Narrow Results

Food price forecasts in the agricultural sector have always been a vital matter to a wide variety of market participants. In this work, we approach this forecast problem for the weekly wholesale food price index in the Chinese market during a 10-year period of January 1, 2010–January 3, 2020. To facilitate the analysis, we propose the use of the nonlinear auto-regressive neural network. Technically, we investigate forecast performance, based upon the relative root mean square error (RRMSE) as the evaluation metrics, corresponding to one hundred and twenty settings that cover different algorithms for model estimations, numbers of hidden neurons and delays, and ratios for splitting the data. Our experimental result suggests the construction of the neural network with three delays and 10 hidden neurons, which is trained through the Levenberg–Marquardt algorithm, as the forecast model. It leads to high accuracy and stabilities with the RRMSEs of 1.93% for the training phase, 2.16% for the validation phase, and 1.95% for the testing phase. Comparisons of forecast accuracy between the proposed model and some other machine learning models, as well as traditional time-series econometric models, suggest that our proposed model leads to statistically significant better performance. Our results could benefit different forecast users, such as policymakers and various market participants, in policy analysis and market assessments.

We give a brief introduction to deterministic chaos and a link between chaotic deterministic models and stochastic time series models. We argue that it is often natural to determine the embedding dimension in a noisy environment first in any systematic study of chaos. Setting the stochastic models within the framework of non-linear autoregression, we introduce the notion of a generalized partial autocorrelation and an order. We approach the estimation of the embedding dimension via order determination of an unknown non-linear autoregression by cross-validation, and give justification by proving its consistency under global boundedness. As a by-product, we provide a theoretical justification of the final prediction error approach of Auestad and Tjøstheim. Some illustrations based on the Hénon map and several real data sets are given. The bias of the residual sum of squares as essentially a noise variance estimator is quantified.