We study the construction of regression designs, when the random errors are autocorrelated. Our model of dependence assumes that the spectral density g(~o) of the error process is of the form g ( o ) = (1 -a)go(~O ) + ~gl(o), where go(CO) is uniform (corresponding to uncorrelated errors), ct ~ [0, 1) is fixed, and gx(to) is arbitrary. We consider regression responses which are exactly, or only ...

This paper considers forecasting the conditional mean and variance from a single-equation dynamic model with autocorrelated disturbances following an ARMA process, and innovations with time-dependent conditional heteroskedasticity as represented by a linear GARCH process. Expressions for the minimum MSE predictor and the conditional MSE are presented. We also derive the formula for all the theo...

tion Classifica ject Sub s Mathematic 2000 62M10, 62G05. Abstract This paper presents an alternative approach to wavelet smoothing procedure for a time series model of signal added to autocorrelated stationary errors. The aim is to estimate the signal globally with near minimum risk. The usual approach to this problem is to threshold the wavelet coefficients with different thresholds in each le...

The combination of uncertain demand and lead times for installing capacity creates the risk of shortage during the lead time, which may have serious consequences for a service provider with dependent customers. This paper analyzes a model of capacity expansion with autocorrelated random demand and a fixed lead time for adding capacity. To provide a specified level of service, a discrete time ex...

The accurate estimation of covariance matrices is essential for many signal processing and machine learning algorithms. In high dimensional settings the sample covariance is known to perform poorly, hence regularization strategies such as analytic shrinkage of Ledoit/Wolf are applied. In the standard setting, i.i.d. data is assumed, however, in practice, time series typically exhibit strong aut...

Partial functions play an essential role in the semantics of programs as a means to formalize non-terminating computations and computations terminating in an exception or error situation. However, when properly formalized, partial functions and errors often complicate underlying formalisms and reasoning systems. In this paper we focus on term rewriting systems, and discuss how partial functions...

Let pn/qn be the n-th convergent of a real irrational number α, and let εn = αqn−pn. In this paper we investigate various sums of the type ∑ m εm, ∑ m |εm|, and ∑ m εmx m. The main subject of the paper is bounds for these sums. In particular, we investigate the behaviour of such sums when α is a quadratic surd. The most significant properties of the error sums depend essentially on Fibonacci nu...