IFNN Manual: Integrated Framework for Neural Network and Conventional Modelling

Series: Research Reports of the Institute for Economic Geography and GIScienc

SIM User's Manual. A Flexible Toolbox for Spatial lnteraction Modelling.

Series: Research Reports of the Institute for Economic Geography and GIScienc

Stationary and integrated autoregressive neural network processes

We consider autoregressive neural network (ARNN) processes driven by additive noise. Sufficient conditions on the network weights (parameters) are derived for the ergodicity and stationarity of the process. It is shown that essentially the linear part of the ARNN process determines whether the overall process is stationary. A generalization to the case of integrated ARNN processes is given. Least squares training (estimation) of the stationary models and testing for non-stationarity are discussed. The estimators are shown to be consistent and expressions on the limiting distributions are given.Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science

On the ergodicity and stationarity of the ARMA (1,1) recurrent neural network process

In this note we consider the autoregressive moving average recurrent neural network ARMA-NN(1, 1) process. We show that in contrast to the pure autoregressive process simple ARMA-NN processes exist which are not irreducible. We prove that the controllability of the linear part of the process is sufficient for irreducibility. For the irreducible process essentially the shortcut weight corresponding to the autoregressive part determines whether the overall process is ergodic and stationary.Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science

On the stationarity of autoregressive neural network models

We analyze the asymptotic behavior of autoregressive neural network (AR-NN) processes using techniques from Markov chains and non-linear time series analysis. It is shown that standard AR-NNs without shortcut connections are asymptotically stationary. If linear shortcut connections are allowed, only the shortcut weights determine whether the overall system is stationary, hence standard conditions for linear AR processes can be used.Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science

Cointegration and exchange market efficiency. An analysis of high frequency data.

A cointegration analysis on a triangle of high frequency exchange rates is presented. Market efficiency requires the triangle to be cointegrated and the cointegration term to be a martingale difference sequence. We find empirical evidence against market efficiency for very short time horizons: The cointegration term does not behave like a martingale difference sequence. In an out-of-sample forecasting study the cointegrated vector autoregressive (VAR) model is found to be superior to the naive martingale. Finally, a simple trading strategy shows that the VAR also has a significant forecast value in economic terms even after accounting for transaction costs. (author's abstract)Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science