On the non-negative first-order exponential bilinear time series model

In this paper the bilinear model BL(1,0,1,1) driven by exponential distributed innovations is studied in some detail. Conditions under which the model is strictly stationary as well as some properties of the stationary distribution are discussed. Moreover, parameter estimation is also addressed. (C) 2005 Elsevier B.V. All rights reserved

Fitting Broadband Diffusion by Cable Modem in Portugal

The purpose of this article is to described the evolution of the number of residential subscribers of broadband fixed access by cable modem, in Portugal, on the period from 2000–2009. The pattern of evolution is estimated by fitting several models to the series, namely the following: exponential, Gompertz, Logistic, Bass and Michaelis-Menten. We fit the models to the data by nonlinear least squares, except in the exponential model where the linear version is fitted by ordinary least squares, using the internet freely available program R. This comparative study is in line with many others on the diffusion of technological innovations in the telecommunications sector, where the point is finding out if there is an early or a late take-off phenomenon. The Michaelis-Menten model is introduced for the first time in this approach. It allows to predict the later evolution in the series and reveals a qualitatively different behavior.Broadband, Technological Innovations, Diffusion Growth Models, Nonlinear Least Squares

Forecasting Australian Macroeconomic variables, evaluating innovations state space approaches

Innovations state space time series models that encapsulate the exponential smoothing methodology have been shown to be an accurate forecasting tool. These models for the first time are applied to Australian macroeconomic data. In addition new multivariate specifications are outlined and demonstrated to be accurate.exponential smoothing, state space models, multivariate time series, macroeconomic variables

Option pricing for GARCH-type models with generalized hyperbolic innovations

In this paper, we provide a new dynamic asset pricing model for plain vanilla options and we discuss its ability to produce minimum mispricing errors on equity option books. Given the historical measure, the dynamics of assets are modeled by Garch-type models with generalized hyperbolic innovations and the pricing kernel is an exponential affine function of the state variables, we show that the risk neutral distribution is unique and implies again a generalized hyperbolic dynamics with changed parameters. We provide an empirical test for our pricing methodology on two data sets of options respectively written on the French CAC 40 and the American SP 500. Then, using our theoretical result associated with Monte Carlo simulations, we compare this approach to natural competitors in order to test its efficiency. More generally, our empirical investigations analyze the ability of specific parametric innovations to reproduce market prices in the context of an exponential affine specification of the stochastic discount factor.Generalized hyperbolic distribution, option pricing, incomplete markets, CAC 40, SP 500, GARCH-type models.

Forecasting Compositional Time Series with Exponential Smoothing Methods

Compositional time series are formed from measurements of proportions that sum to one in each period of time. We might be interested in forecasting the proportion of home loans that have adjustable rates, the proportion of nonagricultural jobs in manufacturing, the proportion of a rock's geochemical composition that is a specific oxide, or the proportion of an election betting market choosing a particular candidate. A problem may involve many related time series of proportions. There could be several categories of nonagricultural jobs or several oxides in the geochemical composition of a rock that are of interest. In this paper we provide a statistical framework for forecasting these special kinds of time series. We build on the innovations state space framework underpinning the widely used methods of exponential smoothing. We couple this with a generalized logistic transformation to convert the measurements from the unit interval to the entire real line. The approach is illustrated with two applications: the proportion of new home loans in the U.S. that have adjustable rates; and four probabilities for specified candidates winning the 2008 democratic presidential nomination.compositional time series, innovations state space models, exponential smoothing, forecasting proportions

Multivariate exponential smoothing for forecasting tourist arrivals to Australia and New Zealand

In this paper we propose a new set of multivariate stochastic models that capture time varying seasonality within the vector innovations structural time series (VISTS) framework. These models encapsulate exponential smoothing methods in a multivariate setting. The models considered are the local level, local trend and damped trend VISTS models with an additive multivariate seasonal component. We evaluate their performances for forecasting international tourist arrivals from eleven source countries to Australia and New Zealand.Holt-Winters’ method, Stochastic seasonality, Vector innovations state space models.

Option Pricing under GARCH models with Generalized Hyperbolic distribution (II) : Data and Results

In this paper, we provide a new dynamic asset pricing model for plain vanilla options and we discuss its ability to produce minimum mispricing errors on equity option books. The data set is the daily log returns of the French CAC40 index, on the period January 2, 1988, October 26, 2007. Under the historical measure, we adjust, on this data set, an EGARCH model with Generalized Hyperbolic innovations. We have shown (Chorro, Guégan and Ielpo, 2008) that when the pricing kernel is an exponential affine function of the state variables, the risk neutral distribution is unique and implies again a Generalized Hyperbolic dynamic, with changed parameters. Thus, using this theoretical result associated to Monte Carlo simulations, we compare our approach to natural competitors in order to test its efficiency. More generally, our empirical investigations analyze the ability of specific parametric innovations to reproduce market prices in the context of the exponential affine specification of the stochastic discount factor.Generalized Hyperbolic Distribution, Option pricing, Incomplete market, CAC40.

Automatic Time Series Forecasting: The forecast Package for R

Automatic forecasts of large numbers of univariate time series are often needed in business and other contexts. We describe two automatic forecasting algorithms that have been implemented in the forecast package for R. The first is based on innovations state space models that underly exponential smoothing methods. The second is a step-wise algorithm for forecasting with ARIMA models. The algorithms are applicable to both seasonal and non-seasonal data, and are compared and illustrated using four real time series. We also briefly describe some of the other functionality available in the forecast package.