Luisa Bisaglia

A comparison of techniques of estimation in long-memory processes

In this paper we discuss the properties of most important estimators of long-range dependence parameters. We compare the properties of these estimators via Monte Carlo experiments. We give an empirical approach for confidence intervals for the different parameter estimates. We then apply these procedures to a real time series to investigate its long-memory properties.

k -Factor GARMA models for intraday volatility forecasting

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.

On the power of the Augmented Dickey–Fuller test against fractional alternatives using bootstrap

Abstract We consider a new bootstrap approach to test for a unit root in fractionally integrated time series. We find that this test always improves the power of the Augmented Dickey–Fuller test.

Testing structural breaks versus long memory with the Box–Pierce statistics: a Monte Carlo study

Several studies have found that occasional-break processes may produce realizations with slowly decaying autocorrelations, which is hardly distinguished from the long memory phenomenon. In this paper we suggest the use of the Box–Pierce statistics to discriminate long memory and occasional-break processes. We conduct an extensive Monte Carlo experiment to examine the finite sample properties of the Box–Pierce and other simple tests statistics in this framework. The results allow us to infer important guidelines for applied statistics in practice.

An Empirical Strategy to Detect Spurious Effects in Long Memory and Occasional-Break Processes

Long-range dependence and structural changes in level are intimely related phenomena and it is very difficult to separate the two effects. In this article, we present an empirical procedure to distinguish between long-memory and occasional-break processes. An extensive Monte Carlo experiment illustrates the performance of the procedure and an application to real data is also included.

ARFIMA processes and outliers: a weighted likelihood approach

In this paper, we consider the problem of robust estimation of the fractional parameter, d,  in long memory autoregressive fractionally integrated moving average processes, when two types of outliers, i.e. additive and innovation, are taken into account without knowing their number, position or intensity. The proposed method is a weighted likelihood estimation (WLE) approach for which needed definitions and algorithm are given. By an extensive Monte Carlo simulation study, we compare the performance of the WLE method with the performance of both the approximated maximum likelihood estimation (MLE) and the robust M-estimator proposed by Beran (Statistics for Long-Memory Processes, Chapman & Hall, London, 1994). We find that robustness against the two types of considered outliers can be achieved without loss of efficiency. Moreover, as a byproduct of the procedure, we can classify the suspicious observations in different kinds of outliers. Finally, we apply the proposed methodology to the Nile River annual minima time series.

Prediction intervals for farima processes by bootstrap methods

In this paper we introduce a procedure to compute prediction intervals for FARIMA (p d q) processes, taking into account the variability due to model identification and parameter estimation. To this aim, a particular bootstrap technique is developed. The performance of the prediction intervals is then assessed and compared to that of standard bootstrap percentile intervals. The methods are applied to the time series of Nile River annual minima.

Bayesian nonparametric forecasting for INAR models

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.

Do laws impact opioids consumption? A breakpoint analysis based on Italian sales data

Purpose In 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 methods Five 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. Results Drug 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. Conclusion Between 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.

Bootstrap approaches for estimation and confidence intervals of long memory processes

In this work, we investigate an alternative bootstrap approach based on a result of Ramsey [F.L. Ramsey, Characterization of the partial autocorrelation function, Ann. Statist. 2 (1974), pp. 1296–1301] and on the Durbin–Levinson algorithm to obtain a surrogate series from linear Gaussian processes with long range dependence. We compare this bootstrap method with other existing procedures in a wide Monte Carlo experiment by estimating, parametrically and semi-parametrically, the memory parameter d. We consider Gaussian and non-Gaussian processes to prove the robustness of the method to deviations from normality. The approach is also useful to estimate confidence intervals for the memory parameter d by improving the coverage level of the interval.