Econometric Analysis with Vector Autoregressive Models

Handbook of Computational Econometrics

Volumn , Issue , 2009, Pages 281-319

  Lütkepohl, Helmut ^a  

^a EUROPEAN UNIVERSITY INSTITUTE   (Italy)

Author keywords

Bayesian estimation of VARs; Econometric analysis with vector autoregressive models; Estimation with linear restrictions; Levels VAR representation; Residual autocorrelation tests; Structural form models; VAR processes; VARs and VECMs for forecasting; VECM representation; Vector autoregressive (VAR) models and forecasting and economic analysis

Indexed keywords

EID: 84889416013     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9780470748916.ch8     Document Type: Chapter

References (165)

1. Ahn SK 1988 Distribution for residual autocovariances in multivariate autoregressive models with structured parameterization. Biometrika 75, 590-593.
2. Ahn SK and Reinsel GC 1990 Estimation of partially nonstationary multivariate autoregressive models. Journal of the American Statistical Association 85, 813-823.
3. Akaike H 1973 Information theory and an extension of the maximum likelihood principle. In Proc. 2nd Int. Symp. on Information Theory (eds Petrov B and Csaki F), pp. 267-281. Academiai Kiado, Budapest.
4. Akaike H 1974 A new look at the statistical model identification. IEEE Transactions on Automatic Control AC-19, 716-723.
5. Amisano G and Giannini C 1997 Topics in Structural VAR Econometrics, 2nd edn. Springer, Berlin.
6. Anderson TW 1951 Estimating linear restrictions on regression coefficients for multivariate normal distributions. Annals of Mathematical Statistics 22, 327-351.
7. Andrews DWK 1993 Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821-856.
8. Andrews DWK and Ploberger W 1994 Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62, 1383-1414.
9. Angrist JD, Imbens GW and Rubin DB 1996 Identification of causal effects using instrumental variables. Journal of the American Statistical Association 91, 444-472.
10. Baillie RT 1981 Prediction from the dynamic simultaneous equation model with vector autoregressive errors. Econometrica 49, 1331-1337.
11. Balke NS and Fomby TB 1997 Threshold cointegration. International Economic Review 38, 627-645.
12. Banerjee A, Dolado JJ, Galbraith JW and Hendry DF 1993 Co-integration, Error-Correction, and the Econometric Analysis of Non-Stationary Data. Oxford University Press, Oxford.
13. Bartel H and Lutkepohl H 1998 Estimating the Kronecker indices of cointegrated echelon form VARMA models. Econometrics Journal 1, C76-C99.
14. Basu AK and Sen Roy S 1987 On asymptotic prediction problems for multivariate autoregressive models in the unstable nonexplosive case. Calcutta Statistical Association Bulletin 36, 29-37.
15. Bauwens L and Lubrano M 1996 Identification restrictions and posterior densities in cointegrated Gaussian VAR systems. In Advances in Econometrics, Vol. 11, Part B, pp. 3-28. JAI Press, Greenwich, CT.
16. Benkwitz A, Lutkepohl H and Neumann M 2000 Problems related to bootstrapping impulse responses of autoregressive processes. Econometric Reviews 19, 69-103.
17. Benkwitz A, Lutkepohl H and Wolters J 2001 Comparison of bootstrap confidence intervals for impulse responses of German monetary systems. Macroeconomic Dynamics 5, 81-100.
18. Berkowitz J and Kilian L 2000 Recent developments in bootstrapping time series. Econometric Reviews 19, 1-48.
19. Bernanke B 1986 Alternative explanations of the money-income correlation. Carnegie-Rochester Conference Series on Public Policy 25, 49-99.
20. Bernanke BS and Mihov I 1998 Measuring monetary policy. Quarterly Journal of Economics 113, 869-902.
21. Bhansali RJ 1978 Linear prediction by autoregressive model fitting in the time domain. Annals of Statistics 6, 224-231.
22. Bhansali RJ 2002 Multi-step forecasting. In A Companion to Economic Forecasting (eds Clements MP and Hendry DF), pp. 206-221. Blackwell, Oxford.
23. Blanchard O and Quah D 1989 The dynamic effects of aggregate demand and supply disturbances. American Economic Review 79, 655-673.
