Ayman Amin

Menoufia University · Department of Statistics, Mathematics and Insurance

In this article we present a Bayesian prediction of multiplicative seasonal autoregressive moving average (SARMA) processes using the Gibbs sampling algorithm. First, we estimate the unobserved errors using the nonlinear least squares (NLS) method to approximate the likelihood function. Second, we employ conjugate priors on the model parameters and...

In this paper we discuss the multistage sequential estimation of the variance of the Rayleigh distribution using the three-stage procedure that was presented by Hall (Ann. Stat. 9(6):1229–1238, 1981). Since the Rayleigh distribution variance is a linear function of the distribution scale parameter’s square, it suffices to estimate the Rayleigh dist...

We present a full Bayesian analysis of multiplicative double seasonal autoregressive (DSAR) models in a unified way, considering identification (best subset selection), estimation, and prediction problems. We assume that the DSAR model errors are normally distributed and introduce latent variables for the model lags, and then we embed the DSAR mode...

Reliability is the key factor for software system quality. Several models have been introduced to estimate and predict reliability based on results of software testing activities. Software Reliability Growth Models (SRGMs) are considered the most commonly used to achieve this goal. Over the past decades, many researchers have discussed SRGMs’ assum...

Seasonal autoregressive (SAR) time series models have been extended to fit time series exhibiting multiple seasonalities. However, hardly any research in Bayesian literature has been done on modelling multiple seasonalities. In this article, we propose a full Bayesian analysis of triple SAR (TSAR) models for time series with triple seasonality, con...

Triple seasonal autoregressive (TSAR) models have been introduced to model time series date with three layers of seasonality; however, the Bayesian identification problem of these models has not been tackled in the literature. Therefore, in this paper, we have the objective of filling this gap by presenting a Bayesian procedure to identify the best...

Seasonal autoregressive (SAR) models have many applications in different fields, such as economics and finance. It is well known in the literature that these models are nonlinear in their coefficients and that their Bayesian analysis is complicated. Accordingly, choosing the best subset of these models is a challenging task. Therefore, in this pape...

In this paper we extend autoregressive models to fit time series that have three layers of seasonality, i.e. triple seasonal autoregressive (TSAR) models, and we introduce the Bayesian inference for these TSAR models. Assuming the TSAR model errors are normally distributed and employing three priors, i.e. Jeffreys', g, and normal-gamma priors, on t...

In last few decades some researchers have extended existing time series models to fit high frequency time series characterized by exhibiting multiple seasonalities. In the Bayesian framework, most of the work in this direction is only at the level of double seasonality. Therefore, in this paper we have the objective to fill part of this gap by exte...

In this work we extend autoregressive models to fit time series with triple seasonalities; and present the Bayesian estimation for the triple seasonal autoregressive (TSAR) models via Gibbs sampler. First, by assuming the errors are normally distributed and employing the normal-gamma and g priors for the model parameters, we derive the full conditi...

This paper discusses the sequential estimation of the scale parameter of the Rayleigh distribution using the three-stage sequential sampling procedure proposed by Hall (Ann. Stat. 1981, 9, 1229-1238). Both point and confidence interval estimation are considered via a unified optimal decision framework, which enables one to make the maximum use of t...

In this paper we use the Gibbs sampling algorithm to present a Bayesian analysis to multiplicative double seasonal autoregressive (DSAR) models, considering both estimation and prediction problems. Assuming the model errors are normally distributed and using natural conjugate and g priors on the initial values and model parameters, we show that the...

In this paper, we introduce a real-time fault detection technique based on statistical EWMA control charts for detecting power switch open circuit faults in inverter feeding induction motor drives. The proposed algorithm is able to detect simultaneously double and triple switches open circuit faults, besides single open circuit faults.

In this paper we first review the existing Bayesian identification methods for the autoregressive (AR) models, and we then present an extensive simulation-based comparison of these Bayesian identification methods applied to AR models.

Chaos theory as one of the nonlinear dynamic tools can be useful in explaining the dynamics of financial markets, since chaotic models are capable of exhibiting behaviors similar to those observed in financial data. With the aim of this paper to apply the chaos theory to the Egyptian stock market, the researcher first presents the basic features of...

Number of Pilgrims (in millions) to Saudi Arabia's Mecca in the last 27 years, more details (In Arabic) are available: https://aymanamin-ar.netlify.com/post/hajj/

This is an initial outcome of our study: divorce and illiteracy in Egypt, based on census-2017 (it is in Arabic and still incomplete)

In this paper we first study the statistical characteristics of the major Egyptian stock market indices, i.e. EGX 100, EGX 70 and EGX 30, using descriptive statistics, stationarity tests and power spectrum analysis. After that, we use Brock-Dechert-Scheinkman (BDS) test to detect the nonlinearity in these indices after removing their linear depende...

In this paper we review the existing Bayesian identification techniques for the moving average (MA) models that can be classified as testing based identification and posterior mass function based identification. In order to improve the Bayesian identification of MA models, we present a new Bayesian identification method that is based on the posteri...

In this report we aim to study illiteracy in Egypt (In arabic and Incomplete Report).

Seasonal autoregressive (SAR) models have been modified and extended to model high frequency time series characterized by exhibiting double seasonal patterns. Some researchers have introduced Bayesian inference for double seasonal autoregressive (DSAR) models; however, none has tackled the problem of Bayesian identification of DSAR models. Therefor...

In this paper we use the Kullback-Leibler divergence to measure the distance between the posteriors of the autoregressive (AR) model coefficients, aiming to evaluate mathematically the sensitivity of the coefficients posterior to different types of priors, i.e. Jeffreys’, g, and natural conjugate priors. In addition, we evaluate the impact of the p...

