Algorithms for Linear Time Series Analysis: With R Package

Our ltsa package implements the Durbin-Levinson and Trench algorithms and provides a general approach to the problems of fitting, forecasting and simulating linear time series models as well as fitting regression models with linear time series errors. For computational efficiency both algorithms are implemented in C and interfaced to R. Examples are given which illustrate the efficiency and accuracy of the algorithms. We provide a second package FGN which illustrates the use of the ltsa package with fractional Gaussian noise (FGN). It is hoped that the ltsa will provide a base for further time series software.

Algorithms for Linear Time Series Analysis: With R Package

Our ltsa package implements the Durbin-Levinson and Trench algorithms and provides a general approach to the problems of fitting, forecasting and simulating linear time series models as well as fitting regression models with linear time series errors. For computational efficiency both algorithms are implemented in C and interfaced to R. Examples are given which illustrate the efficiency and accuracy of the algorithms. We provide a second package FGN which illustrates the use of the ltsa package with fractional Gaussian noise (FGN). It is hoped that the ltsa will provide a base for further time series software

Persistence and Anti-persistence: Theory and Software

Persistent and anti-persistent time series processes show what is called hyperbolic decay. Such series play an important role in the study of many diverse areas such as geophysics and financial economics. They are also of theoretical interest. Fractional Gaussian noise (FGN) and fractionally-differeneced white noise are two widely known examples of time series models with hyperbolic decay. New closed form expressions are obtained for the spectral density functions of these models. Two lesser known time series models exhibiting hyperbolic decay are introduced and their basic properties are derived. A new algorithm for approximate likelihood estimation of the models using frequency domain methods is derived and implemented in R. The issue of mean estimation and multimodality in time series, particularly in the simple case of one short memory component and one hyperbolic component is discussed. Methods for visualizing bimodal surfaces are discussed. The exact prediction variance is derived for any model that admits an autocovariance function and integrated (inverse-differenced) by integer d. A new software package in R, arfima, for exact simulation, estimation, and forecasting of mixed short-memory and hyperbolic decay time series. This package has a wider functionality and increased reliability over other software that is available in R and elsewhere

Statistics and Computing (2001) 11, 57–65 Mean likelihood estimators

The use of Mathematica in deriving mean likelihood estimators is discussed. Comparisons are made between the mean likelihood estimator, the maximum likelihood estimator, and the Bayes estimator based on a Jeffrey’s noninformative prior. These estimators are compared using the mean-square error criterion and Pitman measure of closeness. In some cases it is possible, using Mathematica, to derive exact results for these criteria. Using Mathematica, simulation comparisons among the criteria can be made for any model for which we can readily obtain estimators. In the binomial and exponential distribution cases, these criteria are evaluated exactly. In the firstorder moving-average model, analytical comparisons are possible only for n = 2. In general, we find that for the binomial distribution and the first-order moving-average time series model the mean likelihood estimator outperforms the maximum likelihood estimator and the Bayes estimator with a Jeffrey’s noninformative prior. Mathematica was used for symbolic and numeric computations as well as for the graphical display of results. A Mathematica notebook which provides the Mathematica code used in this article is available