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Long range dependent processes occur in many fields, it is important to monitor these processes to early detect their shifts. This paper considers the problem of detecting changes in an I(d) process or an ARFIMA(p,d,q) process by statistical control charts. The control limits of EWMA and EWRMS control charts of I(d) processes are established and analytic forms are derived. The average run lengths of these control charts are estimated by Monte Carlo simulations. In addition, we illustrate the performance of the control charts by empirical examples of I(d) processes and ARFIMA(1,d,1) processes.

Syfte: Syftet med studien var att ge en utökad förståelse för hur användandet av produktplacering kan påverka tittarnas syn på en TV- serie. Metod: Ett avsnitt av den svenska TV- serien Solsidan användes på grund av dess omfattande kritik mot användandet av produktplaceringar. Empirin samlades in genom en kombination av enkäter och fokusgrupper där 21 respondenter deltog och där de fick se ett avsnitt ur serien. Teori: Teorier om minnesprocessen, varumärkeskännedom, informationshanteringsprocessen, olika dimensioner av produktplacering samt dess för- och nackdelar har använts för att sammanlänkas med studiens resultat. Slutsats: Produktplacering medförde ingen förändrad syn på TV- serien Solsidan av olika anledningar: A)    Samtliga respondenter hade en positiv inställning till produktplacering. B)    I snitt uppmärksammades endast 29 % av placeringarna. C)    De varumärken som uppmärksammades var mycket bra integrerade och påverkade inte tittarupplevelsen negativt. D)    Produktplaceringen gjorde handlingen mer realistisk och trovärdig då respondenterna kunde relatera till liknande händelser. / Purpose: The purpose of this study was to provide an enhanced understanding about how the use of product placement can affect the opinion of a TV series.   Methodology: The Swedish TV- series Solsidan was used because of its criticism about product placement. The empirical data was collected by a combination of surveys and focus groups in which 21 respondents participated and watched one episode of the series.   Theories: Theories about the memory process, brand awareness, information processing, different dimensions of product placement and its pros and cons where used to conjoin to the results.   Conclusion: Product placement did not affect the opinion on the TV- series Solsidan for different reasons: A)     All respondents had a positive attitude towards product placement. B)    The recall of the placements was on average no higher than 29 %. C)    The brands that where noticed where well integrated and did not affect the viewing experience negatively. D)    Product placement made the scene more realistic and credible as the respondents could relate to similar situations.

The main goal of this research is to estimate the model parameters and to detect multiple change points in the long memory parameter of Gaussian ARFIMA(p, d, q) processes. Our approach is Bayesian and inference is done on wavelet domain. Long memory processes have been widely used in many scientific fields such as economics, finance and computer science. Wavelets have a strong connection with these processes. The ability of wavelets to simultaneously localize a process in time and scale domain results in representing many dense variance-covariance matrices of the process in a sparse form. A wavelet-based Bayesian estimation procedure for the parameters of Gaussian ARFIMA(p, d, q) process is proposed. This entails calculating the exact variance-covariance matrix of given ARFIMA(p, d, q) process and transforming them into wavelet domains using two dimensional discrete wavelet transform (DWT2). Metropolis algorithm is used for sampling the model parameters from the posterior distributions. Simulations with different values of the parameters and of the sample size are performed. A real data application to the U.S. GNP data is also reported. Detection and estimation of multiple change points in the long memory parameter is also investigated. The reversible jump MCMC is used for posterior inference. Performances are evaluated on simulated data and on the Nile River dataset.

In applications, the true underlying model of an observed time series is typically unknown or has a complicated structure. A common approach is to approximate the true model by autoregressive (AR) equation whose orders are chosen by information criterions such as AIC, BIC and Parsen's CAT and whose parameters are estimated by the least square (LS), the Yule Walker (YW) or other methods. However, as sample size increases, it often implies that the model order has to be refined and the parameters need to be recalculated. In order to avoid such shortcomings, we propose the Regularized AR (RAR) approximation and illustrate its applications in frequency detection and long memory process forecasting. The idea of the RAR approximation is to utilize a “long" AR model whose order significantly exceeds the model order suggested by information criterions, and to estimate AR parameters by Regularized LS (RLS) method, which enables to estimate AR parameters with different level of accuracy and the number of estimated parameters can grow linearly with the sample size. Therefore, the repeated model selection and parameter estimation are avoided as the observed sample increases. We apply the RAR approach to estimate the unknown frequencies in periodic processes by approximating their generalized spectral densities, which significantly reduces the computational burden and improves accuracy of estimates. Our theoretical findings indicate that the RAR estimates of unknown frequency are strongly consistent and normally distributed. In practice, we may encounter spurious frequency estimates due to the high model order. Therefore, we further propose the robust trimming algorithm (RTA) of RAR frequency estimation. Our simulation studies indicate that the RTA can effectively eliminate the spurious roots and outliers, and therefore noticeably increase the accuracy. Another application we discuss in this thesis is modeling and forecasting of long memory processes using the RAR approximation. We demonstration that the RAR is useful in long-range prediction of general ARFIMA(p,d,q) processes with p > 1 and q > 1 via simulation studies.