24. Boswijk HP 2000 Mixed normality and ancillarity in I(2) systems. Econometric Theory 16, 878-904.
25. Boswijk HP and Doornik JA 2004 Identifying, estimating and testing restricted cointegrated systems:an overview. Statistica Neerlandica 58, 440-465.
26. Breitung J, BrUggemann R and LUtkepohl H 2004 Structural vector autoregressive modeling and impulse responses. In Applied Time Series Econometrics (eds Lutkepohl H and Kratzig M), pp. 159-196. Cambridge University Press, Cambridge.
27. Brüggemann R 2004 Model Reduction Methods for Vector Autoregressive Processes. Springer, Berlin.
28. Briiggemann R and Lutkepohl H 2001 Lag selection in subset VAR models with an application to a US monetary system. In Econometric Studies:A Festschrift in Honour of Joachim Frohn (eds Friedmann R, Knuppel L and Lutkepohl H), pp. 107-128. LIT Verlag, Munster.
29. Briiggemann R and Lutkepohl H 2005 Practical problems with reduced-rank ML estimators for cointegration parameters and a simple alternative. Oxford Bulletin of Economics and Statistics 67, 673-690.
30. Briiggemann R, Lutkepohl H and Saikkonen P 2006 Residual autocorrelation testing for vector error correction models. Journal of Econometrics 134, 579-604.
31. Candelon B and Lutkepohl H 2001 On the reliability of Chow-type tests for parameter constancy in multivariate dynamic models. Economics Letters 73, 155-160.
32. Canova F 2007 Methods for Applied Macroeconomic Research. Princeton University Press, Princeton, NJ.
33. Christiano LJ, Eichenbaum M and Evans C 1999 Monetary policy shocks:What have we learned and to what end? In Handbook of Macroeconomics, Vol. 1A (eds Taylor JB and Woodford M), pp. 65-148. Elsevier, Amsterdam.
34. Christiano LJ, Eichenbaum M and Evans C 2005 Nominal rigidities and the dynamic effects of a shock to monetary policy. Journal of Political Economy 113, 1-45.
35. Clements MP and Hendry DF 1998 Forecasting Economic Time Series. Cambridge University Press, Cambridge.
36. Clements MP and Hendry DF 1999 Forecasting Non-Stationary Economic Time Series. MIT Press, Cambridge, MA.
37. Cogley T and Sargent TJ 2001 Evolving post-world war II US inflation dynamics. NBER Macroeconomics Annual 16, 331-373.
38. Del Negro M and Schorfheide F 2004 Priors from general equilibrium models for VARs. International Economic Review 45, 643-673.
39. Doan T, Litterman RB and Sims CA 1984 Forecasting and conditional projection using realistic prior distributions. Econometric Reviews 3, 1-144.
40. Dolado JJ and Lutkepohl H 1996 Making Wald tests work for cointegrated VAR systems. Econometric Reviews 15, 369-386.
41. Doornik JA and Hansen H 1994 A practical test of multivariate normality. Unpublished paper, Nuffield College, Oxford.
42. Doornik JA and Hendry DF 1997 Modelling Dynamic Systems Using PcFiml 9.0 for Windows. International Thomson Business Press, London.
43. Dufour JM and Renault E 1998 Short run and long run causality in time series:theory. Econometrica 66, 1099-1125.
44. Dufour JM, Pelletier D and Renault E 2006 Short run and long run causality in time series:inference. Journal of Econometrics 132, 337-362.
45. Edgerton D and Shukur G 1999 Testing autocorrelation in a system perspective. Econometric Reviews 18, 343-386.
46. Engle RF and Granger CWJ 1987 Cointegration and error correction:representation, estimation and testing. Econometrica 55, 251-276.
47. Engle RF and Yoo BS 1987 Forecasting and testing in cointegrated systems. Journal of Econometrics 35, 143-159.
48. Escribano A and Mira S 2002 Nonlinear error correction models. Journal of Time Series Analysis 23, 509-522.
49. EViews 2000 EViews 4.0 User's Guide. Quantitative Micro Software, Irvine, CA.
50. Fachin S and Bravetti L 1996 Asymptotic normal and bootstrap inference in structural VAR analysis. Journal of Forecasting 15, 329-341.
