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The value of the theoretical constant used to scale daily volatility to both a five-day volatility estimate and a ten-day volatility estimate is compared with empirical estimates using a volatility modeling framework. Five composite stock indexes are analyzed to determine the different behaviors of scaling across markets. Both developed and emerging markets are considered, to provide additional detail to the comparisons. The results provided are considered in a value-at-risk application. While using the square-root-of-time rule on a weekly or ten-day basis is appropriate in certain cases, for time series with a linear dependence component the rule can drastically err from observed volatility levels. It is demonstrated that there are potential hazards when using the square-root-of-time rule for risk or compliance purposes.

Releasing business microdata is a challenging problem for many statistical agencies. Businesses with distinct continuous characteristics such as extremely high income could easily be identified while these businesses are normally included in surveys representing the population. In order to provide data users with useful statistics while maintaining confidentiality, some statistical agencies have developed online based tools to allow users to specify and request tables created from microdata. These tools only release perturbed cell values generated from automatic output perturbation algorithms in order to protect each underlying observation against various attacks, such as differencing attacks. An example of the perturbation algorithms has been proposed by Thompson et al. (2013). The algorithm focuses largely on reducing disclosure risks without addressing much on data utility. As a result, the algorithm has limitations, including a limited scope of applicable cells and uncontrolled utility loss. In this paper we introduce a new algorithm for generating perturbed cell values. As a comparison, The new algorithm allows more control over utility loss, while it could also achieve better utility-disclosure tradeoffs in many cases, and is conjectured to be applicable to a wider scope of cells.

An aggregate series is a time series resulting from the aggregation of two or more sub-series. Two model-based approaches to seasonal adjustment of the aggregate series include a univariate and multivariate basic structural model. In a previous study [2], the variance of the seasonally adjusted series for the two approaches were compared using a range of true parameter values for a fixed length series. This paper compares the model-based univariate and multivariate approaches for different series lengths using the estimated parameters. A simulation study compares two outcomes: the accuracy of the estimated parameters of the aggregate series, and the naïve bias in the prediction error variance. The results show that for the two cases studied, the use of the multivariate approach in the estimation of parameters improves the accuracy of the parameter estimates of the aggregated series. This was especially true for short to medium length time series. The relative efficiencies of the seasonally adjusted aggregated series also showed good gains for the multivariate model. For one of the cases, there was a substantial decrease in the naïve bias with the use of the multivariate model. Bias correction is also discussed for the two approaches.

Lin (2014) developed a framework of the method of the sample-moment-based density approximant, for estimating the probability density function of microdata based on noise multiplied data. Theoretically, it provides a promising method for data users in generating the synthetic data of the original data without accessing the original data; however, technical issues can cause problems implementing the method. In this paper, we describe a software package called MaskDensity14, written in the R language, that uses a computational approach to solve the technical issues and makes the method of the sample-moment-based density approximant feasible. MaskDensity14 has applications in many areas, such as sharing clinical trial data and survey data without releasing the original data.

There is a continuing interest in the analysis of gene architecture and gene expression to determine the relationship that may exist. Advances in high-quality sequencing technologies and large-scale resource datasets have increased the understanding of relationships and cross-referencing of expression data to the large genome data. Although a negative correlation between expression level and gene (especially transcript) length has been generally accepted, there have been some conflicting results arising from the literature concerning the impacts of different regions of genes, and the underlying reason is not well understood. The research aims to apply quantile regression techniques for statistical analysis of coding and noncoding sequence length and gene expression data in the plant, Arabidopsis thaliana, and fruit fly, Drosophila melanogaster, to determine if a relationship exists and if there is any variation or similarities between these species. The quantile regression analysis found that the coding sequence length and gene expression correlations varied, and similarities emerged for the noncoding sequence length (5' and 3' UTRs) between animal and plant species. In conclusion, the information described in this study provides the basis for further exploration into gene regulation with regard to coding and noncoding sequence length.

Basak and Ho (2004) derived numerical formulas for the mean first passage time of ARMA models using the integral equation approach. Recently, the ESTAR model has become a popular model for the analysis of economic and financial data. Some researchers used the ESTAR model to analyze real exchange rates, purchasing power parity (PPP) deviations, and arbitrage processes. This article shows that under certain conditions, the integral equation approach can still be used for the ESTAR model. Numerical schemes of the mean first passage time for ESTAR(1) and ESTAR(2) models are proposed in this article. The applications of the schemes for real exchange rates between Australian and New Zealand dollars as well as for pairs trading following the ESTAR(1) model are provided. Copyright Grace Scientific Publishing, LLC.

