台灣人口出生率研究

本文將研究台灣近20年(共計240筆資料)出生率的研究。首先我們先熟悉變數結構，包括敘述性統計量、散佈圖、ACF、PACF。接著我們以前220筆資料為訓練集，利用時間序列分析正規的方法(包括鑑定、估計、偵測)建構出生率的ARMA模型。接著我們用剩下的20筆測試模型的預測能力，發現有些期數的預測誤差不小，我們認為只有用出生率建構時間序列模型可能不太夠，需要引進其他能夠解釋出生率的變數來加強預測能力。因此，我們找了結婚率當作解釋變數，欲建構轉換函數模型，建構方法包括LTF法、CCF法。最後，延續轉換函數模型，我們考慮利用出生率以及結婚率來探討多元時間序列模型之間的動態結構，以二元時間序列模型描述彼此的關聯性。

關鍵字

自我相關函數；自我迴歸過程；交錯相關係數法；線性轉換函數法；移動平均模型；偏自我相關函數

並列摘要

In this study, we focused on birth rate (total 240 data) in nearly 20 years. First of all, we did exploratory data analysis to take a look the data structure, including some statistics, scatter plot, ACF and PACF. Next, we used first 220 data as our training data set, and used the standard methods (identifiability, estimation, and prediction) in time series analysis to construct ARMA model for birth rate. After constructing the model, we used remained 20 data to test the validity of ARMA model, and we found that there existed some large prediction error. We guessed that it was not powerful enough to construct model by birth rate only, so we tried to find out another variable to fit model, and tried to improve the ability of prediction. In this case, we used the rate of marriage as our explanatory variable to construct the transfer function model, which was including crossing correlation function (CCF) and linear transfer function (LTF), and we also checked their validity. Finally, we used birth rate and rate of marriage to discuss multivariate time series model, and we could describe the relation of two variables.