Asymptotic Properties of Neural Network Sieve Estimators

Neural networks have become one of the most popularly used methods in machine learning and artificial intelligence. Due to the universal approximation theorem (Hornik et al., 1989), a neural network with one hidden layer can approximate any continuous function on compact support as long as the number of hidden units is sufficiently large. Statistically, a neural network can be classified into a nonlinear regression framework. However, if we consider it parametrically, due to the unidentifiability of the parameters, it is difficult to derive its asymptotic properties. Instead, we consider the estimation problem in a nonparametric regression framework and use the results from sieve estimation to establish the consistency, the rates of convergence and the asymptotic normality of the neural network estimators. We also illustrate the validity of the theories via simulations.

Basis Function Matrix-Based Flexible Coefficient Autoregressive Models: A Framework for Time Series and Nonlinear System Modeling

We propose, in this paper, a framework for time series and nonlinear system modeling, called the basis function matrix-based flexible coefficient autoregressive (BFM-FCAR) model. It has very flexible nonlinear structure. We show that many famous nonlinear time series models can be derived under this framework by choosing the proper basis function matrices. Some probabilistic properties (the conditions of geometrical ergodicity) of the BFM-FCAR model are investigated. Taking advantage of the model structure, we present an efficient parameter estimation algorithm for the proposed framework by using the variable projection method. Finally, we show how new models are generated from the proposed framework.

The Phillips curve in Iran: econometric versus artificial neural networks

In this paper, we develop a function of inflation, unemployment, liquidity and real effective exchange rate by applying Autoregressive Distributed Lag (ARDL) and Artificial Neural Networks (ANN). We employ the aforementioned methods to derive the so-called Phillips curve. For the empirical objective, our primary purpose is explicitly to compare two types of the Phillips curve models obtained by ANN and the econometric methods, ARDL. Then we can check the behavior of the Phillips curve in Iran. We demonstrate that the Phillips curve for the empirical data in Iran differs slightly across ANN than econometric methods. In other words, according to the structure of Iran's economy, the ANN technique outshines the other one in terms of goodness of fit and prognosis capability. Finally, under two scenarios inflation would be forecasted in Iran up to 2025. Our findings point out that the trend of price changes in Iran would have an increasing trend in the considered period.

Prediction of transcriptional profiles of Synechocystis PCC6803 by dynamic autoregressive modeling of DNA microarray data

Time-series profiles of gene expression generated by DNA microarrays possess sufficient information for building dynamic models of transcriptional behavior. This, however, requires properly designed experiments and sufficient independent data to validate such models. Here we report the use of AutoRegressive with eXogenous input (ARX) models to fit dynamic gene expression data obtained by subjecting cultures of the photosynthetic bacterium Synechocystis PCC6803 to consecutive light-to-dark transitions. Autoregressive with exogenous input models of appropriate complexity were selected by applying Akaike's information criterion (AIC) such as to maximize agreement between model predictions with experimental data without overfitting. These models were subsequently used to design the experimental profile of an optimal validating data set. Predictions from these models were tested in a second experiment and were found to match well with the validation data. Additionally, the models with the least error in predicting the expression profiles of the validation data set exactly match the model complexity predicted by AIC. Such models offer insights into cellular responses to environmental conditions and form the basis for hypothesizing and quantifying relationships that are presently poorly understood at the level of fundamental mechanisms.