Abstract: Non-negativity constraints on the parameters of the GARCH(p, q) process may be relaxed without giving up the requirement that the conditional variance remains non-negative with probability 1. In this paper we look into the consequences of adopting these less severe constraints in the GARCH(2, 2) case and its two second-order special cases, GARCH(2, 1) and GARCH(1, 2). This is done by comparing the autocorrelation function of squared observations under these two sets of constraints. The less severe constraints allow more flexibility in the shape of the autocorrelation function than the constraints restricting the parameters to be non-negative.

Abstract: The sections in this article are 1 Stlf Methods 2 Hybrid Statistical Methods for STLF: an Example 3 Prospective of the Development of the Stlf Methods Keywords: load forecasting; general exponential smoothing; power spectrum analysis; nonlinear temperature sensitive load model; auto-regressive model; partial autocorrelation analysis; artificial neural networks

Abstract: A statistical procedure for detection of periodic autocorrelation in time series data is presented. Intuitively, the probability of a zero-crossing at time t should be inversely related to the correlation between observations at times t and t− 1. Explicit formulas displaying this inverse relationship are given for mean-zero periodically correlated time series with certain distributional structures. A test statistic based on this relationship is developed. This testing method provides a robust approach to detection of periodic autocorrelation. Analysis of simulated and actual data sets illustrates the usefulness of the proposed method.

Abstract: T. M. L. Wigley et al . ([1][1]) compare the autocorrelation function of the observed hemispheric temperature records to the autocorrelation function of similar records of control climate model simulations. When the models are unforced, the differences between the autocorrelation functions are

Abstract: A method to estimate a nonstationary power spectrum with adaptive selection of autoregressive order is proposed. Time-varying PARCOR (partial autocorrelation coefficient) and AR (autoregressive) order are estimated from time series data. The data are assumed to be observations of vibration that contain abrupt change of spectrum due to arrivals of different signal, structural changes of vibrating object, etc. The model that consists of an autoregressive model with time-varying PARCORs and time-varying order is used. The time-varying PARCORs are estimated by a Monte Carlo filter, and the time-varying order is estimated by genetic algorithm. An application to analysis of seismic wave data is reported.

Abstract: This article describes a new method for designing control sensors and performing distance measurement in Intelligent Transportation Systems (ITS). Using a technique which involves correlation methods, distance estimation is achievable from a single image.

Abstract: Long term dependence in time series can be modelled by fractionally integrated ARMA (ARFIMA) models. For an ARFIMA process it is however impossible to identify the order of the short memory polynomials by inspection of the autocorrelation and partial autocorrelation functions. Instead information criteria such as AIC, BIC and HQIC are used to identify the order. This paper investigates the performance of the three information criteria when identifying the order in an ARFIMA model. The impression is that BIC outperforms AIC and HQIC, at least for the ARFIMA models used in this simulation. The overall performance of the information criteria, however, is poor for mixtures of AR and MA processes. Introducing long memory increases the likelihood of identifying the correct orders.

Abstract: Time series analysis of population abundance is not based on assumptions about the dynamics of populations, but sometimes the results can be interpreted biologically. At other times the results are difficult to interpret. To better understand the results of a time series analysis of a walleye fish population, as it related to the walleye's life history, I compared a time series analysis of walleye field data with a time series analysis of simulated data from a population dynamics model. In the simulations, the nature of the time lags could be identified by changing model parameters. The simulations indicated that a partial autocorrelation coefficient (PAC) at lag 1 would result from density dependence, that a PAC at lag 5 would result from the time required for maturation, and that a negative sign at lag 5 would result from high larval survival. The simulation results help in the interpretation of the PACs obtained in the time series analysis of field data.

Abstract: This paper introduces an approach to the estimation of missing initial autocorrelation coefficients. The method is based on employing the autocorrelation function extrapolation idea, using the thoeretical properties of the autocorrelation matrices. Some theoretical autocorrelation functions are considered for the application of the method and, hence, the interpolation of missing coefficients is investigated empirically. Finally, selection of an estimate from the allowable range (satisfying the theoretical requirements) is also studied.