5.6.3 Stationary Test
Summary
This Stationary Test tool is supported in the Time Series Analysis App. It is used to check the stationary of a time series.
Tutorial
This tutorial uses App’s built-in sample project. To open this sample OPJU file:
- Right click the Time Series Analysis App icon
in the Apps Gallery and choose Show Samples Folder.
- A folder will open. Drag-and-drop the project file TSA Sample.opju into Origin.
Stationary Test
- Expand Project Explorer docked on the left. Select folder Statistics and Test . The Book3 contains data
about Australian total wine sales by wine makers in bottles.
- Highlight Column B, and then click the Time Series Analysis App icon in the Apps Gallery.
- In the dialog, select Statistics and Test and Stationary Test tool.
- In the dialog, set Terms to Include in Regression to Constant, click the OK button.
- Then you will get the Stationarity report.
In the Augmented Dickey-Fuller (ADF) Test result table, P-value < 0.05 that means the time series dataset is stationary.
Algorithm
Stationary Test uses Augmented Dickey–Fuller (ADF) test. If the root of the characteristic equation for a time series is one then that series is said to have a unit root. Such series are nonstationary. NAG function nag_tsa_dickey_fuller_unit (g13awc) is called to calculate ADF test statistic.
The regression model
\[\nabla y_t = \beta_1y_{t-1} + \sum_{i-1}^{p-1}\delta_i\nabla y_{t-i}+\epsilon_t\]
is fitted and the test statistic \(\tau\) constructed as
\[\tau = \frac{\hat{\beta}_1}{\sigma_{11}}\]
where \(\nabla\) is the difference operator, with \(\nabla y_t = y_t - y_{t-1}\), and where \(\hat{\beta}_1\) and \(\sigma_{11}\) are the least squares estimate and associated standard error for \(\beta_1\) respectively.
To test for a unit root with drift the regression model
\[\nabla y_t = \beta_1y_{t-1} + \sum_{i-1}^{p-1}\delta_i\nabla y_{t-i}+\alpha+\epsilon_t\]
is fit and the test statistic \(\tau_\mu\) constructed as
\[\tau_\mu = \frac{\hat{\beta}_1}{\sigma_{11}}\]
To test for a unit root with drift and deterministic time trend the regression model
\[\nabla y_t = \beta_1y_{t-1} + \sum_{i-1}^{p-1}\delta_i\nabla y_{t-i}+\alpha+\beta_2t+\epsilon_t\]
is fit and the test statistic \(\tau_\tau\) constructed as
\[\tau_\tau = \frac{\hat{\beta}_1}{\sigma_{11}}\]
An associated probability can be obtained from nag_prob_dickey_fuller_unit (g01ewc).