Differences Tool

Contents

Summary

The Differences tool is supported in the Time Series Analysis App. It is used to transform a non-stationary time series into a stationary one.
A stationary time series has constant mean, variance, and autocorrelation over time, which makes it easier to model and forecast.

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.

Differences

  1. Expand Project Explorer docked on the left. Select folder Transform and Decompose and go to sheet "Sheet1" in workbook "Airpass".
    Simple Time Series Analysis 01 00.png
  2. Click the Time Series Analysis App icon Time Series Analysis icon.png in the Apps Gallery. Click the button Differences under the Tranform and Decompose tab to open the app dialog.
    Simple Time Series Analysis 01 0.png
  3. Select Col(B) as Time Series. For this seasonal time series dataset (the seasonal period is 12 months), select Seasonal Difference as Type, set Order to 1 and Period to 12.
    Simple Time Series Analysis 01 a.png
  4. Click OK button to get the difference result.
    Simple Time Series Analysis 01 b.png
The results you get here is calculated by formula: C[i+12]=B[i+12]-B[i]

Algorithm

Differences tool calculates non-seasonal and seasonal differencing on a time series.

This app calls nag_tsa_diff (g13aac) function [1] to calculate.

Given a time series xi, i = 1, 2, ..., n, after non-seasonal differencing of order d and seasonal differencing of order D with period s, the transformation can be expressed as:

\notag\begin{alignat}{2}\nabla^d \nabla_s^D x_i &= \nabla^d \nabla_s^{D-1} x_{i+s} - \nabla^d \nabla_s^{D-1} x_{i} \\ &= \nabla^{d-1} \nabla_s^{D} x_{i+1} - \nabla^{d-1} \nabla_s^{D} x_{i} \qquad\text{for } i=1,\, 2,\, \cdots,\, (n - d - D \cdot s)\end{alignat}

The first n - d - D \cdot s elements in the result are missing values.

Reference

1. nag_tsa_diff (g13aac)