51. Findley DF 1986 On bootstrap estimates of forecast mean square errors for autoregressive processes. In Computer Science and Statistics:The Interface (ed. Allen DM), pp. 11-17. North-Holland, Amsterdam.
52. Fisher LA and Huh H 1999 Weak exogeneity and long-run and contemporaneous identifying restrictions in VEC models. Economics Letters 63, 159-165.
53. Foschi P and Kontoghiorghes EJ 2003 Estimation of VAR models:computational aspects. Computational Economics 21, 3-22.
54. Galí J 1999 Technology, employment, and the business cycle:Do technology shocks explain aggregate fluctuations? American Economic Review 89, 249-271.
55. Gatu C and Kontoghiorghes EJ 2005 Computing all possible subset models derived from a VAR process. Computational Management Science 4, 253-278.
56. Gatu C and Kontoghiorghes EJ 2006 Estimating all possible SUR models with permuted exogenous data matrices derived from a VAR process. Journal of Economic Dynamics and Control 30, 721-739.
57. Gatu C, Kontoghiorghes EJ, Gilli M and Winker P 2008 An efficient branch-and-bound strategy for subset vector autoregressive model selection. Journal of Economic Dynamics and Control 32, 1949-1963.
58. Geweke J 1996 Bayesian reduced rank regression in econometrics. Journal of Econometrics 75, 121-146.
59. Ghysels E and Osborn DR 2001 The Econometric Analysis of Seasonal Time Series. Cambridge University Press, Cambridge.
60. Giannini C 1992 Topics in Structural VAR Econometrics. Springer, Heidelberg.
61. Gonzalo J and Ng S 2001 A systematic framework for analyzing the dynamic effects of permanent and transitory shocks. Journal of Economic Dynamics and Control 25, 1527-1546.
62. Gonzalo J and Pitarakis JY 1999 Dimensionality effect in cointegration analysis. In Cointegration, Causality, and Forecasting. A Festschrift in Honour of Clive W.J. Granger (eds Engle R and White H), pp. 212-229. Oxford University Press, Oxford.
63. Gourieroux C and Monfort A 1997 Time Series and Dynamic Models. Cambridge University Press, Cambridge.
64. Granger CWJ 1969 Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424-438.
65. Granger CWJ 1981 Some properties of time series data and their use in econometric model specification. Journal of Econometrics 16, 121-130.
66. Granger CWJ 1982 Generating mechanisms, models, and causality. In Advances in Econometrics (ed. Hildenbrand W), pp. 237-253. Cambridge University Press, Cambridge.
67. Granger CWJ 2001 Overview of nonlinear macroeconometric empirical models. Macroeconomic Dynamics 5, 466-481.
68. Grigoletto M 1998 Bootstrap prediction intervals for autoregressions:some alternatives. International Journal of Forecasting 14, 447-456.
69. Hamilton JD 1994 Time Series Analysis. Princeton University Press, Princeton, NJ.
70. Hannan EJ and Deistler M 1988 The Statistical Theory of Linear Systems. John Wiley & Sons, Inc., New York.
71. Hannan EJ and Quinn BG 1979 The determination of the order of an autoregression. Journal of the Royal Statistical Society B41, 190-195.
72. Hansen BE 1997 Approximate asymptotic p values for structural-change tests. Journal of Business and Economic Statistics 15, 60-67.
73. Hansen H and Johansen S 1999 Some tests for parameter constancy in cointegrated VAR-models. Econometrics Journal 2, 306-333.
74. Hansen PR 2003 Structural changes in the cointegrated vector autoregressive model. Journal of Econometrics 114, 261-295.
75. Hatanaka M 1996 Time-Series-Based Econometrics:Unit Roots and Co-Integration. Oxford University Press, Oxford.
76. Heckman JJ 2000 Causal parameters and policy analysis in econometrics:a twentieth century retrospective. Quarterly Journal of Economics 105, 45-97.
77. Hendry DF 1995 Dynamic Econometrics. Oxford University Press, Oxford.
78. Hendry DF and Krolzig HM 2001 Automatic Econometric Model Selection with PcGets. Timberlake Consultants Press, London.
79. Hoover KD 2001 Causality in Macroeconomics. Cambridge University Press, Cambridge.
80. Hosking JRM 1980 The multivariate portmanteau statistic. Journal of the American Statistical Association 75, 602-608.
