2.2.2.3 Stationary Test

Contents

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:

  1. Right click the Time Series Analysis App icon Time Series Analysis icon.png in the Apps Gallery and choose Show Samples Folder.
  2. A folder will open. Drag-and-drop the project file TSA Sample.opju into Origin.

Stationary Test

  1. 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.
    Stationary Test 01.png
  2. Highlight Column B, and then click the Time Series Analysis App icon Time Series Analysis icon.png in the Apps Gallery.
  3. In the dialog, select Statistics and Test and Stationary Test tool.
    Stationary Test 02.png
  4. In the dialog, set Terms to Include in Regression to Constant, click the OK button.
    Stationary Test 03.png
  5. Then you will get the Stationarity report.
    Stationary Test 04.png 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).

Reference

  1. nag_tsa_dickey_fuller_unit (g13awc)
  2. nag_prob_dickey_fuller_unit (g01ewc)