A two-phased method for prediction in spatialtemporal domains is proposed. After an ordinary regression model is trained on spatial data, a prediction is adjusted by incorporating autoregressive modeling of residuals in time. The prediction accuracy of the proposed method is evaluated on simulated agricultural data with a significant improvement of accuracy for both linear and non-linear regres...

We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & Poor’s 500 (S&P 500) and several other indices, we obtained good performance using these models in an out-of-sam...

Nonlinear autoregressive moving average with exogenous inputs (NARMAX) models have been successfully demonstrated for modeling the input-output behavior of many complex systems. This paper deals with the proposition of a scheme to provide time series prediction. The approach is based on a recurrent NARX model obtained by linear combination of a recurrent neural network (RNN) output and the real...

We consider kernel quantile estimates for drift and scale functions in nonlinear stochastic regression models. Under a general dependence setting, we establish asymptotic point-wise and uniform Bahadur representations for the kernel quantile estimates. Based on those asymptotic representations, central limit theorems are obtained. Applications to nonlinear autoregressive models and linear proce...

In this paper, the geometric ergodicity of a non-linear AR model with an ARCH term is discussed. Two non-vacuous and mild sufficient conditions are given. The results obtained modify the vacuous part and reduce the restriction of Masry and Tjφstheim (1995)’s conditions, and lay a foundation for statistical inference of the model (e.g. Mckeague and Zhang (1994) and Masry and Tjφstheim (1995)). I...

It generally is difficult, if not impossible, to fully understand and interpret nonlinear time series models by considering the estimated values of the model parameters only. To shed light on the characteristics and implications of a nonlinear model it can then be useful to consider the effects of shocks on the future patterns of the time series variable. Most interest in such impulse response ...

The authors give easy-to-check sufficient conditions for the geometric ergodicity and the finiteness of the moments of a random process xt = φ(xt−1, . . . , xt−p)+ tσ(xt−1, . . . , xt−q) in which φ : IR → IR, σ : IR → IR and ( t) is a sequence of independent and identically distributed random variables. They deduce strong mixing properties for this class of nonlinear autoregressive models with ...

Identification of non-linear finite impulse response (N-FIR) models is studied. In particular the selection of model structure, i.e., to find the best regressors, is examined. In this paper it is shown that a statistical method, the analysis of variance, is a better alternative than exhaustive search among all possible regressors, in the identification of the structure of non-linear FIR-models....

We would like to start by congratulating the authors for having written this important paper. Prediction intervals are popular in economics and finance (e.g. they are often used by Central Banks to measure point forecasts uncertainty). The paper provides a unifying treatment of bootstrap prediction intervals for autoregression models, which are one of the workhorse models for economic forecasti...