morana, C. (2013) Oil Price Dynamics, Macro-Finance Interactions and the Role of Financial Speculation. Journal of Banking and Finance, 37, 206-226.
http://dx.doi.org/10.1016/j.jbankfin.2012.08.027
[69] Bagliano, F.C. and Morana, C. (2014) Determinants of US Financial Fragility Conditions. Research in International Business and Finance, 30, 377-392.
http://dx.doi.org/10.1016/j.ribaf.2012.08.003

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.