The efficiency and relationship between future and spot index prices has been investigated in literature by using different approaches. In this paper, the efficiency and relationship between the log future prices and the log spot prices is investigated for each contract based on cointegration model with a time trend. A new pairs trading strategy for stock prices cointegrated with time trend is proposed in this paper. Formulas used to evaluate the trading strategy are derived and the necessary conditions for making profit out of selected pairs of assets are discussed. S and P 500 future contracts prices of Mar98, Jun98 and Sep98 as well as their corresponding spot index prices are considered in this paper. Our empirical studies show that the strategy proposed in this paper works very well and produces very significant high return for those selected pairs. The average return per trade for all periods and all those pairs are above 10% .

Using noise multiplied data to protect confidential data has recently drawn some attention. Understanding the probability property of the underlying confidential data based on their masked data is of interest in confidential data analysis. This paper proposes the approach of sample-moment-based density approximant based on noise multiplied data and provides a new manner for approximating the density function of the underlying confidential data without accessing the original data. The approach of sample-moment-based density approximant is an extension of the approach of moment-based density approximant, which is mathematically equivalent to traditional orthogonal polynomials approaches to the probability density function (Provost, 2005). This paper shows that, regardless of a negligible probability, a moment-based density approximant can be well approximated by its sample-moment-based approximant if the size of the sample used in the evaluation is reasonable large. Consequently, a density function can be reasonably approximated by its sample-moment-based density approximant. This paper focuses on the properties and the performance of the approach of the sample-moment-based density approximant based on noise multiplied data. Due to the restriction on the number of pages, some technical issues on implementing the approach proposed in practice will be discussed in another paper.

A framework, the sample-moment-based density approximant , for estimating the probability density function based on noise multiplied data was proposed in Lin (2014). Based on the framework, an R package, MaskDensity10.R, is built in this paper. The package is available from http://www.uow.edu.au/~yanxia/Confidential_data_analysis/. The framework is developed for continuous univeriates (see Lin, 2014). With the techniques of nonparametric smoothing and K-means clustering integrated, MaskDensity10.R can be used for estimating the mass functions of categorical variables. The same R package, MaskDensity10.R, can be used by the data agency to create the masked data set, as well as used by the end-user to obtain the approximation of the density function of the original data set based on masked data. Simulation studies and real life data applications of MaskDensity10.R are presented in this paper. The risk of disclosure in the application of the R package to microdata is discussed, particularly for category data.

Since the introduction of augmented Dickey-Fuller unit root tests, many new types of unit root tests have been developed. Developments in nonlinear unit root tests occurred to overcome poor performance of standard linear unit root tests for nonlinear processes. Venetis et al. (2009) developed a unit root test for the k-ESTAR(p) model where k is the number of equilibrium levels and p is the order of autoregressive terms. Their approach may cause singularity problem because some of the regressors might be collinear. To overcome the problem, they move collinear regressors into the error term. This paper extends the work of Venetis et al. (2009). Using a new approach given in this paper, the singularity problem can be avoided without worrying the issue of collinearity. For some cases, simulation results show that our approach is better than other unit root tests.

Several tests for cointegration among non-stationary financial time series have been developed including the Dicky Fuller (1979) unit root tests, the Cointegration Regression Durbin-Watson test (1983), the Wild Bootstrap test (2003) and the Johansen likelihood ratio tests (1988). The Johensen's tests appeared to provide superior results when the tests were originally applied to situations where the cointegration errors were normally distributed. However, substantial empirical evidences show that financial time series tend to be nonnormal in their distribution which may, in turn, lead to non-normal GARCH type cointegration error distributions. The question addressed in this paper is whether the Johansen's tests are still more powerful than the alternative tests when the underlying cointegration errors are non-normally distributed. Lee and Tse (1996) examined the performance of Johansen's tests compared with DF tests and CRDW test when cointegration errors are fitted by GARCH(1,1) model with normal and student-t error distributions. This paper extends their work. More cointegration tests with a wide range of error distributions are considered. Our simulation results indicate that the performance of power of the Johansen's tests in capturing cointegration between financial time series is still higher than alternative tests even when the cointegration errors are not normally distributed (a skewed student-t distribution gives the best results). However, the best size performance is given by the Dicky Fuller test using the skewed generalized error distribution.

This paper considers the scenario that all data entries in a confidentialised unit record file were masked by multiplicative noises, regardless of whether unit records are sensitive or not and regardless of whether the masked variables are dependent or independent variables in the underlying regression analysis. A technique is introduced in this paper to show how to estimate parameters in a regression model, which is originally fitted by unmasked data, based on masked data. Several simulation studies and a real-life data application are presented.

The information of copy number alterations (gains and losses) in tumour genomes can be used to discovery cancer-causing genes. The estimate of copy number can be obtained from the estimate copy number ratio. The higher the depth of underlying sequencing data, the more accurate the estimate of copy number ratio. At the same time, the higher depth of a sequencing data used in copy number analysis, the more cost of data analysis. To develop a method for identifying a necessary depth of sequencing data for copy number analysis before test data are produced is of interest. In this paper, we proposed an algorithm of equal acceptance regions for detecting copy number ratios. This algorithm can be used to determine the depth of sequencing data required for copy number analysis. Copyright © 2012 Inderscience Enterprises Ltd.

