Thursday, Aug 10: 8:30 AM - 10:20 AM

0143

Contributed Papers

0143

Contributed Papers

Metro Toronto Convention Centre

Room: CC-803B

Business and Economic Statistics Section

We are interested in the estimation of nonparametric regression model with correlated random errors under a random design setup, where the random errors are assumed to follow an autoregressive and moving average (ARMA) process and the covariates can also be serially correlated. Instead of the existing two-step method which estimates the model in a sequential fashion, a spline-based method is developed to estimate the mean function and ARMA parameters simultaneously. We establish the desirable asymptotic properties of the proposed approach under mild regularity conditions. Our numerical analyses, including both simulation studies and the examination of a real world dataset, show that the proposed method provides better model fitting and forecasting ability than the two-step method and the performance supports the established theoretical results.

nonparametric model with correlated errors

oracally efficient estimation

oracally efficient estimation

In this talk, we will propose a Dickey-Fuller type test for unit root moving average (MA) model. The MA model with unit root is a classical time series model and has been studied extensively over the years. Furthermore, the unit root test of this model is also important in applications, for example, in testing stationarity of AR processes (Kwiatkowski et al. (1992)) and in testing cointegration (Shin (1994)).

The score test (Tanaka (1990)) is a representative test for the unit root test in the MA model, but its asymptotic power deviates from that of the envelop power function and there is room for improving the power.

We propose a new test method based on the test method used by Dolado, Gonzalo and Mayoral (2002) and Lobato and Velasco (2007) for the long memory process. The power of the proposed test has been compared with the score test by Monte Carlo simulations, and it has been found that the power is almost equivalent when the alternative hypothesis is close to the null hypothesis, and significantly increases when the alternative hypothesis is more than a certain distance from the null hypothesis.

The score test (Tanaka (1990)) is a representative test for the unit root test in the MA model, but its asymptotic power deviates from that of the envelop power function and there is room for improving the power.

We propose a new test method based on the test method used by Dolado, Gonzalo and Mayoral (2002) and Lobato and Velasco (2007) for the long memory process. The power of the proposed test has been compared with the score test by Monte Carlo simulations, and it has been found that the power is almost equivalent when the alternative hypothesis is close to the null hypothesis, and significantly increases when the alternative hypothesis is more than a certain distance from the null hypothesis.

Time Series Analysis

Moving Average

Unit Roots

ARMA

Stationarity

Hypothesis Testing

Moving Average

Unit Roots

ARMA

Stationarity

Hypothesis Testing

We make a simple observation that facilitates valid likelihood-based inference for the parameters of the popular ARFIMA or FARIMA model without requiring stationarity by allowing the upper bound for the memory parameter to exceed 0.5. We observe that estimating the parameters of a single non-stationary ARFIMA model is equivalent to estimating the parameters of a sequence of stationary ARFIMA models. This enables improved inference because many standard methods perform poorly when estimates are close to the boundary of the parameter space. It also allows us to leverage the wealth of likelihood approximations that have been introduced for estimating the parameters of a stationary process. We explore how estimation of the memory parameter depends on the upper bound and introduce adaptive procedures for choosing. Via simulations, we examine the performance of our adaptive procedures for estimating the memory parameter when the true value is as large as 2.5. Our adaptive procedures estimate the memory parameter well, can be used to obtain confidence intervals for the memory parameter that achieve nominal coverage rates, and perform favorably relative to existing alternative

long memory

ARFIMA

FARIMA

time series

stationarity

ARFIMA

FARIMA

time series

stationarity

Estimating conditional variance functions is of great relevance in theory and practice.

A nonparametric method is proposed to estimate conditional variance functions in a

regression model setting with correlated noise. In this method, polynomial splines are used

to approximate the transfer function and the conditional variance function, and the noise

is assumed to follow an Autoregressive-Moving Average (ARMA) process. It is shown via

simulations that any one of the three components in this model (the ARMA parameters,

the conditional variance function, and the transfer function) can be estimated as if the

other two components are known by replacing them with their respective preliminary

estimates. Additionally, the conditional variance function estimate is guaranteed to be

positive. It is also shown that by modelling the serial correlation in the noise, the efficiency

in the nonparametric estimation of both the transfer function and the conditional variance

function is improved. By using polynomial splines, this method is not only flexible but also

computationally efficient. The usefulness of this model is illustrated through a real data

example.

A nonparametric method is proposed to estimate conditional variance functions in a

regression model setting with correlated noise. In this method, polynomial splines are used

to approximate the transfer function and the conditional variance function, and the noise

is assumed to follow an Autoregressive-Moving Average (ARMA) process. It is shown via

simulations that any one of the three components in this model (the ARMA parameters,

the conditional variance function, and the transfer function) can be estimated as if the

other two components are known by replacing them with their respective preliminary

estimates. Additionally, the conditional variance function estimate is guaranteed to be

positive. It is also shown that by modelling the serial correlation in the noise, the efficiency

in the nonparametric estimation of both the transfer function and the conditional variance

function is improved. By using polynomial splines, this method is not only flexible but also

computationally efficient. The usefulness of this model is illustrated through a real data

example.

Regression

Nonparametric smoothing

Semiparametric

Heteroscedasticity

Time series analysis

Financial statistics

Nonparametric smoothing

Semiparametric

Heteroscedasticity

Time series analysis

Financial statistics

We propose a regime-switching asymmetric long memory model, Multiple Regime HYGARCH (MR-HYGARCH), where the regime of an asset return is determined by the observed asymmetry in both short-term and long-term past periods. This is in contrast to existing threshold asymmetric models that determine the regime based on just one past period. The regime is determined based on the nature of the return(s) in the short-term period (previous day or week) and the preponderance of positive or negative returns over the long-term period, which may be the past month or the quarter. A Monte-Carlo experiment conducted designed to evaluate the methodology shows accurate estimation of the model parameters using the quasi-maximum likelihood method. Application to several real-life data sets show superior performance compared to existing models based on Bayesian Information Criterion.

GARCH models

Asymmetric volatility

Regime-switching

Long-memory

Conditional Variance

Asymmetric volatility

Regime-switching

Long-memory

Conditional Variance