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.

This thesis applies Atheoretical Regression Trees (ART) to the problem of locating changes in mean in a time series where the number and location of those changes are unknown. We undertook an extensive simulation study into ART's performance on a range of time series. We found ART to be a useful addition to currently established structural break methodologies such as the CUSUM and that due to Bai and Perron. ART was found to be useful in the analysis of long time series which are not practical to analyze with the optimal procedure of Bai and Perron. ART was applied to a long standing problem in the analysis of long memory time series. We propose two new methods based on ART for distinguishing between true long memory and spurious long memory due to structural breaks. These methods are fundamentally different from current tests and procedures intended to discriminate between the two sets of competing models. The methods were subjected to a simulation study and shown to be effective in discrimination between simple regime switching models and fractionally integrated processes. We applied the new methods to 16 realized volatility series and concluded they were not fractionally integrated series. All 16 series had mean shifts, some of which could be identified with historical events. We applied the new methods to a range of geophysical time series and concluded they were not fractional Gaussian noises. All of the series examined had mean shifts, some of which could be identified with known climatic changes. We conclude that our new methods are a significant advance in model discrimination in long memory series.

Mannheim, Univ., Diss., 2006.

Zugl.: Dortmund, Techn. Univ., Diss., 2008

Zugl.: Dortmund, Techn. Univ., Diss., 2008.

The statements that include sufficient detail to identify the probability distributions of future prices are asset price dynamics. In this research, using the empirical methods that could explain the historical prices and discuss about how prices change we investigate various important characteristics of the dynamics of asset pricing. The volatility changes can explain very important facts about the asset returns. Volatility could gauge the variability of prices over time. In order to do the volatility modelling we use the conditional heteroskedasticitc models. One of the most powerful tools to do so is using the idea of autoregressive conditional heteroskedastic process or ARCH models, which fill the gap in both academic and practical literature. In this work we detect the asymmetric volatility effect and investigate long memory properties in volatility in Canadian stock market index, using daily data from 1979 through 2015. On one hand, we show that there is an asymmetry in the equity market index. This is an important indication of how information impacts the market. On the other hand, we investigate for the long-range dependency in volatility and discuss how the shocks are persistence. By using the long memory-GARCH models, we not only take care of both short and long memory, but also we compute the d parameter that stands for the fractional decay of the series. By considering the breaks in our dataset, we compare our findings on different conditions to find the most suitable fit. We present the best fit for GARCH, EGARCH, APARCH, GJR-GARCH, FIGARCH, FIAPARCH, and FIEGARCH models.

To guide action, animals anticipate what events will occur, and when they will occur, based on experience. How animals anticipate future events is an unsettled question. Although reinforcement learning is often used to model anticipation, it is resource-intensive outside of the simplest scenarios. In this dissertation, I show evidence of memory that is persistent and carries timing information, and specify an algorithm for how animals might anticipate the identity and timing of future events. This dissertation consists of two studies. In the first study, I found that identity and timing of remembered odors are jointly represented in the same cells in the dentate gyrus and lateral entorhinal cortex. Further, odor memories persist well after new odors emerge. The study analyzed results from an experiment conducted by Woods et al. (2020) on mice passively exposed to separate odors for a period of 20 s per exposure. The results are consistent with a memory framework known as timing using inverse Laplace transform (TILT). In the second study, I constructed a computational algorithm based on the TILT memory framework to anticipate the identity and timing of future events. The algorithm generates predictions based on memories of past events, and stored associations between cues and outcomes. The algorithm is resource-efficient even when the future depends on the indefinite past. The algorithm is scale-invariant and works well with chains of events. Together, the studies support a novel computational mechanism which anticipates what events will occur, and when they will occur. The algorithm could be applied in machine learning in cases of long-range dependence on history. These studies predict that behavioral and neural responses of animals could depend on events well into the past. / 2024-03-13T00:00:00Z

