目前時間序列資料的統計分析方法主要是以時間為定義域的自迴歸整合移動平均 (ARIMA)模型與以頻率為定義域的快速傅立葉轉換(FFT)模型。應用ARIMA或FFT模型都需要假設時間序列資料具有平穩性，但是實務上的資料可能在不同時間具有不同頻率的週期性變化，因此本文根據希爾伯特-黃轉換(HHT)建立時間序列的分析與推論。針對單筆時間序列進行HHT後，利用卡方適合度檢定與Ljung-Box檢定或杜賓-瓦特森檢定選取數個較高頻率的本質模態函數使合併成為為雜訊，然後整合其他較低頻率的本質模態函數為訊號，最後根據自助法針對該訊號或無參數模型建立統計推論。本文也討論如何利用HHT建立迴歸模型描述兩筆時間序列的統計相關性。文中利用2008年1月29日桃園竹圍漁港之海水位資料說明HHT雜訊在氣象海嘯研究的應用，也利用2013年1月至2017年12月桃農綜合農產品批發市場甘藍菜初秋品種之交易資料說明交易價格的時間變化。最後討論甘藍菜交易重量與交易價格的相關性。就海水位資料而言，HHT雜訊比FFT更能偵測到氣象海嘯的起始時間。 HHT訊號則比ARIMA或FFT更能適當的描述甘藍菜交易價量比的時間變化，而引入交易重量的HHT訊號能提供甘藍菜交易價格的較佳預測。基本上，當時間序列的週期隨時間變化時，應用本文所建立的HHT統計方法可以更適當的推論時間序列資料的變化或趨勢。;The current statistical analysis methods for time series are mainly based on autoregressive integrated moving average (ARIMA) and Fast Fourier Transform (FFT). Both the ARIMA and FFT assume that the time series data under study is stationary. However in practice, data may have different periods at different time. Therefore, this article considers the analysis of time series by using the statistical inference based on the Hilbert-Huang transform (HHT). The time series is decomposed by the HHT into several Intrinsic Mode Functions (IMFs), the goodness of fit test along with the Ljung-Box test or Durbin-Watson test are used to choose and combined several IMFs of high frequencies integrated to be the noise, and the other IMFs are integrated as the signal. Finally, we can build statistical inference for signal or nonparametric model based on bootstrap method. This article also discusses how to use the HHT to construct a regression model for the statistical relationship of two time series. This article uses the data of sea level recorded at the Zhuwei Fishing Harbor on Jan. 29th, 2008, to illustrate the application of HHT’s noise, and uses the transaction price of the early autumn varieties of cabbage from Taoyuan Agricultural products marketing from Jan. 2013 to Dec. 2017 to describe the variation of the transaction price over time. Finally, how the transaction weight and the transaction price is correlated is discussed. In terms of sea level data, the noise of HHT can detect the start time of meteorological tsunami more accurately than FFT. For the cabbage data, the HHT is more suitable than ARIMA or FFT to show the variation of the ratio of price and weight. Moreover, the HHT signal of the transaction weight provide a better prediction of the transaction price. To sum up, when the period of time series changes with time, applying the HHT statistical method established in this article can be more reasonably for describing the variation or trend of the time series.
