Echo State Network Forecast Model For Preliminary Estimation of The Chained CPI-U

Calculation of the Chained CPI-U requires monthly item-area expenditure shares from the same time-period as item-area price index relatives. Yet, cell-level expenditure data only become available four quarters after the price data. In the interim, the BLS issues a preliminary estimate of the index using a Constant Elasticity of Substitution model. We propose an alternative method for preliminary estimation that instead retains the Tornqvist formula for aggregation and forecasts the missing item-area expenditure data using a set of hierarchical Echo State Networks (ESNs), a class of Recurrent Neural Networks in which reservoir and input couplings are randomized.

ESNs are flexible, nonlinear, hidden variable models that can predict series with complex temporal dynamics after a relatively simple training process. We develop an iterative procedure to forecast a vector of item expenditures for a given area based on its past expenditure data as well as past and concurrent price data. Additionally, we include the option to supplement the ESN neuron states with discrete Fourier modes at the seasonal frequencies to improve prediction among items with strong seasonal components.

Time series

Price indices

Echo State Networks

Neural Networks 

Section on Statistical Learning and Data Science