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This paper studies the ability of the k -factor GARMA processes to model and forecast the volatility of an intraday financial time series. Forecasting results from the k -factor GARMA model are obtained and compared with those produced by a conventional SARIMA model.

PurposeIn Italy, where the adoption of opioid analgesics in pain management has been historically poor, an increase in opioids consumption occurred between 2000 and 2015. The aim of this study is to assess, through specific time series analyses for trend changes, the impact of different intervening factors – such as the availability of new drugs, the observance of clinical guidelines, changes in prescription regulations, and in reimbursement policies – on opioids sales to community pharmacies in Italy, focusing on the time period 2000–2010.Materials and methodsFive opioids were considered: codeine, tramadol, buprenorphine, morphine, and fentanyl. The analysis is based on sales data collected at wholesale distributors. For each one of the five drugs, time series of the number of Defined Daily Doses per thousand inhabitants per day in the period 2000–2010 were analyzed, and an estimation of breakpoints was performed using segmented linear regression.ResultsDrug sales underwent a sharp increase in 2000–2010, although on different scales. Segmented regression analysis highlighted different potential breakpoints, corresponding to either a significant change in value and/or in slope. Sales of the five opioids were affected by at least one relevant event, often due to a synergy of regulatory, marketing, and technological factors. The effect of reimbursement changes has proved important.ConclusionBetween 2000 and 2010, regulatory, technological, and reimbursement changes significantly influenced opioid sales to community pharmacies in Italy. The sales of relatively new drug products seem to be less influenced by changes in reimbursement and regulatory policies than that of more established products, suggesting that physicians are more comfortable with “old” drugs, since their clinical use is supported by established clinical guidelines and protocols.

A nonparametric Bayesian method for producing coherent predictions of count time series with the nonnegative integer-valued autoregressive process is introduced. Predictions are based on estimates of h-step-ahead predictive mass functions, assuming a nonparametric distribution for the innovation process. That is, the distribution of errors are modeled by means of a Dirichlet process mixture of rounded Gaussians. This class of prior has large support on the space and probability mass functions and can generate almost any kind of count distribution, including over/under-dispersion and multimodality. An efficient Gibbs sampler is developed for posterior computation, and the method is used to analyze a dataset of visits to a web site.

In this paper we analyse some bootstrap techniques to make inference in INAR( p) models. First of all, via Monte Carlo experiments we compare the performances of these methods when estimating the thinning parameters in INAR( p) models; we state the superiority of model-based INAR bootstrap approaches on block bootstrap in terms of low bias and Mean Square Error. Then we adopt the model-based bootstrap methods to obtain coherent predictions and confidence intervals in order to avoid difficulty in deriving the distributional properties. Finally, we present an empirical application.