this paper: ftp://ftp.cs.colorado.edu/pub/Time-Series/MyPapers/experts.ps.Z,

this article we review some of these developments. For a given time series X 1 ; . . . ; X n , nonparametric techniques are used to analyze various features of interest. Generally, the idea underlying many of these techniques is that the characteristic of interest is allowed to have a general form which is approximated increasingly precisely with growing sample size. For example, if a process is assumed to be composed of periodic components, a general form of spectral density may be assumed which can be approximated with increasing precision when the sample size gets larger. Similarly, if the autocorrelation structure of a stationary process is of interest the spectral density may be estimated as a summary of the second moment properties. A brief review of this classical method of nonparametric time series analysis is given in Section 2. Because the final objective of many time series analyses is prediction, it is often of interest to study the conditional means, conditional variances or complete conditional densities in some period, given the past of the process. When a point prediction is the final objective, an estimate of some conditional mean may be desired, while the conditional variances are needed if interval forecasts or assessments of future volatility are desired. Moreover, if higher order moments of a series are potentially important, the focus may be on estimating the complete conditional density. In order to analyze the conditional mean nonparametrically one may, for instance, start from a model of the form

The rapid time variation of mobile radio channels is often modeled as a random process with second order moments reflecting vehicle speed, bandwidth and the scattering environment. These statistics typically show that there is little room for prediction of channel properties such as received power or complex taps of the impulse response coefficients, at least when linear predictor structures are considered. We use mutual information estimation to measure statistical dependencies in sequences of wideband mobile radio channel data and find significant nonlinear dependencies, far exceeding the linear component. Based on these upper limits for the predictability of channel evolution over time intervals up to 30 ms ahead, we develop practical nonlinear predictor systems using Multivariate Adaptive Regression Splines (MARS). We demonstrate computationally efficient schemes that increase the prediction horizon beyond 10 ms, compared to less than 4 ms with linear predictors at comparable predi...

Summary. We propose a lag selection method for non-linear additive autoregressive models that is based on spline estimation and the Bayes information criterion. The additive structure of the autoregression function is used to overcome the ‘curse of dimensionality’, whereas the spline estimators effectively take into account such a structure in estimation. A stepwise procedure is suggested to implement the method proposed. A comprehensive Monte Carlo study demonstrates good performance of the method proposed and a substantial computational advantage over existing local-polynomial-based methods. Consistency of the lag selection method based on the Bayes information criterion is established under the assumption that the observations are from a stochastic process that is strictly stationary and strongly mixing, which provides the first theoretical result of this kind for spline smoothing of weakly dependent data.

Neural networks have a burgeoning literature in nonlinear time series. We consider here a variant of the conventional neural network model, called the stochastic neural network, that can be used to approximate complex nonlinear stochastic systems. We show how the EM algorithm can be used to develop efficient estimation schemes that have much lower computational complexity than those for conventional neural networks. This enables us to carry out model selection procedures such as the BIC to choose the number of hidden units and the input variables for each hidden unit. On the other hand, stochastic neural networks are shown to have the universal approximation property of neural networks. Other important properties of the proposed model are also given, and model-based multi-step ahead forecasts are provided. For illustration, we fit stochastic neural network models to several real and simulated time series. Our results show that the fitted models improve postsample forecasts over conventional neural networks and other nonlinear/nonparametric models.

c ○ Hamidreza Zareipour 2006I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. This thesis addresses two main issues: first, forecasting short-term electricity market prices; and second, the application of short-term electricity market price forecasts to operation planning of demand-side Bulk Electricity Market Customers (BEMCs). The Ontario electricity market is selected as the primary case market and its structure is studied in detail. A set of explanatory variable candidates is then selected accordingly, which may explain price behavior in this market. In the process of selecting the explanatory variable candidates, some important issues, such as direct or indirect effects of the variables on price behavior, availability of the variables before real-time, choice of appropriate forecasting horizon and market time-line, are taken into account. Price and demand in three neighboring electricity markets, namely, the New York, New England, and PJM electricity markets, are also considered among the explanatory variable candidates.

We consider the estimation and identification of the components (endogenous and exogenous) of additive nonlinear ARX time series models. We employ local polynomial fitting scheme coupled with projections. We establish the weak consistency (with rates) and the asymptotic normality of the projection estimates of the additive components. Expressions for the asymptotic bias and variance are given. Keywords: Additive nonlinear regression model; ARX time series; central limit theorem; local polynomial fitting; projection method. AMS (1991) Subject Classification: 62G07, 62H10, 60F05. 3 1 Introduction Let fX l ; Y l g 1 l=\Gamma1 be jointly stationary discrete-time processes. Among the nonlinear time series models popular in the econometrics literature is the bivariate ARX model: Y l = e g 1 (Y l\Gammaq ; : : : ; Y l\Gamma1 ) + e g 2 (X l\Gammap ; : : : ; X l ) + e l ; (1.1) X l = e g 3 (X l\Gammap ; : : : ; X l\Gamma1 ) + " l ; (1.2) where fe l g and f" l g are independent series each...

this paper is to propose a flexible, data-adaptive, univariate time series modelling approach which has more predictive power than the inherently restrictive parametric models. First of all, we describe the problem of interest. If y represents a single response variable that depends on a vector of

We present a novel method for analysing space-time data when response data is given at a finite number of locations and the aim is to predict the response at a new location, where only a short run of data is available. This is the type of dataset that is typically available when attempting to analyse wind velocity data and we demonstrate our method, and compare it to that introduced by Haslett and Raftery (1989), on a set of data collected from the island of Crete in Greece. Typically the distance between locations is used to define the correlation matrix between responses at distinct locations even though this cannot always be justified. The peculiarity presented in our data is that the sites are in a complex topography so differences in the local characteristics of the wind stations, the direction of the prevailing winds, and other unobserved covariates can all lead to unsuitable model fitting. We use a nonparametric model to avoid these problems and demonstrate its predictive power ...

this paper is to revisit the information contained in financial variables using nonlinear, nonparametric methods, in particular, multivariate adaptive regression splines (MARS)