在進行時間數列分析前，研究人員常常需要決定應該使用何種資料頻率較為適當。 為了能夠擁有較多的樣本觀測值，通常試著使用頻率較高的時間數列資料來作分析。然 而，在進行時間數列實證研究時，所面臨到的經常是資料頻率與時間長短皆不同。常用 的作法是將各資料的時間間隔依照其資料的特性（流量或存量變數）分別利用加總或採 系統抽樣的方式轉換成相同頻率的資料。過去有很多文獻說明資料經由其頻率的整合會 潛在破壞變數間之關係。這種方式除了會損失資料本身的訊息之外，還可能影響變數間 之關係，進而導致做了不適當的決策與建議。 本計畫之主要目的列述如下： 1. 本計畫第一年度首先將研究時間間隔對於這四種不同型態的資料：加法型、乘法 型、系統抽樣或多期平均，對於兩兩變數間相關性及簡單迴歸的影響，並推廣至 複迴歸模式下的架構，作一個完整的說明。 2. 本計畫第二年度將此議題應用在股票報酬變異對於其預測績效之影響。藉由不同 的時間間隔，針對不同的預測模型，包括：GARCH,、EGARCH、類神經網路和 混合式模型比較其樣本外之預測能力。另外，在產品供應鏈中，每一個零售商之 需求過程是序列相關之時間數列。不同的時間間隔將會影響兩變數間之相關性， 同時資訊分享的價值也將會受到資料頻率的影響。因此，第二年度將研究不同的 時間間隔對於零售需求與降低之存貨持有成本兩變數間相關性的影響。
In time series analysis of a given set of variables, practitioners often have to decide whether to use monthly, quarterly, or annual data. They usually try to use the time series data of the higher frequency in order to increase the number of observations. However, time series data of different frequencies and different time spans are often available to empirical studies. They are usually changed to a common time interval through temporal aggregation or systematic sampling, depending on whether the variables are flow variables or stock variables respectively. Several papers have documented the fact that time aggregation potentially distorts the relationship between variables. This approach, apart from losing information, may defeat the purpose of using the association between variables so as to make a correct decision or to forecast a key variable of interest. The objectives of this project can be summarized as follows: 1. In the first year, the objective of this work is to investigate the problem of the time interval effect of the association between two variables that are additive, multiplicative, systematically sampled or temporal aggregated. We also study the impact on model structure and parameter estimation in simple and multiple regression models. 2. In the second year, we discuss and compare recent innovations in forecast stock return volatility by using various time intervals. Out-of-sample comparisons reveal that semiparametric ANN model captures volatility effects overlooked by GARCH, EGARCH models. We also demonstrate that the forecasting performance in forecast combining with artificial neural networks and linear regression models. Moreover, the correlation coefficient between retailers’demands will not be independent of the differencing interval. The value of information sharing will also be affected by the time interval employed. In the second year, this project also studies the impact of various arbitrary time intervals on the correlation coefficient between retailers’ demands and the reduction in the inventory holding cost in a supply chain.