In this paper we present a Bayesian methodology to identify the order of double seasonal autoregressive (DSAR) models. Assuming the model errors are normally distributed and using conjugate priors on the model parameters, we derive the joint posterior mass function of the model order in a closed-form. Accordingly, the posterior mass function can be...

In this paper we use the Kullback-Leibler divergence to measure the distance between the posteriors of the autoregressive (AR) model order, aiming to evaluate mathematically the sensitivity of the model identification to different types of priors of the model parameters. In particular, we consider three priors for the AR model coefficients, namely...

In this paper, we present a Bayesian analysis of double seasonal autoregressive moving average (DSARMA) models. We first consider the problem of estimating unknown lagged errors in the moving average part using nonlinear least squares (NLS) method, and then using natural conjugate and Jeffreys' priors we approximate the marginal posterior distribut...

In this paper we use the Gibbs sampling algorithm to develop a Bayesian inference for multiplicative double seasonal moving average (DSMA) models. Assuming the model errors are normally distributed and using natural conjugate priors, we show that the conditional posterior distribution of the model parameters and variance are multivariate normal and...

In this paper we use the Gibbs sampling algorithm to develop a Bayesian inference for multiplicative double seasonal autoregressive moving average (DSARMA) models. Assuming the model errors are normally distributed and using Jeffryes’ and natural conjugate priors, we show that the conditional posterior distribution of the model parameters and the v...

This paper aims at comparing the accuracy of the two approaches, the analytical approximations and the Markov Chain Monte Carlo approaches, for MA and ARMA model via an extensive simulation studies. In addition, real life examples are analyzed using the methods of the two approaches.

This chapter gives a summary of the state-of-the-art approaches from different research fields that can be applied to continuously forecast future developments of time series data streams. More specifically, the input time series data contains continuously monitored metrics that quantify the amount of incoming workload units to a self-aware system....

There is an increasing global attention to the need to tackle inequality, especially its spatial dimensions. This is because of the negative implications of spatial inequality on the economic growth and poverty. Amidst a growing concern about increasing inequality, the spatial dimensions of inequality have begun to attract considerable policy inter...

In this paper we develop a Bayesian inference for a multiplicative double seasonal autoregressive (DSAR) model by implementing a fast, easy and accurate Gibbs sampling algorithm. We apply the Gibbs sampling to approximate empirically the marginal posterior distributions after showing that the conditional posterior distribution of the model paramete...

In this pap er we develop a Bayesian inference for multiplicative double seasonal moving average (DSMA) model by implementing a fast, easy and accurate Gibbs sampling algorithm. We first show that the conditional posterior distribution of the model parameters and the variance are multivariate normal and inverse gamma respectively, and then we apply...

This paper introduces a fast, easy and accurate Gibbs sampling algorithm to develop a Bayesian inference for a multiplicative seasonal autoregressive moving average (SARMA) model. The proposed algorithm generates from normal and inverse gamma distributions and does not involve any Metropolis-Hastings generation. Simulated examples and a real data s...

This paper summarizes our earlier contributions on reactive and proactive detection of quality of service problems. The first contribution is applying statistical control charts to reactively detect QoS violations. The second contribution is applying time series modeling to proactively detect potential QoS violations.

Predicting future values of Quality of Service (QoS) attributes can assist in the control of software intensive systems by preventing QoS violations before they happen. Currently, many approaches prefer Autoregressive Integrated Moving Average (ARIMA) models for this task, and assume the QoS attributes' behavior can be linearly modeled. However, th...

Design of embedded systems involves a number of architecture decisions which have a significant impact on its quality. Due to the complexity of today's systems and the large design options that need to be considered, making these decisions is beyond the capabilities of human comprehension and makes the architectural design a challenging task. Sever...

Availability of several web services having a similar functionality has led to using quality of service (QoS) attributes to support services selection and management. To improve these operations and be performed proactively, time series ARIMA models have been used to forecast the future QoS values. However, the problem is that in this extremely dyn...

Currently software systems operate in highly dynamic contexts, and consequently they have to adapt their behavior in response to changes in their contexts or/and requirements. Existing approaches trigger adaptations after detecting violations in quality of service (QoS) requirements by just comparing observed QoS values to predefined thresholds wit...

As modern software systems operate in a highly dynamic context, they have to adapt their behaviour in response to changes in their operational environment or/and requirements. Triggering adaptation depends on detecting quality of service (QoS) violations by comparing observed QoS values to predefined thresholds. These threshold-based adaptation app...

Software Reliability is considered the key factor for software system quality. Several models have been presented to estimate and predict this reliability, and Software Reliability Growth models (SRGMs) are the most commonly used for this goal. SRGMs assumptions, applicability and predictability are important issues and need to be addressed. This r...

This paper introduces a fast, easy and accurate Gibbs sampling algorithm to develop a Bayesian inference for multiplicative seasonal ARMA model. The proposed algorithm generates from normal and inverse gamma distributions and does not involve any Metropolis-Hastings generation. Simulated examples and a real data set are used to illustrate the propo...

This paper develops a Bayesian inference for a multiplicative seasonal ARMA model by implementing a fast, easy and accurate Gibbs sampling algorithm. The proposed algorithm does not involve any Metropolis-Hastings generation but is generated from normal and inverse gamma distributions. The proposed algorithm is illustrated using simulated examples...

The Ministry of Health and Population, in collaboration with the ministries and agencies concerned with the population problem. Developed a National Strategic Plan 2007-2017, to reach total fertility rate of (2.1 children per woman) by 2017 at the National level. Accordingly, this study is seeking to develop the quantitative values for the monitori...

In this report, we first review the international experiences of House Price Index (HPI), and we then propose a methodology to apply this index in Egypt. (This report is in Arabic.)