This article investigates the detection and identification problems for changing of regimes about non-linear time series process. We apply the concept of genetic algorithm and AIC criterion to test the changing of regimes. This way is different from traditional detection methods According to our statistical decision procedure, the mean of moving average and the genetic detection for the underlying time series will be considered to decide change points. Finally, an empirical application about the detection and identification of change points for the Taiwan Business Cycle is illustrated.

The huge volume of time series data generated in many applications poses new challenges in the techniques of data storage, transmission, and computation. Further more, when the time series are in the form of streaming data, new problems emerge and new techniques are required because of the streaming characteristics, e.g. high volume, high speed and continuous flowing. Approximate representation is one of the most efficient and effective solutions to address the large-volume-high-speed problem. In this thesis, we propose a dynamic representation scheme for streaming time series. Existing methods use a unitary function form for the entire approximation task. In contrast, our method adopts a set of function candidates such as linear function, polynomial function(degree ≥ 2), and exponential function. We provide a novel segmenting strategy to generate subsequences and dynamically choose candidate functions to approximate the subsequences. / Since we are dealing with streaming time series, the segmenting points and the corresponding approximate functions are incrementally produced. For a certain function form, we use a buffer window to find the local farthest possible segmenting point under a user specified error tolerance threshold. To achieve this goal, we define a feasible space for the coefficients of the function and show that we can indirectly find the local best segmenting point by the calculation in the coefficient space. Given the error tolerance threshold, the candidate function representing more information by unit parameter is chosen as the approximate function. Therefore, our representation scheme is more flexible and compact. We provide two dynamic algorithms, PLQS and PLQES, which involve two and three candidate functions, respectively. We also present the general strategy of function selection when more candidate functions are considered. In the experimental test, we examine the effectiveness of our algorithms with synthetic and real time series data sets. We compare our method with the piecewise linear approximation method and the experimental results demonstrate the evident superiority of our dynamic approach under the same error tolerance threshold.

<p>Economic growth around the world has not been equal for a long time. Some economics grow faster while others grow slower. But economists have predicted that the slower growing economics will eventually converge with the faster growing economy as some point in the future. This is known as the convergence hypothesis. In this study, we test this hypothesis for Ghana and the Western Europeans countries with UK been a proxy for these countries, using time series data to determine whether or not it holds. We determine how fast or slow this convergence process is by using the returns to scale concept on Ghana’s economy and latter account for factor that determines economic growth in sectors. The study supported the null hypothesis of convergence i.e. Ghana is catching up with the Western European countries. The study also shown that Ghana growth accounting exhibit decreasing returns meaning convergence is relatively slow and also signifies that Ghana is not on a balanced growth path (this refers to the simultaneous, coordinated expansion of several sectors of the economy). The study showed a negative relationship between GDP and labour both in the long run and short run relationship. Again the study showed a positive relationship between GDP and capital, Agric and Industrial sector. Lastly, the study showed a negative relationship between GDP and AID and Service in the long run and positive relationship in the short run.</p>

Thesis (Ph. D.)--University of Rhode Island, 2005. / Typescript. Includes bibliographical references (v. 2: leaves 582-593).

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 110-114).

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We investigate conditions for the ergodicity of threshold autoregressive time series by embedding the time series in a general state Markov chain and apply a FosterLyapunov drift condition to demonstrate ergodicity of the Markov chain. We are particularly interested in demonstrating V uniform ergodicity where the test function V () is a function of a norm on the statespace. In this dissertation we provide conditions under which the general state space chain may be approximated by a simpler system, whether deterministic or stochastic, and provide conditions on the simpler system which imply V uniform ergodicity of the general state space Markov chain and thus the threshold autoregressive time series embedded in it. We also examine conditions under which the general state space chain may be classified as transient. Finally, in some cases we provide conditions under which central limit theorems will exist for the V uniformly ergodic general state space chain.

Economic growth around the world has not been equal for a long time. Some economics grow faster while others grow slower. But economists have predicted that the slower growing economics will eventually converge with the faster growing economy as some point in the future. This is known as the convergence hypothesis. In this study, we test this hypothesis for Ghana and the Western Europeans countries with UK been a proxy for these countries, using time series data to determine whether or not it holds. We determine how fast or slow this convergence process is by using the returns to scale concept on Ghana’s economy and latter account for factor that determines economic growth in sectors. The study supported the null hypothesis of convergence i.e. Ghana is catching up with the Western European countries. The study also shown that Ghana growth accounting exhibit decreasing returns meaning convergence is relatively slow and also signifies that Ghana is not on a balanced growth path (this refers to the simultaneous, coordinated expansion of several sectors of the economy). The study showed a negative relationship between GDP and labour both in the long run and short run relationship. Again the study showed a positive relationship between GDP and capital, Agric and Industrial sector. Lastly, the study showed a negative relationship between GDP and AID and Service in the long run and positive relationship in the short run.