In applications, the true underlying model of an observed time series is typically unknown or has a complicated structure. A common approach is to approximate the true model by autoregressive (AR) equation whose orders are chosen by information criterions such as AIC, BIC and Parsen's CAT and whose parameters are estimated by the least square (LS), the Yule Walker (YW) or other methods. However, as sample size increases, it often implies that the model order has to be refined and the parameters need to be recalculated. In order to avoid such shortcomings, we propose the Regularized AR (RAR) approximation and illustrate its applications in frequency detection and long memory process forecasting. The idea of the RAR approximation is to utilize a “long" AR model whose order significantly exceeds the model order suggested by information criterions, and to estimate AR parameters by Regularized LS (RLS) method, which enables to estimate AR parameters with different level of accuracy and the number of estimated parameters can grow linearly with the sample size. Therefore, the repeated model selection and parameter estimation are avoided as the observed sample increases. We apply the RAR approach to estimate the unknown frequencies in periodic processes by approximating their generalized spectral densities, which significantly reduces the computational burden and improves accuracy of estimates. Our theoretical findings indicate that the RAR estimates of unknown frequency are strongly consistent and normally distributed. In practice, we may encounter spurious frequency estimates due to the high model order. Therefore, we further propose the robust trimming algorithm (RTA) of RAR frequency estimation. Our simulation studies indicate that the RTA can effectively eliminate the spurious roots and outliers, and therefore noticeably increase the accuracy. Another application we discuss in this thesis is modeling and forecasting of long memory processes using the RAR approximation. We demonstration that the RAR is useful in long-range prediction of general ARFIMA(p,d,q) processes with p > 1 and q > 1 via simulation studies.

In this paper, we study the parameter estimation of the multiple linear time series regression model with long memory stochastic regressors and innovations. Robinson and Hidalgo (1997) and Hidalgo and Robinson (2002) proposed a class of frequency-domain weighted least squares estimates. Their estimates are shown to achieve the Gauss-Markov bound with standard convergence rate. In this study, we proposed a time-domain generalized LSE approach, in which the inverse autocovariance matrix of the innovations is estimated via autoregressive coefficients. Simulation studies are performed to compare the proposed estimates with Robinson and Hidalgo (1997) and Hidalgo and Robinson (2002). The results show the time-domain generalized LSE is comparable to Robinson and Hidalgo (1997) and Hidalgo and Robinson (2002) and attains higher efficiencies when the autoregressive or moving average coefficients of the FARIMA models have larger values. A variance reduction estimator, called TF estimator, based on linear combination of the proposed estimator and Hidalgo and Robinson (2002)'s estimator is further proposed to improve the efficiency. Bootstrap method is applied to estimate the weights of the linear combination. Simulation results show the TF estimator outperforms the frequency-domain as well as the time-domain approaches.

The main goal of this research is to estimate the model parameters and to detect multiple change points in the long memory parameter of Gaussian ARFIMA(p, d, q) processes. Our approach is Bayesian and inference is done on wavelet domain. Long memory processes have been widely used in many scientific fields such as economics, finance and computer science. Wavelets have a strong connection with these processes. The ability of wavelets to simultaneously localize a process in time and scale domain results in representing many dense variance-covariance matrices of the process in a sparse form. A wavelet-based Bayesian estimation procedure for the parameters of Gaussian ARFIMA(p, d, q) process is proposed. This entails calculating the exact variance-covariance matrix of given ARFIMA(p, d, q) process and transforming them into wavelet domains using two dimensional discrete wavelet transform (DWT2). Metropolis algorithm is used for sampling the model parameters from the posterior distributions. Simulations with different values of the parameters and of the sample size are performed. A real data application to the U.S. GNP data is also reported. Detection and estimation of multiple change points in the long memory parameter is also investigated. The reversible jump MCMC is used for posterior inference. Performances are evaluated on simulated data and on the Nile River dataset.

This graduate report is a description of my artistic development through the graduate program at the University of Texas at Austin. It records my development and growth as an artist in relationship to the concepts, materials, and processes I have been investigating and exploring in the past three years. The graduate report focuses on three important concerns to which I’ve been dedicated. First, materials are imperative to my work. I physically collect and use my father’s ordinary objects and transform them with raw materials, such as clay, flour, honey, chocolate, beeswax, and petroleum jelly. The decision of choosing raw materials is based on my personal and cultural experiences. I am particularly interested in exploiting raw materials because I believe these raw materials can trigger a particular memory, place, or relationship that I want to preserve and remember. Second, my process of making involves ritualistic aspects with repetitive acts. I believe that everyday practices are a way of reconstructing relationships and remembering home. I am interested in embracing emotional attributes that may be simple activities: spraying a piece daily to keep it wet or sewing a personal object until it is impossible to sew. Finally, through the relationship among the objects, repeated actions, and an anticipation that evokes magical power and charged energy, I methodically transform objects. I do this to celebrate emotions and to preserve not only these personal objects but also my memories of home. / text