| dc.contributor.advisor | 薛慧敏 | zh_TW |
| dc.contributor.advisor | Hsueh, Huey-Miin | en_US |
| dc.contributor.author (Authors) | 黃詩涵 | zh_TW |
| dc.contributor.author (Authors) | Huang, Shih-Han | en_US |
| dc.creator (作者) | 黃詩涵 | zh_TW |
| dc.creator (作者) | Huang, Shih-Han | en_US |
| dc.date (日期) | 2024 | en_US |
| dc.date.accessioned | 5-Aug-2024 13:59:52 (UTC+8) | - |
| dc.date.available | 5-Aug-2024 13:59:52 (UTC+8) | - |
| dc.date.issued (上傳時間) | 5-Aug-2024 13:59:52 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0111354020 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/152778 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 統計學系 | zh_TW |
| dc.description (描述) | 111354020 | zh_TW |
| dc.description.abstract (摘要) | 時間序列分析是統計學中分析具有時間順序的資料點的方法，主要解釋資料趨勢和季節性變化，被廣泛應用於多個領域。近年來，除了一般常見的連續型態資料，在生醫、資訊、自然領域也可見類別型態時間序列資料。針對最簡化的類別型態時間序列—二元時間序列資料，Jentsch與Reichmann（2019）提出了廣義二元自迴歸（gbAR，generalized binary Autoregressive）模型及廣義二元自迴歸移動平均（gbARMA，generalized binary Autoregressive Moving Average）模型來描述前後觀測值的正負相關趨勢，他們在論文中主要介紹該模型的性質，以一實例說明模型估計的結果，但未深入研究模型估計的表現。我們針對gbAR模型提出兩種依據赤池信息量準則（AIC，Akaike Information Criterion）選取模型階數的方法：在第一個方法中，我們確實推導各階gbAR模型對應的AIC；第二個便捷的分析方法—將資料視為連續型時間序列並配適AR模型，以各階AR模型對應的AIC準則選取階數。透過模擬研究，我們發現雖然第一個方法在多數情況有較高準確率，但兩者差異不大。我們也透過一個實例來應用這兩個方法。最終，我們認為在時間有限的情況下，可以將二元時間序列資料直接配適AR模型，並利用現有的公開且免費的電腦計算套件選取階數。給定階數後，再在gbAR模型下進行模型配適、估計參數等資料分析。 | zh_TW |
| dc.description.abstract (摘要) | Time series analysis is a statistical method for analyzing sequential data points over time. It helps in understanding data trends and seasonal changes and is widely applied to various fields. In recent years, in addition to continuous-type time series, categorical time series data has also gained prominence in biomedicine, information science, and the natural sciences. Specifically, binary time series is the simplest form. Jentsch and Reichmann (2019) propose the generalized binary autoregressive (gbAR) model and the generalized binary autoregressive moving average (gbARMA) model, which enable the description of positive and/or negative correlations between observations in a binary time series. In their study, the authors introduce the properties of these models. Except for providing an illustrative real example, they do not investigate the performance of statistical inference. In this study, we focus on the problem of order selection of the gbAR model. We propose two methods based on the Akaike Information Criterion (AIC) to evaluate their performance. In the first method, the AICs corresponding to various gbAR models are derived. In the second method, we naively treat the data as a continuous time series and select the order based on the AIC criterion corresponding to AR models. We compare the two methods through a simulation study. A real example is also provided for demonstration. We find that the first method has higher accuracy than the second one. However, the difference between the two methods is slight. In summary, we conclude that for order selection of a gbAR model, simply using the existing public computer packages developed for AR models can produce satisfactory results. | en_US |
| dc.description.tableofcontents | 第一章 緒論 7
第二章 研究方法 11
第一節 資料 11
第二節 gbAR模型 11
一、gbAR(p) 11
二、gbAR模型的定態條件 13
三、gbAR模型的性質 13
四、Yule-Walker方程式與估計 14
五、階數p的選取—AIC準則 15
第三章 模擬 18
第一節 階數p=1之模擬實驗 19
第二節 階數p=2之模擬實驗 26
第三節 階數p=3之模擬實驗 33
第四章 實例分析 43
第五章 結論 47
參考文獻 49 | zh_TW |
| dc.format.extent | 4761475 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0111354020 | en_US |
| dc.subject (關鍵詞) | 自迴歸 | zh_TW |
| dc.subject (關鍵詞) | 廣義二元自迴歸 | zh_TW |
| dc.subject (關鍵詞) | 二元時間序列 | zh_TW |
| dc.subject (關鍵詞) | 模型選取 | zh_TW |
| dc.subject (關鍵詞) | 赤池訊息量準則 | zh_TW |
| dc.subject (關鍵詞) | gbAR | en_US |
| dc.subject (關鍵詞) | AR | en_US |
| dc.subject (關鍵詞) | Binary time series | en_US |
| dc.subject (關鍵詞) | Model selection | en_US |
| dc.subject (關鍵詞) | AIC | en_US |
| dc.title (題名) | 二元時間序列分析：運用AIC準則選取gbAR模型的階數 | zh_TW |
| dc.title (題名) | Using AIC for Order Selection in a gbAR Model for Binary Time Series | en_US |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (參考文獻) | Akaike, H. (1974). A new look at the statistical model identification. IEEE transactions on automatic control, 19(6), 716-723.
Fokianos, K., & Kedem, B. (2003). Regression theory for categorical time series. Statistical science, 18(3), 357-376.
Guttorp, P. (1986). On binary time series obtained from continuous time point processes describing rainfall. Water Resources Research, 22(6), 897-904.
Jacobs, P. A., & Lewis, P. A. W. (1982). Stationary discrete autoregressive-moving average time series generated by mixtures (p. 0039). Naval Postgraduate School.
Jentsch, C., & Reichmann, L. (2019). Generalized binary time series models. Econometrics, 7(4), 47.
Schwarz, G. (1978). Estimating the dimension of a model. The annals of statistics, 461-464.
Shao, J. (1997). An asymptotic theory for linear model selection. Statistica sinica, 221-242.
Shumway, R. H., Stoffer, D. S., & Stoffer, D. S. (2000). Time series analysis and its applications (Vol. 3). New York: springer.
Stoffer, D. S., Scher, M. S., Richardson, G. A., Day, N. L., & Coble, P. A. (1988). A Walsh—Fourier Analysis of the Effects of Moderate Maternal Alcohol Consumption on Neonatal Sleep-State Cycling. Journal of the American Statistical Association, 83(404), 954-963.
Tymchuk, A. P., & Iepik, M. (2022). Forecasting of Categorical Time Series Using Computing with Words Model.
Whittle, P. (1951). Hypothesis testing in time series analysis. (No Title).
Wold, H. (1938). A study in the analysis of stationary time series (Doctoral dissertation, Almqvist & Wiksell).
劉祥雯(2016). 以統計模型分析肺癌發生率及死亡率之長期趨勢. 國立臺灣大學流行病學與預防醫學研究所學位論文, 2016, 1-95.
吳易樺、黃朝熙、劉子衙（2014）。時間序列模型對我國產業成長預測之優劣比較。應用經濟論叢，(96)，35-68。doi:10.3966/054696002014120096002
張永鵬、方俊傑、彭德興、康淵、王俊傑（2016）。統計製程管制於砂輪再削銳時機之判斷。技術學刊，31(2)，69-75。 | zh_TW |
