動態資料往往隨著時間區間取法或測量工具的不同而有差異,此種不確定的特質我們稱為模糊性。但是傳統的時間數列仍是以確定的觀察值來記錄具有模糊性的動態資料。為了更完整的表示一個動態過程,我們考慮模糊時間數列(fuzzy time series)以具有不確定性的模糊集合來取代明確的數值,保持原來的模糊性。

本文探討模糊時間數列中模糊自我迴歸模式(fuzzy autoregressive model簡寫為 FAR 模式)的建構過程,並分別利用此模式來預測中央政府總預算和匯率。FAR 模式乃根據Box-Jenkins(1970)所提出的 ARMA 三階段模式建立的流程並推廣Zadeh(1965)所提出的模糊集合理論而來。在這過程中 ,我們考慮人類思維方法,使FAR 模式更具有彈性且適合未來預測時的需要。而對於所討論的動態過程,也不需要任何模式上的假設(例如:線性或穩定 ),因此 FAR 模式的適用範圍極為廣泛,更不會因為模式的誤判而導致預測時的嚴重錯誤。最後,我們將 FAR 模式的預測結果與傳統 ARMA 模式做比較。

文中關於模糊時間數列的一些性質,例如:模糊趨勢(fuzzy trend)和模糊穩定(fuzzy stationary),由於傳統文獻中沒有加以討論,本文亦提出定義和新的看法。

Representations of dynamic data are always different as the time interval or measuring tool change. We call these characteristics of uncertainty fuzziness. But traditional time series use crisp observations to record a fuzzy dynamic process. To completely represent, we consider fuzzy time series replacing the crisp numbers with fuzzy sets and preserve original fuzziness. In this paper, the fuzzy

autoregressive model (FAR model) of fuzzy time series is studied and used to forecast the Central government expenditure and exchange rates, respectively. The modeling process is according to Box- Jenkins' (1970) method of ARMA model and merged with the fuzzy set theory proposed by Zadeh (1965). Reasonable human judgements and ways of thinking are taken into consideration throughout the modeling process to make the FAR model more elastic and appropriate for forecasting. Unlike certain incorrectly identified models which lead to inaccurate forecasts, the FAR model can be widely applied due to its not having any assumptions on the original time series (e.g., linearity and stationarity). Finally, the performances of the FAR model to Central government expenditure and exchange rates are compared with that of the traditional ARMA model. Additionally, some properties about fuzzy time series, e.g., fuzzy trend and fuzzy stationary, have not been studied in the literature, and we propose definitions and new opinions.

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