Wilfredo Palma

An intervention analysis of air quality data at Santiago, Chile

Abstract Air quality data at Santiago, Chile (PM10, PM2.5 and ozone) from 1989 to 1998 are analyzed with the goal of estimating trends in and impacts of public policies on air quality levels. Those policies, in effect since the late 1980s, have been essentially aimed at PM10 pollution abatement. The analyses show that fall and winter air quality has been improving consistently, specially the PM2.5 levels. The estimated trends for the monthly averages of PM10 concentrations range from −1.5 to −3.3% per annum, whereas the trends for monthly averages of PM2.5 concentrations range from −5 to −7% per annum. The monthly averages of ground ozone daily maxima do not have a significant trend for two of the downtown monitor sites; at the other three monitoring sites (including the one with the highest impacts) there is a clear downward trend between −5 and −3% per annum. The seasonal averages of a declimatized ozone production rate show a downward trend from 1988 through 1995, and no additional improvements have occurred thereafter. These mixed results for ground ozone levels are ascribed to a shift in the magnitude and spatial distribution of emissions in the city, and so there is a need for additional ozone abatement policies and further research on air pollution abatement options.

Estimation of seasonal fractionally integrated processes

This paper discusses the estimation of fractionally integrated processes with seasonal components. In order to estimate the fractional parameters, we propose several estimators obtained from the regression of the log-periodogram on different bandwidths selected around and/or between the seasonal frequencies. For comparison purposes, the semi-parametric method introduced in Geweke and Porter-Hudak (1983) and Porter-Hudak (1990) and the maximum-likelihood estimates (ML) are also considered. As indicated by the Monte Carlo simulations, the performance of the estimators proposed is good even for small sample sizes.

A Class of Antipersistent Processes

We introduce a class of stationary processes characterized by the behaviour of their infinite moving average parameters. We establish the asymptotic behaviour of the covariance function and the behaviour around zero of the spectral density of these processes, showing their antipersistent character. Then, we discuss the existence of an infinite autoregressive representation for this family of processes, and we present some consequences for fractional autoregressive moving average models.

An efficient estimator for locally stationary Gaussian long-memory processes

This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying parametric formulation of these models is introduced and a Whittle likelihood technique is proposed for estimating the parameters involved. Large sample properties of these Whittle estimates such as consistency, normality and efficiency are established in this work. Furthermore, the finite sample behavior of the estimators is investigated through Monte Carlo experiments. As a result from these simulations, we show that the estimates behave well even for relatively small sample sizes.

Estimating seasonal long-memory processes: a Monte Carlo study

This paper discusses extensions of the popular methods proposed by Geweke and Porter-Hudak [Geweke, J. and Porter-Hudak, S., 1983, The estimation and application of long memory times series models. Journal of Time Series Analysis, 4(4), 221–238.] and Fox and Taqqu [Fox, R. and Taqqu, M.S., 1986, Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Annals of Statistics, 14, 517–532.] for estimating the long-memory parameter of autoregressive fractionally integrated moving average models to the estimation of long-range dependent models with seasonal components. The proposed estimates are obtained from a selection of harmonic frequencies chosen between the seasonal frequencies. The maximum likelihood method given in Beran [Beran, J., 1994, Statistic for Long-Memory Processes (New York: Chapman & Hall).] and the semi-parametric approaches introduced by Arteche and Robinson [Arteche, J. and Robinson, P.M., 2000, Semiparametric inference in seasonal and cyclical long memory processes. Journal of Time Series Analysis, 21(1), 1–25.] are also considered in the study. Our finite sample Monte Carlo investigations indicate that the proposed methods perform well and can be used as alternative estimating procedures when the data display both long-memory and cyclical behavior.

Statistical analysis of autoregressive fractionally integrated moving average models in R

The autoregressive fractionally integrated moving average (ARFIMA) processes are one of the best-known classes of long-memory models. In the package afmtools for R, we have implemented a number of statistical tools for analyzing ARFIMA models. In particular, this package contains functions for parameter estimation, exact autocovariance calculation, predictive ability testing and impulse response function computation, among others. Furthermore, the implemented methods are illustrated with applications to real-life time series.

Estimation and forecasting of long-memory processes with missing values

This paper addresses the issues of maximum likelihood estimation and forecasting of a long-memory time series with missing values. A state-space representation of the underlying long-memory process is proposed. By incorporating this representation with the Kalman filter, the proposed method allows not only for an efficient estimation of an ARFIMA model but also for the estimation of future values under the presence of missing data. This procedure is illustrated through an analysis of a foreign exchange data set. An investment scheme is developed which demonstrates the usefulness of the proposed approach.

Estimation of Long-Memory Time Series Models: a Survey of Different Likelihood-Based Methods

Since the seminal works by Granger and Joyeux (1980) and Hosking (1981), estimations of long-memory time series models have been receiving considerable attention and a number of parameter estimation procedures have been proposed. This paper gives an overview of this plethora of methodologies with special focus on likelihood-based techniques. Broadly speaking, likelihood-based techniques can be classified into the following categories: the exact maximum likelihood (ML) estimation (Sowell, 1992; Dahlhaus, 1989), ML estimates based on autoregressive approximations (Granger & Joyeux, 1980; Li & McLeod, 1986), Whittle estimates (Fox & Taqqu, 1986; Giraitis & Surgailis, 1990), Whittle estimates with autoregressive truncation (Beran, 1994a), approximate estimates based on the Durbin–Levinson algorithm (Haslett & Raftery, 1989), state-space-based maximum likelihood estimates for ARFIMA models (Chan & Palma, 1998), and estimation of stochastic volatility models (Ghysels, Harvey, & Renault, 1996; Breidt, Crato, & de Lima, 1998; Chan & Petris, 2000) among others. Given the diversified applications of these techniques in different areas, this review aims at providing a succinct survey of these methodologies as well as an overview of important related problems such as the ML estimation with missing data (Palma & Chan, 1997), influence of subsets of observations on estimates and the estimation of seasonal long-memory models (Palma & Chan, 2005). Performances and asymptotic properties of these techniques are compared and examined. Inter-connections and finite sample performances among these procedures are studied. Finally, applications to financial time series of these methodologies are discussed.

Data analysis using regression models with missing observations and long-memory: an application study

The objective of this work is to propose a statistical methodology to handle regression data exhibiting long memory errors and missing values. This type of data appears very often in many areas, including hydrology and environmental sciences, among others. A generalized linear model is proposed to deal with this problem and an estimation strategy is developed that combines both classical and Bayesian approaches. The estimation methodology proposed is illustrated with an application to air pollution data which shows the impact of the long memory in the statistical inference and of the missing values on the computations. From a Bayesian standpoint, genuine priors are considered for the parameters of the model which are justified within the context of the air pollution model derivation.

Estimation of tropical sea level anomaly by an improved Kalman filter

Abstract Kaiman filter theory and autoregressive time series are used to map sea level height anomalies in the tropical Pacific. Our Kalman filters are implemented with a linear state space model consisting of evolution equations for the amplitudes of baroclinic Kelvin and Rossby waves and data from the Pacific tide gauge network. In this study, three versions of the Kalman filter are evaluated through examination of the innovation sequences, that is, the time series of differences between the observations and the model predictions before updating. In a properly tuned Kalman filter, one expects the innovation sequence to be white (uncorrelated, with zero mean). A white innovation sequence can thus be taken as an indication that there is no further information to be extracted from the sequence of observations. This is the basis for the frequent use of whiteness, that is, lack of autocorrelation, in the innovation sequence as a performance diagnostic for the Kalman filter. Our long-wave model embodies the c...