A lot of relevant literature indicates that stock market returns for the non-linear because the stock market is volatility asymmetry. To explore the impact between the stock and macroeconomic variables, it is necessary to analyze by nonlinear model, otherwise they will be a model set of problems. I adopt a threshold autoregressive modle to analyze the relationship between the ETF return on the exchange rate and economic growth. In this study, the ETF return is the threshold variable. First, in order to rearrange the linear test regression (Arrang Regression) with the F-statistic testing whether the nonlinear effect of the grid search to find the residual sum of squares, determine the optimal threshold of backward and thresholds value. To identify the threshold, it is estimated a two-regime model analysis in positive and negative reward, the correlation between exchange rate and ETF returns Spillover effect to explain economic growth for the ETF returns and how it affects, then the data drawn into a grid map, find the number of possible structural transition point, and finally AIC formula to calculate the value of the two -regime with the three-regime model of AIC and the minimum value is the optimal model.

This paper reexamines the long-run real interest rate parity of the OECD countries by using the unit root test proposed by Ng and Perron (2001) and by the application of simulation to establish the small sample distribution under the null and the alternative hypothesis. By using the small sample distribution of the unit root statistics, we can make sure that first, size distortions are not the reasons contributing to the rejection of the fact that the alternative hypothesis is unit root. Second, the inference that the low power is not necessary causes the not rejecting the alternative hypothesis is correct. If still can not decide which distributions might cause the real interest difference series by comparing the unit root statistics and the relative location of the small sample distribution, we test that whether the series are asymmetric in those countries which we can not decide what kind of distributions they are by the threshold autoregression model proposed by Caner and Hansen (2001). Finally, the empirical results indicate that the RIPH holds in Australia¡BBelgium¡BCanada¡BFinland¡BFrance¡BGermany¡BJapan and Sweden whenever data frequency under linear time series model. Under quarterly data of Italy and United Kingdom and monthly data of Denmark, it turns out that the data have the traits of nonlinear time series model. Besides, the evidence of supporting the long-run real interest rate parity can not be reached and the phenomena that partial unit root exist in United Kingdom and Denmark.

MSc (Statistics) / Department of Statistics / Over the years researchers have been modeling inflation rate in Ghana using linear models such as Autoregressive Integrated Moving Average (ARIMA), Autoregressive Moving Average (ARMA) and Moving Average (MA). Empirical research however, has shown that financial data, such as inflation rate, does not follow linear patterns. This study seeks to model and forecast inflation in Ghana using nonlinear models and to establish the existence of nonlinear patterns in the monthly rates of inflation between the period January 1981 to August 2016 as obtained from Ghana Statistical Service. Nonlinearity tests were conducted using Keenan and Tsay tests, and based on the results, we rejected the null hypothesis of linearity of monthly rates of inflation. The Augmented Dickey-Fuller (ADF) was performed to test for the presence of stationarity. The test rejected the null Hypothesis of unit root at 5% significant level, and hence we can conclude that the rate of inflation was stationary over the period under consideration. The data were transformed by taking the logarithms to follow nornal distribution, which is a desirable characteristic feature in most time series. Monthly rates of inflation were modeled using threshold models and their fitness and forecasting performance were compared with Autoregressive (AR ) models. Two Threshold models: Self-Exciting Threshold Autoregressive (SETAR) and Logistic Smooth Threshold Autoregressive (LSTAR) models, and two linear models: AR(1) and AR(2), were employed and fitted to the data. The Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) were used to assess each of the fitted models such that the model with the minimum value of AIC and BIC, was judged the best model. Additionally, the fitted models were compared according to their forecasting performance using a criterion called mean absolute percentage error (MAPE). The model with the minimum MAPE emerged as the best forecast model and then the model was used to forecast monthly inflation rates for the year 2017. The rationale for choosing this type of model is contingent on the behaviour of the time-series data. Also with the history of inflation modeling and forecasting, nonlinear models have proven to perform better than linear models. The study found that the SETAR and LSTAR models fit the data best. The simple AR models however, out-performed the nonlinear models in terms of forecasting. Lastly, looking at the upward trend of the out-sample forecasts, it can be predicted that Ghana would experience double digit inflation in 2017. This would have several impacts on many aspects of the economy and could erode the economic gains i made in the year 2016. Our study has important policy implications for the Central Bank of Ghana which can use the data to put in place coherent monetary and fiscal policies that would put the anticipated increase in inflation under control.

本研究採用門檻迴歸模型 (Threshold Autoregression Model)，試圖找出董監事等內部人之申報轉讓比率、持股比率及質押比率等門檻值，進而分析門檻值以內及以外，指標對於代理變數：融資成長率、營收成長率以及本益比與加權指數報酬率的影響程度與方向。本研究實證結果發現： 一、在申報轉讓比率方面： 當申報轉讓比率低於門檻值，存在所謂的群聚效果。當申報轉讓比率高於門檻值時，市場動能與加權指數報酬率無顯著關係，投資人於此階段進行投資決策時應該要謹慎小心。 二、在持股比率方面： 在持股比率低於門檻值時，加權指數報酬率對於前期營收成長率表現的修正幅度較大，意謂著董監事等內部人根據其對未來營收資訊掌握的優勢，反應其對營收資訊的真實性，而藉由持股轉讓的行為，使加權指數大幅度的修正。 三、在質押比率方面： 不管高於或低於門檻值，均無法利用董監事等內部人質押比率為門檻變數來分析本益比效果對加權指數報酬率的影響。造成其檢定失效的原因，可能是樣本小且模型受到極端值的影響所造成。