The Performance of Artificial Neural Networks and Tier-Structured Information Transmission in Identifying Aggregate Consumption Patterns in New Zealand

Abstract

This study explores the value of information transmission in training heterogeneous Artificial Neural Network (ANN) models to identify patterns in the growth rate of aggregate per-capita consumption spending in New Zealand. A tier structure is used to model how information passes from one ANN to another. A group of ‘tier 1’ ANNs are first trained to identify consumption patterns using economic data. ANNs in subsequent tiers are also trained to identify consumption patterns, but they use the patterns constructed by ANNs trained in the preceding tier (secondary information) as inputs. The model's results suggest that it is possible for ANNs downstream to outperform ANNs trained using empirical data directly on average. This result, however, varies from time period to time period. Increasing access to secondary information is shown to increase the similarity of heterogeneous predictions by ANNs in lower tiers, but not substantially affect average accuracy.

Notes

1 See Zhang, Patuwo & Hu (1998), Vellido, Lisboa & Vaughan (1999), and Kourentzes & Crone (2010) for examples and descriptions of the main advantages and disadvantages of using ANNs.

1 Farhat (2014) explicitly mentions applications to agent-based models. Agent-based models (ABMs) are computational simulation models where populations of heterogeneous agents, each with their own characteristics and information, interact with each other in a virtual space. Their interactions and decisions are determined by a prescribed set of rules chosen by the researcher. As they relate to each other at the local level (micro-interaction), aggregate (macroscopic) phenomena emerge. For examples of this work, see Tesfatsion (2002, 2005), Tesfatsion & Judd (2006), Gatti, Di Guilmi, Gaffeo, Giulioni, Gallegati & Palestrini (2005), Mirowski (2007), Gaffeo, Gatti, Desiderio & Gallegati (2008) and Raberto, Teglio & Cincotti (2008).

3 A ‘bias term’ is akin to the ‘constant term’ in regression analyses.

4 Hornik, Stinchcombe & White (1989) and Hornik (1991) show that ANNs can approximate any functional relationship between inputs and outputs with arbitrary precision provided that there are a sufficient number of hidden layers (hence, they are known as ‘universal approximators’). Cybenko (1989), Hornik, Stinchcombe & White (1990), and Barron (1993) note that ANNs with a single layer (like Figure 1) may also be universal approximators provided that the activation functions used in the model satisfy certain properties (namely, smoothness) and the number of activation functions (H) is large enough.

5 A₁ makes no transformation to the input data and γ₁ is fixed to 1. The ANN is, in effect, a linear econometric model of the form augmented by a non-linear function,

6 In this study, when an ANN is trained multiple times, the training set and validation set always differ across simulation due to the random allocation of the data. The forecast set, however, will be the same across trained ANNs to make them comparable.

7 See Beltratti et al. (1996) or Warner & Misra (1996) for a more detailed description of the weight updating process for the basic BP algorithm.

8 Data for 1992Q1 is used for the first value of c_t-1. The standard score (or z-value) for each data point is used in place of the actual data. As a result, each re-scaled data point is measured as the number of standard deviations the raw data is above its series mean. Using data re-scaled in this way improves the efficiency of the ANN training process.