Hierarchical Forecasting

Accurate forecasts of macroeconomic variables are crucial inputs into the decisions of economic agents and policy makers. Exploiting inherent aggregation structures of such variables, we apply forecast reconciliation methods to generate forecasts that are coherent with the aggregation constraints. We generate both point and probabilistic forecasts for the first time in the macroeconomic setting. Using Australian GDP we show that forecast reconciliation not only returns coherent forecasts but also improves the overall forecast accuracy in both point and probabilistic frameworks.

[1]  F. Petropoulos,et al.  Improving forecasting by estimating time series structural components across multiple frequencies , 2014 .

[2]  Dazhi Yang,et al.  Reconciling solar forecasts: Geographical hierarchy , 2017 .

[3]  Arnold Zellner,et al.  A Study of Some Aspects of Temporal Aggregation Problems in Econometric Analyses , 1971 .

[4]  Ted Kramer,et al.  Australian national accounts: National income, expenditure and product , 2015 .

[5]  J. A. Vilar,et al.  Time series clustering based on nonparametric multidimensional forecast densities , 2013 .

[6]  Fotios Petropoulos,et al.  forecast: Forecasting functions for time series and linear models , 2018 .

[7]  Carlos Capistrán,et al.  Multi-horizon inflation forecasts using disaggregated data , 2010 .

[8]  Luiz Koodi Hotta,et al.  The effect of additive outliers on the estimates from aggregated and disaggregated ARIMA models , 1993 .

[9]  Rob J. Hyndman,et al.  Hierarchical Probabilistic Forecasting of Electricity Demand With Smart Meter Data , 2020 .

[10]  George Athanasopoulos,et al.  Hierarchical forecasts for Australian domestic tourism , 2009 .

[11]  Massimiliano Marcellino,et al.  Realtime nowcasting with a Bayesian mixed frequency model with stochastic volatility , 2012, Journal of the Royal Statistical Society. Series A,.

[12]  Takeshi Amemiya,et al.  The Effect of Aggregation on Prediction in the Autoregressive Model , 1972 .

[13]  K. Strimmer,et al.  Statistical Applications in Genetics and Molecular Biology A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics , 2011 .

[14]  Rob J Hyndman,et al.  Grouped Functional Time Series Forecasting: An Application to Age-Specific Mortality Rates , 2016, 1609.04222.

[15]  David Veredas,et al.  Monitoring and forecasting annual public deficit every month: the case of France , 2008 .

[16]  W. H. Williams,et al.  Aggregate Versus Subaggregate Models in Local Area Forecasting , 1976 .

[17]  Rob J. Hyndman,et al.  Forecasting hierarchical and grouped time series through trace minimization , 2015 .

[18]  Amir F. Atiya,et al.  Combination of long term and short term forecasts, with application to tourism demand forecasting , 2011 .

[19]  G. C. Tiao,et al.  Asymptotic behaviour of temporal aggregates of time series , 1972 .

[20]  Rob J. Hyndman,et al.  Optimal combination forecasts for hierarchical time series , 2011, Comput. Stat. Data Anal..

[21]  John J. Seater,et al.  Temporal Aggregation and Economic Time Series , 1995 .

[22]  Rob J. Hyndman,et al.  Fast computation of reconciled forecasts for hierarchical and grouped time series , 2016, Comput. Stat. Data Anal..

[23]  Rob J Hyndman,et al.  Forecasting with Exponential Smoothing: The State Space Approach , 2008 .

[24]  Christoph Weiss,et al.  Essays in hierarchical time series forecasting and forecast combination , 2018 .

[25]  Jiaojiao Dong,et al.  Least Squares-based Optimal Reconciliation Method for Hierarchical Forecasts of Wind Power Generation , 2018 .

[26]  Dipti Srinivasan,et al.  Reconciling solar forecasts: Sequential reconciliation , 2019, Solar Energy.

[27]  Shaun P. Vahey,et al.  Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence , 2015 .

[28]  Rob J. Hyndman,et al.  Probabilisitic forecasts in hierarchical time series , 2018 .

[29]  Fotios Petropoulos,et al.  Forecasting with temporal hierarchies , 2017, Eur. J. Oper. Res..

[30]  Vu,et al.  Time-Varying Combinations of Predictive Densities Using Nonlinear Filtering , 2012 .

[31]  Jeffrey Sohl,et al.  Disaggregation methods to expedite product line forecasting , 1990 .

[32]  Dawit Zerom,et al.  A bootstrap-based non-parametric forecast density , 2008 .

[33]  Luiz Koodi Hotta,et al.  THE EFFECT OF AGGREGATION ON PREDICTION IN AUTOREGRESSIVE INTEGRATED MOVING‐AVERAGE MODELS , 1993 .

[34]  Shaun P. Vahey,et al.  Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence , 2015 .

[35]  Adrian E. Raftery,et al.  Weather Forecasting with Ensemble Methods , 2005, Science.

[36]  J. Geweke,et al.  Comparing and Evaluating Bayesian Predictive Distributions of Asset Returns , 2008 .

[37]  T. Sargent,et al.  Bayesian Fan Charts for U.K. Inflation: Forecasting and Sources of Uncertainty in an Evolving Monetary System , 2005 .

[38]  Farshid Vahid,et al.  Macroeconomic forecasting for Australia using a large number of predictors , 2019, International Journal of Forecasting.

[39]  Rob J. Hyndman,et al.  Forecasting with Exponential Smoothing , 2008 .

[40]  K. Brewer Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models , 1973 .

[41]  Todd E. Clark,et al.  Macroeconomic Forecasting Performance under Alternative Specifications of Time-Varying Volatility , 2015 .

[42]  L. Held,et al.  Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds , 2008 .

[43]  Rob J Hyndman,et al.  Automatic Time Series Forecasting: The forecast Package for R , 2008 .

[44]  Massimiliano Marcellino,et al.  Some Consequences of Temporal Aggregation in Empirical Analysis , 1999 .

[45]  Rob J. Hyndman,et al.  Optimal Forecast Reconciliation for Hierarchical and Grouped Time Series Through Trace Minimization , 2018, Journal of the American Statistical Association.

[46]  Marco A. Villegas,et al.  Supply chain decision support systems based on a novel hierarchical forecasting approach , 2018, Decis. Support Syst..

[47]  George Athanasopoulos,et al.  Forecasting: principles and practice , 2013 .