This thesis is focused on mathematical modelling of exchange rate CZK/USD in 1991 - 2014. Time series was divided into 5 parts. First Box-Jenkins methodology models were examined, especially ARIMA model. Unfortunately, the model could not be used because none of the time series showed correlation. The time series is considered as a white noise. The data appear to be completely random and unpredictable. The time series have not constant variance neither normal distribution and therefore GARCH volatility model was used as the second model. It is better not to divide time series when using model of volatility. Volatility model contributes to more accurate prediction than the standard deviation. Results were calculated in RStudio software and MS Excel.

近年來由於亞洲金融風暴的肆虐，產生經濟不景氣，使得失業的問題逐漸受到社會所關注，本論文企圖以三個時間序列方法：1.單變量ARIMA模型；2.轉換函數(TF)模型；3.向量自迴歸(VAR)模型來建立台灣地區的失業率時間序列預測模型。資料則是利用台灣地區民國75年1月至民國87年12月的失業率月資料作實證預測分析，為了知道資料是否來自時間趨勢模型，測試是否經過差分消掉一部份的記憶會發生預測的誤差，所以先以多步(multi-step)預測和一步(one-step)預測的方法計算出民國88年1月至88年12月預測值，而預測評估準則則採用(1)MAPE、RMSPE、MPE及泰爾不等係數(THEIL)；(2)變化方向誤差與趨勢變化誤差兩大方向來做預測比較。最後將算出的12期預測值與行政院主計處整體統計資料庫中所得到的失業率實際值利用預測評估準則做比較，結果發現一步預測法較多步預測法準確；而向量自迴歸模型(VAR)在大部份的預測期數上有較小的MAPE、RMSPE、MPE及THEIL值，因為此VAR模型考慮了在變數之間的共整合現象，有助於模型的預測，所以有較好預測的能力；反而是較複雜的ARIMA模型及轉換模型預測能力稍差一點。 / In this thesis, we plan to construct three time series models to forecast the Taiwan unemployment Rate. These time series models are ARIMA model、transfer function (TF) model and Vector Autoregressive (VAR) model. The data set consists of monthly observations for the period 75:1-87:12 for unemployment rate. We want to know if the data came from time trend model. First, we use multi-step forecasting and one-step forecasting to calculate 12 forecasted values from 88:01-88:12. Then We compare the prediction performance of these two methods by using：(1) MAPE、RMSPE、MPE and Theil’s Inequality Coefficient (THEIL)；(2) Direction of Change Error and trend Change Error etc. It is found that one-step forecasting is more correct than multi-step forecasting and the forecasting performance of VAR model is improved by explicitly taking account of cointegration between the variables in the model，so VAR model has lower MAPE、RMSPE、MPE and THEIL for most horizons. However，the more parsimonious ARIMA and transfer function models have higher MAPE、RMSPE、MPE for most horizons.

本篇論文擴充Ang et al. (2007)之基本架構,分別建構台灣各式月資料與季資料的物價指數預測模型,並進行預測以及實證分析。我們用以衡量通貨膨脹率的指標為 CPI 年增率與核心CPI 年增率。我們比較貨幣模型、成本加成模型、6 種不同設定的菲力浦曲線模型、3 種期限結構模型、隨機漫步模型、 AO 模型、ARIMA 模型、VAR 模型、主計處(DGBAS)、中經院(CIER) 及台經院(TIER) 之預測。藉由此研究,我們可以完整評估出文獻上常用之各式月資料及季資料預測模型的優劣。 我們實證結果顯示,在月資料預測模型樣本外預測績效表現方面, ARIMA 模 型對 2 種通貨膨脹率指標的樣本外預測能力表現最好。至於季資料預測模型樣本外預測績效表現, ARIMA 模型對未來核心 CPI 年增率的樣本外預測能力表現最好; 然而,對於 CPI 年增率為預測目標的預測模型則不存在最佳的模型。此外,實證分析中我們也發現本研究所建構的模型預測表現仍遜於主計處的預測,但部份模型的樣本外預測能力表現則比中經院與台經院的預測為佳。 / This paper compares the forecasting performance of inflation in Taiwan. We conduct various inflation forecasting methods (models) for two inflation measures(CPI growth rate and core-CPI growth rate) by using monthly and quarterly data. Besides the models of Ang et al. (2007), we also consider some macroeconomic models for comparison. We compare some Monetary models, Mark-up models, six variants of Phillips curve models, three variants of term structure models, a Random walk model, an AO model, an ARIMA model, and a VAR model. We also compare the forecast ability of these model with three different survey forecasts (the DGBAS, CIER, and TIER surveys). We summarized our findings as follows. The best monthly forecasting model for both inflation measures is ARIMA model. For quarterly core-CPI inflation, ARIMA model is also the best model; however, when comparing the quarterly forecasts for CPI inflation, there does not exist the best one. Besides, we also found that the DGBAS survey outperforms all of our forecasting methods/models, but some of our forecasting models are better than the CIER and TIER surveys in terms of MAE.