81. Hosking JRM 1981a Equivalent forms of the multivariate portmanteau statistic. Journal of the Royal Statistical Society B43, 261-262.
82. Hosking JRM 1981b Lagrange-multiplier tests of multivariate time series models. Journal of the Royal Statistical Society B43, 219-230.
83. Hubrich K, Lutkepohl H and Saikkonen P 2001 A review of systems cointegration tests. Econometric Reviews 20, 247-318.
84. Ingram BF and Whiteman CH 1994 Supplanting the 'Minnesota' prior:forecasting macroeconomic time series using real business cycle model priors. Journal of Monetary Economics 34, 497-510.
85. Jarque CM and Bera AK 1987 A test for normality of observations and regression residuals. International Statistical Review 55, 163-172.
86. Johansen S 1988 Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231-254.
87. Johansen S 1995 Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press, Oxford.
88. Johansen S 1997 Likelihood analysis of the I(2) model. Scandinavian Journal of Statistics 24, 433-462.
89. Johansen S 2002 A small sample correction for the test of cointegrating rank in the vector autoregressive model. Econometrica 70, 1929-1961.
90. Johansen S 2006 Statistical analysis of hypotheses on the cointegrating relations in the I (2) model. Journal of Econometrics 132, 81-115.
91. Kabaila P 1993 On bootstrap predictive inference for autoregressive processes. Journal of Time Series Analysis 14, 473-484.
92. Kemp GCR 1999 The behavior of forecast errors from a nearly integrated AR(1) model as both sample size and forecast horizon become large. Econometric Theory 15, 238-256.
93. Kilian L 1998a Confidence intervals for impulse responses under departures from normality. Econometric Reviews 17, 1-29.
94. Kilian L 1998b Small-sample confidence intervals for impulse response functions. Review ofEco-nomics and Statistics 80, 218-230.
95. Kilian L and Chang PL 2000 How accurate are confidence intervals for impulse responses in large VAR models?. Economics Letters 69, 299-307.
96. Kim JH 1999 Asymptotic and bootstrap prediction regions for vector autoregression. International Journal of Forecasting 15, 393-403.
97. King RG, Plosser CI, Stock JH and Watson MW 1991 Stochastic trends and economic fluctuations. American Economic Review 81, 819-840.
98. Kleibergen F and Paap R 2002 Priors, posteriors and Bayes factors for a Bayesian analysis of cointegration. Journal of Econometrics 111, 223-249.
99. Kleibergen F and van Dijk HK 1994 On the shape of the likelihood/posterior in cointegration models. Econometric Theory 10, 514-551.
100. Koop G 1992 Aggregate shocks and macroeconomic fluctuations:a Bayesian approach. Journal of Applied Econometrics 7, 395-411.
101. Koop G, Strachan R, van Dijk H and Villani M 2005 Bayesian approaches to cointegration. In Palgrave Handbook of Econometrics, Vol. 1, Econometric Theory (eds Patterson K and Mills TC). Palgrave Macmillan, Basingstoke.
102. Kratzig M 2004 The software JMulTi. In Applied Time Series Econometrics (eds Lutkepohl H and Kratzig M), pp. 289-299. Cambridge University Press, Cambridge.
103. Lanne M and Lutkepohl H 2008 Identifying monetary policy shocks via changes in volatility. Journal of Money, Credit and Banking 40, 1131-1149.
104. Lanne M and Lutkepohl H 2009 Structural vector autoregressions with nonnormal residuals. Journal of Business and Economic Statistics 27, in press.
105. Lee KC, Pesaran MH and Pierse RG 1992 Persistence of shocks and its sources in a multisectoral model of UK output growth. Economic Journal 102, 342-356.
106. Lewis R and Reinsel GC 1985 Prediction of multivarate time series by autoregressive model fitting. Journal of Multivariate Analysis 16, 393-411.
107. Li H and Maddala GS 1996 Bootstrapping time series models. Econometric Reviews 15, 115-158.
108. Li WK and McLeod AI 1981 Distribution of the residual autocorrelations in multivariate ARMA time series models. Journal of the Royal Statistical Society B43, 231-239.
109. Litterman RB 1986 Forecasting with Bayesian vector autoregressions-five years of experience. Journal of Business and Economic Statistics 4, 25-38.
