Shelton Peiris

Estimation for regression with infinite variance errors

This paper addresses the problem of modelling time series with nonstationarity from a finite number of observations. Problems encountered with the time varying parameters in regression type models led to the smoothing techniques. The smoothing methods basically rely on the finiteness of the error variance, and thus, when this requirement fails, particularly when the error distribution is heavy tailed, the existing smoothing methods due to [1], are no longer optimal. In this paper, we propose a penalized minimum dispersion method for time varying parameter estimation when a regression model generated by an infinite variance stable process with characteristic exponent @a @e (1, 2). Recursive estimates are evaluated and it is shown that these estimates for a nonstationary process with normal errors is a special case.

Analysis of short time series with an over-dispersion model

There are certain situations where one observes several short time series. For instance, in testing the effect of a drug on patients, a doctor may obtain 3 or 4 blood pressure measurements every three hours from several patients; thus we have several short time series to deal with. In this paper, we address the estimation of the correlation parameter of a first order autoregressive process from a short time series. The proposed estimators are compared using a simulation study. Parameter estimation based on the method of maximum likelihood when there is extra source of variation in the model seems to give better results.

Approximate Asymptotic Variance-Covariance Matrix for the Whittle Estimators of GAR(1) Parameters

Generalized Autoregressive (GAR) processes have been considered to model some features in time series. The Whittles estimates have been investigated for the GAR(1) process by a simulation study by Shitan and Peiris (2008). This article derives approximate theoretical expressions for the enteries of the asymptotic variance-covariance matrix for those estimates of GAR(1) parameters. These results are supported by a simulation study.

Time Series Properties of the Class of Generalized First-Order Autoregressive Processes with Moving Average Errors

A new class of time series models known as Generalized Autoregressive of order one with first-order moving average errors has been introduced in order to reveal some hidden features of certain time series data. The variance and autocovariance of the process is derived in order to study the behaviour of the process. It is shown that in special cases these new results reduce to the standard ARMA results. Estimation of parameters based on the Whittle procedure is discussed. We illustrate the use of this class of model by using two examples.

Estimation and forecasting with logarithmic autoregressive conditional duration models

Efficient estimation of Log-ACD models using the estimating functions (EF) method.Study the finite sample behavior of new estimators through a simulation study.Compare the results via the EF and maximum likelihood (ML) methods.Apply the EF and ML methods for duration data for ACD models.Compare forecast abilities for ACD models through the EF and ML methods. This paper presents a semi-parametric method of parameter estimation for the class of logarithmic ACD (Log-ACD) models using the theory of estimating functions (EF). A number of theoretical results related to the corresponding EF estimators are derived. A simulation study is conducted to compare the performance of the proposed EF estimates with corresponding ML (maximum likelihood) and QML (quasi maximum likelihood) estimates. It is argued that the EF estimates are relatively easier to evaluate and have sampling properties comparable with those of ML and QML methods. Furthermore, the suggested EF estimates can be obtained without any knowledge of the distribution of errors is known. We apply all these suggested methodology for a real financial duration dataset. Our results show that Log-ACD (1,1) fits the data well giving relatively smaller variation in forecast errors than in Linear ACD (1,1) regardless of the method of estimation. In addition, the Diebold-Mariano (DM) and superior predictive ability (SPA) tests have been applied to confirm the performance of the suggested methodology. It is shown that the new method is slightly better than traditional methods in practice in terms of computation; however, there is no significant difference in forecasting ability for all models and methods.

Some Properties of the Generalized Autoregressive Moving Average (GARMA (1, 1; δ1, δ2)) Model

A new class of time series models known as Generalized Autoregressive Moving Average (1, 1; δ1, δ2) has been introduced in order to reveal some features of certain time series data. The authors derive the variance and autocovariance of the process in order to study the behavior of the process. It is shown that these new results reduce to the standard ARMA results. Some numerical results are also provided. Due to the generality of this model, it will be useful for modeling purposes.

Derivation of Kurtosis and Option Pricing Formulas for Popular Volatility Models with Applications in Finance

This article discusses some topics relevant to financial modeling. The kurtosis of a distribution plays an important role in controlling tail-behavior and is used in edgeworth expansion of the call prices. We present derivations of the kurtosis for a number of popular volatility models useful in financial applications, including the class of random coefficient GARCH models. Option pricing formulas for various classes of volatility models are also derived and a simple proof of the option pricing formula under the Black–Scholes model is given.

A note on testing for serial correlation in large number of small samples using tail probability approximations

Abstract A method of testing for serial correlation in large number of independent replications from short, first order autoregressive type time series with zero mean is considered. We use an approach via the Edgeworth expansion to compute the tail probability in order to test the null hypothesis of zero serial correlation at lag 1. Approximate tail probabilities are computed using our results to justify the theory.

Inference for some time series models with random coefficients and infinite variance innovations

Infinite variance processes have attracted growing interest in recent years due to its applications in many areas of statistics. For example, ARIMA time series models with infinite variance innovations are widely used in financial modelling. However, little attention has been paid to incorporate infinite variance innovations for time series models with random coefficients introduced by Nicholls and Quinn [1]. Estimation of model parameters for some special cases are discussed using the least absolute deviation (LAD) estimating function approach when the closed form density is available. It is also shown that these new LAD estimates are superior to some of the existing ones.

Hypothesis testing for some time-series models: a power comparison

Following the general approach for constructing test statistics for stochastic models based on optimal estimating functions by Thavaneswaran (1991), a new test statistic via martingale estimating function is proposed. Applications to some time-series models such as random coefficient autoregressive (RCA) models are discussed. It is shown that the choice of an optimal estimating function according to Godambes (1985) criterion leads to optimal power against a fixed alternative.