Forecasting Aggregated Vector ARMA Processes

1. Prologue.- 1.1 Objective of the Study.- 1.2 Survey of the Study.- 2. Vector Stochastic Processes.- 2.1 Discrete-Time, Stationary Vector Stochastic Processes.- 2.2 Nonstationary Processes.- 2.3 Vector Autoregressive Moving Average Processes.- 2.4 Estimation.- 2.5 Model Specification.- 2.6 Summary.- 3. Forecasting Vector Stochastic Processes.- 3.1 Forecasting Known Processes.- 3.2 Forecasting Vector ARMA Processes with Estimated Coefficients.- 3.3 Forecasting Autoregressive Processes of Unknown Order.- 3.4 Forecasting Nonstationary Processes.- 3.5 Comparing Forecasts.- 3.6 Summary.- 4. Forecasting Contemporaneously Aggregated Known Processes.- 4.1 Linear Transformations of Vector Stochastic Processes.- 4.2 Forecasting Linearly Transformed Stationary Vector Stochastic Processes.- 4.3 Forecasting Linearly Transformed Nonstationary Processes.- 4.4 Linearly Transformed Vector ARMA Processes.- 4.5 Summary and Comments.- 5. Forecasting Contemporaneously Aggregated Estimated Processes.- 5.1 Summary of Assumptions and Predictors.- 5.2 Estimated Coefficients.- 5.3 Unknown Orders and Estimated Coefficients.- 5.4 Nonstationary Processes.- 5.5 Small Sample Results.- 5.6 An Empirical Example.- 5.7 Conclusions.- 6. Forecasting Temporally and Contemporaneously Aggregated Known Processes.- 6.1 Macro Processes.- 6.2 Six Predictors.- 6.3 Comparison of Predictors.- 6.4 Nonstationary Processes.- 6.5 Temporally and Contemporaneously Aggregated Vector ARMA Processes.- 6.6 Conclusions and Comments.- 7. Temporal Aggregation of Stock Variables - Systematically Missing Observations.- 7.1 Forecasting Known Processes with Systematically Missing Observations.- 7.2 Processes With Estimated Coefficients.- 7.3 Processes With Unknown Orders and Estimated Coefficients.- 7.4 Nonstationary Time Series with Systematically Missing Observations.- 7.5 Monte Carlo Results.- 7.6 Empirical Examples.- 7.7 Concluding Remarks.- 7.A Appendix: Proof of Relation (7.2.18).- 8. Temporal Aggregation of Flow Variables.- 8.1 Forecasting with Known Processes.- 8.2 Forecasts Based on Processes with Estimated Coefficients.- 8.3 Forecasting with Autoregressive Processes of Unknown Order.- 8.4 Temporally Aggregated Nonstationary Processes.- 8.5 Small Sample Comparison.- 8.6 Examples.- 8.7 Summary and Conclusions.- 8.A Appendix: Proof of Relation (8.2.23).- 9. Joint tTemporal and Contemporaneous Aggregation.- 9.1 Summary of Processes and Predictors.- 9.2 Prediction Based on Processes with Estimated Coefficients.- 9.3 Prediction Based on Estimated Processes with Unknown Orders.- 9.4 Monte Carlo Comparison of Predictors.- 9.5 Forecasts of U.S. Gross Private Domestic Investment.- 9.6 Summary and Conclusions.- 10. Epilogue.- 10.1 Summary and Conclusions.- 10.2 Some Remaining Problems.- Appendix. Data Used for Examples.