110. Lomnicki ZA 1961 Tests for departure from normality in the case of linear stochastic processes. Metrika 4, 37-62.
111. Lubik TA and Schorfheide F 2004 Testing for indeterminacy:an application to US monetary policy. American Economic Review 94, 190-217.
112. Lutkepohl H 1985 The joint asymptotic distribution of multistep prediction errors of estimated vector autoregressions. Economics Letters 17, 103-106.
113. Lutkepohl H 1993 Testing for causation between two variables in higher dimensional VAR models. In Studies in Applied Econometrics (eds Schneeweiss H and Zimmermann KF), pp. 75-91. Physica-Verlag, Heidelberg.
114. Lutkepohl H 2004 Vector autoregressive and vector error correction models. In Applied Time Series Econometrics (eds Lutkepohl H and Kratzig M), pp. 86-158. Cambridge University Press, Cambridge.
115. Lutkepohl H 2005 New Introduction to Multiple Time Series Analysis. Springer, Berlin.
116. Lutkepohl H 2006a Forecasting with VARMA models. In Handbook of Economic Forecasting, Vol. 1 (eds Elliott G, Granger CWJ and Timmermann A), pp. 287-325. Elsevier, Amsterdam.
117. Lutkepohl H 2006b Vector autoregressive models. In Palgrave Handbook of Econometrics, Vol. 1, Econometric Theory (eds Mills TC and Patterson K), pp. 477-510. Palgrave Macmillan, Basingstoke.
118. Lutkepohl H and Burda MM 1997 Modified Wald tests under nonregular conditions. Journal of Econometrics 78, 315-332.
119. Lutkepohl H and Claessen H 1997 Analysis of cointegrated VARMA processes. Journal of Econometrics 80, 223-239.
120. Lutkepohl H and Kratzig M 2004 Applied Time Series Econometrics. Cambridge University Press, Cambridge.
121. Lutkepohl H and Poskitt DS 1996a Specification of echelon form VARMA models. Journal of Business and Economic Statistics 14, 69-79.
122. Lutkepohl H and Poskitt DS 1996b Testing for causation using infinite order vector autoregressive processes. Econometric Theory 12, 61-87.
123. Lutkepohl H and Reimers HE 1992 Impulse response analysis of cointegrated systems. Journal of Economic Dynamics and Control 16, 53-78.
124. Lutkepohl H and Saikkonen P 1999 Order selection in testing for the cointegrating rank of a VAR process. In Cointegration, Causality, and Forecasting. A Festschrift in Honour of Clive W.J. Granger (eds Engle RF and White H), pp. 168-199. Oxford University Press, Oxford.
125. Lutkepohl H, Saikkonen P and Trenkler C 2004 Testing for the cointegrating rank of a VAR process with level shift at unknown time. Econometrica 72, 647-662.
126. Masarotto G 1990 Bootstrap prediction intervals for autoregressions. International Journal of Forecasting 6, 229-239.
127. Mosconi R and Giannini C 1992 Non-causality in cointegrated systems:representation, estimation and testing. Oxford Bulletin of Economics and Statistics 54, 399-417.
128. Ng S and Perron P 1995 Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag. Journal of the American Statistical Association 90, 268-281.
129. Pagan A 1995 Three econometric methodologies:an update. In Surveys in Econometrics (eds Oxley L, George DAR, Roberts CJ and Sayer S). Basil Blackwell, Oxford.
130. Park JY and Phillips PCB 1988 Statistical inference in regressions with integrated processes:part 1. Econometric Theory 4, 468-497.
131. Park JY and Phillips PCB 1989 Statistical inference in regressions with integrated processes:part 2. Econometric Theory 5, 95-131.
132. Pascual L, Romo J and Ruiz E 2004 Bootstrap predictive inference for ARIMA processes. Journal of Time Series Analysis 25, 449-465.
133. Paulsen J 1984 Order determination of multivariate autoregressive time series with unit roots. Journal of Time Series Analysis 5, 115-127.
134. Pearl J 2000 Causality:Models, Reasoning, and Inference. Cambridge University Press, Cambridge.
135. Penm JHW, Brailsford TJ and Terrell RD 2000 A robust algorithm in sequentially selecting subset time series systems using neural networks. Journal of Time Series Analysis 21, 389-412.
