In this thesis, we study the unit root tests which includes the ADF, PP and KPSS tests, the long memory tests such as the R/S and GPH tests, and the applications of these methods in high frequency financial data analysis. The software SPLUS was adopted to analyze data and correction of the SPLUS program in unit tests are also proposed. To apply these two test methods in high frequency data, we quoted the library, HFlibrary designed by Yan and Zivot in 2003 for preliminary data analysis and propose a new library HFanalysis, which can be used in correcting high frequency data (excluding N.A. value, sorting transactions and retrieve a certain time of transactions), obtaining equi-distanced time intervals and testing for unit root and long memory properties. In additions, we apply this proposed library to simulate the power of traditional unit root methods such as the ADF test and long memory test method such as the R/S and to perform an empirical study. Finally, we explore the power of the ADF for testing data simulated from a threshold unit root model and simulate the percentiles of the null distribution of the following threshold unit root tests: WALD, LM, LR and W£f.

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Purchasing power parity (PPP) is considered as an important theory of explaining how exchange rate varies in the long run. Most of empirical studies in the past adapted linear cointegration method to test the purchasing power parity. However, there are papers point out that exchange rate exists non-linear cointegration and unexplainable bias might exist in testing the purchase power parity theory while using linear cointegration test. The methodology of this study is based on an application of ESTR ECM proposed by Kapetaniosetet al. to enhance the inadequate of linear cointegration test. We analyze the dynamic adjusting behavior of short-term nominal exchange rate with ESTR ECM model while the non-linear cointegratoin exists. The empirical result indicates that the purchase power parity between Taiwan and its major trading countries is confirmed. Among the trading countries, American, Japan and Hong Kong are suitable for using linear error correction model and non-linear error correction model for Singapore and Korea.

This paper applies both the Engle-Granger and Johansen cointegration test procedures to determine the existence of market linkage among high-valued ( Scomberomorus commerson, milkfish ) and low-valued (cod, Taiwan Tilapia ) fish species using monthly average wholesale price data recorded on the Taipei fisheries wholesale market. If the markets for high-valued and low-valued species are linked, say through commodities arbitrage, individual fish prices cannot diverge ¡§too far¡¨ from other fish prices before market forces to operate to restore equilibrium. From the empirical results, it indicates the existence of only one cointegrating vector involving the prices of these species in Taipei fisheries wholesale market, and that a long-run and stable substitute relationship may exist for the Scomberomorus commerson and other low-valued and high-valued species.

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.

The methodology is based on an application of nonlinear ESTR ECM by Kapetanios et al. (2006) to analyze the short-run dynamic adjustment to long-run equilibrium in Taiwan money demand function. We take consideration of Taiwan as a small open economy system, the exchange rate could be included in money demand function. The result indicate that using ESTR ECM to analyze the adjustment behavior of money demand function in Taiwan is better than linear ECM. Our findings point out that the public adjusts at any time for holding money and the speed of adjustment for real balances depends on the size of deviation.

Mainland China and Taiwan successfully joined WTO to be active members in December 2001 and January 2002. They relax economic and trade restrictions from both sides and make the relevant regulations and mechanisms more transparent year by year. Since May 2005, Mainland China implemented preferential policies, such as zero tariff, clearing customs and opening ' the fast roadway ' to many kinds of Taiwan¡¦s fruits, etc.That makes the proportion of Taiwan¡¦s fruits sold in Mainland China improve year by year, and the marketing stronghold expand constantly, too. According to the past documents and experiences, Taiwan fruit is relatively suitable for taking the gift box and up-market route, and aims at the demand of the high consumption group. Because most people in Mainland China consume the goods for freshness or the demands of giving a present, they would not purchase it in usual time. Therefore, we should avoid depending too much on some agricultural products and overly concentrate on the specific country. What we need to do is carrying on the global market survey, opening up the new service stronghold actively in order to improve the competitiveness of agricultural products in our country. In addition, the consumption habits between the South and North of Mainland China are different. We should make variable marketing strategies for different consumption ethnicities and match their demands and preferences. We set up an empirical model by using Time Series Analysis and actual data. The research includes the weight and amount sold to Mainland China, policy of zero tariff, old farmers¡¦ subsidies, areas of fruit trees, transportation and storage, Taiwan¡¦s inflation rate and processed goods of farm production. The main conclusion shows that the effect of zero tariff policy is not good enough to Taiwan¡¦s export sales. The possible reason may be that the cross-strait system is not sound. Finally, we compare the changes in production of Taiwan fruits between Years 2004-2008, and choose three levels of Taiwan fruits. The First one is new stars, like betel nuts, mango, orange, grapefruits and shakya. The second one is keeping it¡¦s level, like jujube, pineapple, guava, papaya, starfruit and wax apple. The third one is lack of competition, like coconut, peach, banana, orange, lemon, plum, persimmon, loquat, etc. The possible reason may be come from outside pressure or not suitable to plant in Taiwan.

This paper examines whether the CPI and real GDP for the US exhibit nonlinear reversion to trend as recently concluded by Beechey and Österholm [Beechey, M. and Österholm, P., 2008. Revisiting the uncertain unit root in GDP and CPI: testing for nonlinear trend reversion. Economics Letters 100, 221-223]. The wild bootstrap is used to correct for non-normality and heteroscedasticity in a nonlinear unit root test. The use of 'wild bootstrapped' critical values affects test conclusions in some cases. Results also are sensitive to the sample period examined.