This dissertation contains five chapters. An introduction and a summary of the research are given in Chapter 1. The other four chapters present theoretical results on the moment structure of GARCH processes. Some chapters also contain empirical examples in order to illustrate applications of the theory. The focus, however, is mainly on statistical theory. Chapter 2 considers the moments of a family of first-order GARCH processes. First, a general condition of the existence of any integer moment of the absolute values of the observations is given. Second, a general expression of this moments as a function of lower-order moments is derived. Third, the kurtosis and the autocorrelation function of the squared and absolute-valued observations are derived. The results apply to a host of different GARCH parameterizations. Finally, the existence, or the lack of it, of the theoretical counterpart to the so-called Taylor effect for some members of this GARCH family is discussed. The asymmetric power ARCH model is a recent addition to time series models that may be used for predicting volatility. Its performance is compared with that of standard models of conditional heteroskedasticity such as GARCH. This has previously been done empirically. In Chapter 3 the same issue is studied theoretically using unconditional fractional moments for the A-PARCH model that are derived for the purpose. The role of the heteroskedasticity parameter of the A-PARCH process is highlighted and compared with corresponding empirical results involving autocorrelation functions of power-transformed absolute-valued return series.In Chapter 4, a necessary and sufficient condition for the existence of the unconditional fourth moment of the GARCH(p,q) process is given as well as an expression for the moment itself. Furthermore, the autocorrelation function of the centred and squared observations of this process is derived. The statistical theory is further illustrated by a few special cases such as the GARCH(2,2) process and the ARCH(q) process.Nonnegativity constraints on the parameters of the GARCH(p,q) model may be relaxed without giving up the requirement of the conditional variance remaining nonnegative with probability one. Chapter 5 looks into the consequences of adopting these less severe constraints in the GARCH(2,2) case and its two second-order special cases, GARCH(2,1) and GARCH(1,2). This is done by comparing the autocorrelation function of squared observations under these two sets of constraints. The less severe constraints allow more flexibility in the shape of the autocorrelation function than the constraints restricting the parameters to be nonnegative. The theory is illustrated by an empirical example. / Revised versions of chapters 2-5 have been published as:He, C. and T. Teräsvirta, "Properties of moments of a amily of GARCH processes" in Journal of Econometrics, Vol. 92, No. 1, 1999, pp173-192.He, C. and T. Teräsvirta, "Statistical Properties of the Asymmetric Power ARCH Process" in R.F. Engle and H. White (eds) Cointegration, causality, and forecasting. Festschrift in honour of Clive W.J. Granger, chapter 19, pp 462-474, Oxford University Press, 1999.He, C. and T. Teräsvirta, "Fourth moment structure of the GARCH(p,q) process" in Econometric Theory, Vol. 15, 1999, pp 824-846.He, C. and T. Teräsvirta, "Properties of the autocorrelation function of squared observations for second order GARCH processes under two sets of parameter constraints" in Journal of Time Series Analysis, Vol. 20, No. 1, January 1999, pp 23-30.

This thesis consists of five self-contained papers, which are all related to the financial markets in the three Baltic States, Estonia, Latvia and Lithuania.  Paper [I] studies the impact of news from the Moscow and New York stock exchanges on the returns and volatilities of the Baltic States' stock market indices using a time series model that accounts for asymmetries in the conditional mean and variance functions. We find that news from New York has stronger e¤ects on returns in Tallinn. High-risk shocks in New York have a stronger impact on volatility in Tallinn, whereas volatility in Vilnius is more in.uenced by high-risk shocks from Moscow. Riga does not seem to be affected by news arriving from abroad. Paper [II] suggests a nonlinear and multivariate time series model framework that enables the study of simultaneity in returns and in volatilities, as well as asymmetric effects arising from shocks and exogenous variables. The model is employed to study the three Baltic States' stock exchanges. Using daily data, we find recursive structures, with returns in Riga, directly depending on returns in Tallinn and Vilnius, and Tallinn on Vilnius. For volatilities, both Riga and Vilnius depend on Tallinn. Paper [III] studies the link between political news, and the returns and volatilities in the Baltic States' stock markets. We find that domestic and foreign non-Russian political news led, on average, to lower uncertainty in the stock markets of Riga and Tallinn in 2001-2003. At the same time, political risk from Russia increased the volatility of the stock market in Tallinn. There is a weak relationship between political risk and the stock market volatility in the Baltic countries in 2004-2007. Paper [IV] studies the impact of market jumps on the time varying return correlations between stock market indices in the Baltic countries. An EARJI-EGARCH model facilitating direct modeling of the time varying return correlations is introduced. The empirical results indicate that there are quite a large number of identified jumps in the emerging Baltic States' stock markets. Isolated market jumps in one of the markets generally have no or small e¤ects on the time-varying correlations. In contrast, simultaneous jumps of equal sign increase the average correlation, in some cases by as much as 100 percent. In Paper [V] the hypothesis that financial development promotes economic growth is tested for the three Baltic countries using a time series approach that allows for interactions between the countries. We find that economic growth is a positive function of financial development, proxied by the amount of bank credit to the private sector, in the long run. The results also show that there is long run interaction between the three Baltic countries.