136. Pesaran MH and Shin Y 1996 Cointegration and speed of convergence to equilibrium. Journal of Econometrics 71, 117-143.
137. Poskitt DS 2003 On the specification of cointegrated autoregressive moving-average forecasting systems. International Journal of Forecasting 19, 503-519.
138. Primiceri GE 2005 Time varying structural vector autoregressions and monetary policy. Review of Economic Studies 72, 821-852.
139. Quenouille MH 1957 The Analysis of Multiple Time-Series. Griffin, London.
140. Quinn BG 1980 Order determination for a multivariate autoregression. Journal of the Royal Statistical Society B42, 182-185.
141. Reinsel GC 1993 Elements of Multivariate Time Series Analysis. Springer, New York.
142. Reinsel GC and Ahn SK 1992 Vector autoregressive models with unit roots and reduced rank structure:estimation, likelihood ratio test, and forecasting. Journal of Time Series Analysis 13, 353-375.
143. Reinsel GC and Lewis AL 1987 Prediction mean square error for non-stationary multivariate time series using estimated parameters. Economics Letters 24, 57-61.
144. Rissanen J 1978 Modeling by shortest data description. Automatica 14, 465-471.
145. Saikkonen P 1992 Estimation and testing of cointegrated systems by an autoregressive approximation. Econometric Theory 8, 1-27.
146. Saikkonen P 2005 Stability results for nonlinear error correction models. Journal of Econometrics 127, 69-81.
147. Saikkonen P and Lutkepohl H 1996 Infinite order cointegrated vector autoregressive processes:estimation and inference. Econometric Theory 12, 814-844.
148. Saikkonen P and Lutkepohl H 2000a Testing for the cointegrating rank of a VAR process with structural shifts. Journal of Business and Economic Statistics 18, 451-464.
149. Saikkonen P and Lutkepohl H 2000b Trend adjustment prior to testing for the cointegrating rank of a vector autoregressive process. Journal of Time Series Analysis 21, 435-456.
150. Saikkonen P, Lutkepohl H and Trenkler C 2006 Break date estimation for VAR processes with level shift with an application to cointegration testing. Econometric Theory 22, 15-68.
151. Sampson M 1991 The effect of parameter uncertainty on forecast variances and confidence intervals for unit root and trend stationary time-series models. Journal of Applied Econometrics 6, 67-76.
152. Schwarz G 1978 Estimating the dimension of a model. Annals of Statistics 6, 461-464.
153. Sims CA 1980 Macroeconomics and reality. Econometrica 48, 1-48.
154. Sims CA 1986 Are forecasting models usable for policy analysis? Quarterly Review, Federal Reserve Bank of Minneapolis 10, 2-16.
155. Sims CA and Zha T 1999 Error bands for impulse responses. Econometrica 67, 1113-1155.
156. Sims CA and Zha T 2006 Were there regime switches in US monetary policy? American Economic Review 96, 54-81.
157. Sims CA, Stock JH and Watson MW 1990 Inference in linear time series models with some unit roots. Econometrica 58, 113-144.
158. Stock JH 1996 VAR, error correction and pretest forecasts at long horizons. Oxford Bulletin of Economics and Statistics 58, 685-701.
159. Strachan RW and Inder B 2004 Bayesian analysis of the error correction model. Journal of Econometrics 123, 307-325.
160. Tay AS and Wallis KF 2002 Density forecasting:a survey. In Companion to Economic Forecasting (eds Clements MP and Hendry DF), pp. 45-68. Blackwell, Oxford.
161. Toda HY and Phillips PCB 1993 Vector autoregressions and causality. Econometrica 61, 1367-1393.
162. Toda HY and Yamamoto T 1995 Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics 66, 225-250.
163. Uhlig H 2005 What are the effects of monetary policy on output? Results from an agnostic identification procedure. Journal of Monetary Economics 52, 381-419.
164. Yamamoto T 1980 On the treatment of autocorrelated errors in the multiperiod prediction of dynamic simultaneous equation models. International Economic Review 21, 735-748.
165. Zellner A 1962 An efficient method of estimating seemingly unrelated regressions and tests of aggregation bias. Journal of the American Statistical Association 57, 348-368.