The dissertation considers an indirect approach for the estimation of the cointegrating parameters, in the sense that the estimators are jointly constructed along with estimating other nuisance parameters. This approach was proposed by Robinson (2008) where a bivariate local Whittle estimator was developed to jointly estimate a cointegrating parameter along with the memory parameters and the phase parameters (discussed in chapter 2). The main contributions of this dissertation is to establish, similar to Robinson (2008), a joint estimation of the memory, cointegrating and phase parameters in stationary and nonstationary fractionally cointegrated models in a multivariate framework. In order to accomplish such task, a general shape of the spectral density matrix, first noted in Davidson and Hashimzade (2008), is utilised to cover multivariate jointly dependent stationary long memory time series allowing more than one cointegrating relation (discussed in chapter 3). Consequently, the notion of the extended discrete Fourier transform is adopted based on the work of Phillips (1999) to allow for the multivariate estimation to cover the non stationary region (explained in chapter 4). Overall, the estimation methods adopted in this dissertation follows the semiparametric approach, in that the spectral density is only specified in a neighbourhood of zero frequency. The dissertation is organised in four self-contained chapters that are connected to each other, in additional to this introductory chapter: • Chapter 1 discusses the univariate long memory time series analysis covering different definitions, models and estimation methods. Consequently, parametric and semiparametric estimation methods were applied to a univariate series of the daily Egyptian stock returns to examine the presence of long memory properties. The results show strong and significant evidence of long memory in the Egyptian stock market which refutes the hypothesis of market efficiency. • Chapter 2 expands the analysis in the first chapter using a bivariate framework first introduced by Robinson (2008) for long memory time series in stationary system. The bivariate model presents four unknown parameters, including two memory parameters, a phase parameter and a cointegration parameter, which are jointly estimated. The estimation analysis is applied to a bivariate framework includes the US and Canada inflation rates where a linear combination between the US and Canada inflation rates that has a long memory less than the two individual series has been detected. • Chapter 3 introduces a semiparametric local Whittle (LW) estimator for a general multivariate stationary fractional cointegration using a general shape of the spectral density matrix first introduced by Davidson and Hashimzade (2008). The proposed estimator is used to jointly estimate the memory parameters along with the cointegrating and phase parameters. The consistency and asymptotic normality of the proposed estimator is proved. In addition, a Monte Carlo study is conducted to examine the performance of the new proposed estimator for different sample sizes. The multivariate local whittle estimation analysis is applied to three different relevant examples to examine the presence of fractional cointegration relationships. • In the first three chapters, the estimation procedures focused on the stationary case where the memory parameter is between zero and half. On the other hand, the analysis in chapter 4, which is a natural progress to that in chapter 3, adjusts the estimation procedures in order to cover the non-stationary values of the memory parameters. Chapter 4 expands the analysis in chapter 3 using the extended discrete Fourier transform and periodogram to extend the local Whittle estimation to non stationary multivariate systems. As a result, the new extended local Whittle (XLW) estimator can be applied throughout the stationary and non stationary zones. The XLW estimator is identical to the LW estimator in the stationary region, introduced in chapter 3. Application to a trivariate series of US money aggregates is employed.

This thesis examines the relationship between the distribution of structural breaks within a data sample and the estimated parameter of long memory. We use Monte Carlo simulations to generate data from processes with specific values of parameters. Subsequently we join the data with various shifts to mean and examine how the estimates of the parameters vary from their true values. We have discovered that the overestimate of the long memory parameter is higher when the breaks are clustered together. It further increases when the signs of the shifts are positively correlated within the clusters while negative correlation reduces the bias. Our findings enable the improvement of robustness of estimators against the presence structural breaks. Powered by TCPDF (www.tcpdf.org)

In the thesis we analyze sixteen commodity futures markets belonging to four families (energy type, grains, metals and other agricultural commodities) utilizing futures prices of front, back and roll futures contracts. As the tests for cointegration between front and back futures prices give us contradictory results we concentrate on roll contracts defined as the difference between front and back commodity futures contracts. We found that all commodity roll futures except natural gas and wheat futures exhibit long memory, which is usually connected with the fractal market hypothesis. Further, we employ specific ARMA and ARFIMA models and rolling window one-day-ahead technique to predict roll futures contract prices. Based on analysis of relation between resulting predictability and liquidity of roll futures contracts we concluded that lowest predictability is linked with the lowest liquidity among all commodities except metals and found evidence that predictability is positively dependent on liquidity among all commodities except metals, lumber, soybean oil and soybeans. The revealed dependence is strongest for energy type commodities. The relations and dependencies on the commodity futures markets are of high importance for all market participants such as hedge managers, investors, speculators and also for...