本論文提出統計方法，檢定動態追蹤資料是非定態，或者服從非線性平滑轉換但穩定之隨機過程。在本文所討論的追蹤資料中，我們假設橫斷面資料間是獨立的，但允許每一橫斷面有自己獨特的序列相關及固定成份。根據各橫斷面資料之自我迴歸參數及轉換速度相等與否，我們將追蹤資料區分成同質與異質兩種。在同質追蹤資料中，我們首先去除各橫斷面獨特的序列相關及固定成份，之後合併正規化後(normalized)的資料以形成追蹤資料單根檢定統計量。至於異質追蹤資料，我們首先運用Kapetanios, Shin and Snell (2003)或Kapetanios and Shin (2003)所提出的方法對每一橫斷面形成單根檢定統計量，之後再運用這些統計量形成追蹤資料單根檢定統計量。我們運用兩種方法形成異質追蹤資料單根檢定統計量：其一是Im, Pesaran and Shin (2003)所提出的方法，將所有橫斷面資料的單根統計量加以平均，並依據此平均值形成統計量；其二是Maddala and Wu (1999)及Choi (2001)所提出的方法，將各橫斷面統計量之p值加以合併，並運用此合併p值來做檢定。
運用序列極限理論(sequential limit theory)，首先令T (時間數列維度)→∞，接下來令N (橫斷面維度)→∞，我們可以證明所提出的統計量在單根的虛無假說之下，各統計量均服從標準常態分配。我們亦運用蒙地卡羅模擬以檢定所提出之統計量的小樣本性質；整體而言，模擬結果證明我們所提出的統計量具有不錯的小樣本性質。運用本論文所提出的檢定方法到OECD實質匯率資料上時，檢定結果提供了支持PPP的證據。

This thesis proposes test procedures to detect the presence of nonstationarity in dynamic panels against nonlinear but globally stationary exponential smooth transition autoregressive dynamic panels. The panels are assumed to be cross sectionally independent but each cross section is allowed to have its own short run dynamics and deterministic components. Based on whether the autoregressive parameters and speed of transition are identical or not across individuals, our panel models are classifies as homogeneous or heterogeneous. In homogeneous panels, we pool all cross section data to form a unit root test statistics after some normalization applied to each cross section data to control for the difference in short run dynamics and deterministic components. Whilst in heterogeneous panels, we first apply time series unit tests proposed by Kapetanios, Shin and Snell (2003) or Kapetanios and Shin (2003) to each cross section and then the panel unit root test statistics are formed by some transformation of these individual unit root test statistics. Two forms of transformation are used: one is the simple average of individual test statistics proposed by Im, Pesaran and Shin (2003) and the other is Fisher combined p-values statistics proposed in Maddala and Wu (1999) and Choi (2001).
By using sequential limit theory, i.e., first T (the time series dimension) →∞ and then N (the cross section dimension) →∞, our test statistics are shown to converge in probability to a standard normal variate under the null of a common unit root. The finite sample properties of proposed test statistics are examined through Monte Carlo simulations. Overall, the simulation results indicate that our proposed test statistics performs well in terms of size and power. Application of the proposed test statistics to OECD real exchange rate data provides some evidence in favor of PPP hypothesis.

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