In this paper, we will focus on State Space Models(SSMs), especially the stochastic volatility model, and lookfor a standard approach for assigning initial values in theQuasi-Likelihood (QL) and Asymptotic Quasi-Likelhood (AQL)estimation procedures.

The Generalized Bernoulli Modeling approach is used to analyze the pattern change in intron sequences of a model plant species Arabidopsis thaliana. The influence of the intron length and the number of GC on the intron sequence pattern changes is examined. Two other gene properties, the gene expression level and the protein function encoded are also assessed. Among the random sampled intron sequences,10.71% of them have been identified to have sequence pattern change. Our study shows that the number of GC and the intron length significantly influence the intron pattern change while the gene expression level and the protein function have little effect. Our results show that for Arabidopsis thaliana, the shorter intron with more number of GC might have a higher chance to have pattern changes detected on its sequence and this piece of information could be used for checking whether the intron is functional introns. This study may be benefit to nthe further study on functions of intron.

A large portion in eukaryotic genomes is introns but their function is not yet fully elucidated. The aims of this study are to employ the generalized Bernoulli modeling approach to estimate the change points based on GC distribution in intron sequences of Arabidopsis thaliana and to investigate whether there is any correlation between gene properties (the gene expression level and the protein function) and these intron pattern changes. The influence of the intron length and the number of GC on the intron sequence pattern changes is demonstrated. Among the random sampled intron sequences, 10.71% have been identified to have pattern changes. The number of GC and the intron length can be considered main factors influencing the intron pattern change. Short introns with high GC number are likely to have higher chance to have pattern changes detected on their sequences. Little influence of gene properties on the pattern change is found in this study. The pattern changes identified in this study may benefit the further investigation on intron functionality.

Supplementary material for Estimating Copy Numbers for Shared Array CGH Data: the Linear-Median Method

An aggregate series is a time series resulting from the aggregation of two or more sub-series. This paper compares a model-based univariate and multivariate approach to seasonal adjustment of the aggregate series for different series lengths. A simulation study compares two outcomes: the accuracy of the estimated parameters of the aggregate series, and the naive bias in the prediction error variance. The results show that for the two examples studied, the use of the multivariate approach in the estimation of parameters improves the accuracy of the parameter estimates of the aggregated series. This was especially the case for short to medium length time series. The relative efficiencies of the seasonally adjusted aggregated series also showed good gains for the multivariate model. For one of the examples, there was a substantial decrease in the naive bias with the use of the multivariate model.

This paper considers parameter estimation for state-space models (SSMs). We propose quasi-likelihood (QL) and asymptotic quasilikelihood (AQL) approaches for the estimation of state-space models. The asymptotic quasi-likelihood (AQL) utilises a nonparametric kernel estimator of the conditional variance covariances matrix Σt to replace the true Σt in the standard quasi-likelihood. The kernel estimation avoids the risk of potential miss-specification of Σt and thus make the parameter estimator more robust. This has been further verified by empirical studies carried out in this paper.

This paper considers parameter estimation for nonlinear and non-Gaussian state-space models with correlation. We propose an asymptotic quasi-likelihood (AQL) approach which utilises a nonparametric kernel estimator of the conditional variance covariances matrix Σt to replace the true Σt in the standard quasi-likelihood. The kernel estimation avoids the risk of potential miss-specification of Σt and thus make the parameter estimator more robust. This has been further verified by empirical studies carried out in this paper.

Transcription is a complicated process which involves the interactions of promoter cis-elements with multiple trans-protein factors. The specific interactions rely not only on the specific sequence recognition between the cis- and trans-factors but also on certain spatial arrangement of the factors in a complex. The relative positioning of involved cis-elements provides the framework for such a spatial arrangement. The distance distribution between gene transcription and translation start sites (TSS-TLS) is the subject of the present study to test an assumption that over evolution, the TSS-TLS distance becomes a distinct character for a given organism. Four representative organisms (Escherichia cloi, Saccharomyces cerevisiae, Arabidopsis thaliana and Homo sapiens) were chosen to study the probability distribution of the distance TSS-TLS. The statistical results show that the distances distributions vary significantly and are not independent of species. There seems a trend of increased length of the distances from simple prokaryotic to more complicated eukaryotic organisms. With the specific distance distribution data, computational promoter prediction tools can be improved for higher accuracy.

In this paper we inverstigate the strong approximation of a linear process with long memory to a Gaussian process. The results are then applied to derive the law of the iterated logarithm and Darling-Erd″os type theorem for long memory processes under i

We propose a simple method of constructing quasi-likelihood functions for dependent data based on conditional-mean-variance relationships, and apply the method to estimating the fractal dimension from box-counting data. Simulation studies were carried out to compare this method with the traditional methods. We also applied this technique to real data from fishing grounds in the Gulf of Carpentaria, Australia.