Clélia M. C. Toloi

Time-Varying Autoregressive Conditional Duration Model

The main goal of this work is to generalize the autoregressive conditional duration (ACD) model applied to times between trades to the case of time-varying parameters. The use of wavelets allows that parameters vary through time and makes possible the modeling of non-stationary processes without preliminary data transformations. The time-varying ACD model estimation was done by maximum-likelihood with standard exponential distributed errors. The properties of the estimators were assessed via bootstrap. We present a simulation exercise for a non-stationary process and an empirical application to a real series, namely the TELEMAR stock. Diagnostic and goodness of fit analysis suggest that the time-varying ACD model simultaneously modeled the dependence between durations, intra-day seasonality and volatility.

COMPARING TIME-VARYING AUTOREGRESSIVE STRUCTURES OF LOCALLY STATIONARY PROCESSES

In this paper, a novel statistical test is introduced to compare two locally stationary time series. The proposed approach is a Wald test considering time-varying autoregressive modeling and function projections in adequate spaces. The covariance structure of the innovations may be also time-varying. In order to obtain function estimators for the time-varying autoregressive parameters, we consider function expansions in splines and wavelet bases. Simulation studies provide evidence that the proposed test has a good performance. We also assess its usefulness when applied to a financial time series.

A note on the Ljung--Box--Pierce portmanteau statistic with missing data

The overall test for lack of fit for time series models proposed by Box and Pierce (1970) and Ljung and Box (1978) is modified to include the case when observations are missing. The missing data mechanism considered here is general and nonparametric.

Wavelet Estimation of Copulas for Time Series

In this paper, we consider estimating copulas for time series, under mixing conditions, using wavelet expansions. The proposed estimators are based on estimators of densities and distribution functions. Some statistical properties of the estimators are derived and their performance assessed via simulations. Empirical applications to real data are also given.

An Autoregressive Model for Time Series of Circular Data

This article focuses on estimating an autoregressive regression model for circular time series data. Simulation studies have shown the difficulties involved in obtaining good estimates from low concentration data or from small samples. It presents an application using real data.

On Residual Variance Estimation in Autoregressive Models

In this paper we consider time series models belonging to the autoregressive (AR) family and deal with the estimation of the residual variance. This is important because estimates of the variance are involved in, for example, confidence sets for the parameters of the model, estimation of the spectrum, expressions for the estimated error of prediction and sample quantities used to make inferences about the order of the model. We consider the asymptotic biases for moment and least squares estimators of the residual variance, and compare them with known results when available and with those for maximum likelihood estimators under normality. Simulation results are presented for finite samples

Transfer Function Models with Time-varying Coefficients

We consider a transfer function model with time-varying coefficients. We propose an estimation procedure, based on the least squares method and wavelet expansions of the time-varying coefficients. We discuss some statistical properties of the estimators and assess the validity of the methodology through a simulation study. We also present an application of the proposed procedure to a real pair of series.

State space Markov switching models using wavelets

Abstract We propose a state space model with Markov switching, whose regimes are associated with the model parameters and regime transition probabilities are modeled using wavelets. The estimation is based on the maximum likelihood method using the EM algorithm and a bootstrap method is proposed in order to assess the distribution of the maximum likelihood estimators. To evaluate the state variables and regime probabilities, the Kalman filter and a probability filter procedure conditional on each possible regime, at each instant, are used. These procedures are evaluated with simulated data and illustrated with the US monthly industrial production index from July 1968 to February 2011.

Residual variance estimation in moving average models

We consider time series models of the MA (moving average) family, and deal with the estimation of the residual variance. Results are known for maximum likelihood estimates under normality, both for known or unknown mean, in which case the asymptotic biases depend on the number of parameters (including the mean), and do not depend on the values of the parameters. For moment estimates the situation is different, because we find that the asymptotic biases depend on the values of the parameters, and become large as they approach the boundary of the region of invertibility. Our approach is to use Taylor series expansions, and the objective is to obtain asymptotic biases with error of o(l/T), where T is the sample size. Simulation results are presented, and corrections for bias suggested.