In this paper, we have employed the Kourtellos et al. (2007) threshold model to examine the relationship between inflation and relative price variability in Hong Kong, Argentina, Germany, Japan, Mexico and Philippines. Empirical results from Hong Kong, Japan and Mexico show that inflation are endogenous variables, and the relationship between these two variables appears to be a V shape for Hong Kong and Japan. However, the relationship appears to be positive for Mexico. Empirical results fail to reject the hypothesis of exogenous inflation for Argentina, Germany and Philippines, and the relationship between these two variables appears to be a V shape for Philippines and Argentina. There is no significant relationship between these two variables for Germany.

In recent years, sleep medicine has attracted many interests. Among many sleep disorder problems, the sleep apnea syndrome is of great importance. One of its side effects is its negative influences on cardiovascular system whose function can be monitored by ECG. The regulation of the heart rate is extremely important for human body. In general, the heart rate variability is controlled by the balance of the sympathetic and the parasympathetic systems whose functions can be influenced by sleep apnea. This work tries to establish the relation between the heart rate variability and AHI (Apnea & hypopnea index). Through the statistical methods, we analyze how the sleep apnea influences the low frequency (LF) and high frequency components of the RR intervals. With BMI, age and AHI as the independent variables, we set up the regression model to predict LF/HF Our results demonstrate that, for men, the linear relationship between the LF/HF and AHI is statistically significant when AHI is higher than 45. This results may shed some light on developing HRV based diagnosis method for sleep apnea.

Abstract Generally speaking, when dealing with some data, our analysis will be limited because of the given data was incompletely or hidden. And these kinds of errors in calculation will arrive at a statistics answer. This thesis adopts an analysis based on the Gibbs sampling trying to recover the part of hidden data. Since we found out whether time series is unit root or not, the effects of the simulated series will be similar to the true value. After observing the differences between the hidden data and the recovered data in unit root, we noticed that the hidden data has a bigger size and a weakened power over the recovered data. Finally, as an example, we give the unsecured loans at the Japanese money market to prove our issues by analyzing the data from January, 1999 to July, 2004. Since we found out that the numerical value of loan is zero at several months these past several years. In order to observe the Japanese money market, if we substitute the data of zero loan and use the traditional way to inspect unit root without taking model of average value into account, the result will be I(0). And if we simulate the hidden data with Gibbs sampling and substitute the data to inspect the Japanese money market without taking model of average value into account, the result will be I(0) also. But if we take model of average value into account, the of the Japanese Money Market will be I(1). And if we simulate the hidden data with Gibbs sampling and substitute the data to inspect the Japanese money market, the result will be I(I) also.

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In this work, we discuss the accuracy of measurements for electromagnetic. The two kinds of antenna we use are Dipole antenna and Broadband antenna. In general, if the antenna measurements we recorded at different frequencies do not exceed the ideal value $pm 4$dB, we would regard this site as a normalized site, otherwise it is not a normalized site(just a measurement exceeds the range). Traditionally, all we use is Dipole antenna, but due to difficulty of operation and inaccuracy of Dipole antenna, we investigate by statistical methods if we may use the Broadband antenna to replace the traditional Dipole antenna to measure. First of all, we introduce the data and procedure in the experiments, and fit a statistical regression model to predict the measurements at different frequencies in different test setups. Then, according to the data we collected, use the change point models to modify the statistical models. Our goal is to find a suitable statistical model for the measurements. Finally, we compare the measurements of Broadband antenna with Dipole antenna in the other experimental conditions keep the same.

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With gradually increasing interdependence of international political and economic environments, part of Asian countries' financial markets reform adopted progressive policies towards liberalization and internationalization. Therefore, the integration of international financial markets has attracted a bunch of scholars to investigate related topics of international stock market. Granger and (1993) documented that most of the economic variables have nonlinear characters. Chelley-Steeley (2004) uses smooth transition regression model to explore the financial market integration of regional and global markets among emerging and developed countries. Smooth transition regression model considered the possibility of nonlinear changes in regression parameters. This paper applies the smooth transition regression model to reinvestigate Chelley-Steeley¡¦s (2004) study of nonlinear relationship of stock markets among some East Asian countries and the United States, Japan and Germany. The main difference of our model and Chelley-Steeley¡¦ model is that we relax his constant market index correlation between two countries by allowing the autoregressive process on market index correlation. Empirical evidences of linear model, original non-linear model and our non-linear extension model show that our non-linear extension model outperformedthe other two models in terms of goodness of fit.