Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Nonseasonal Differencing

This example shows how to take a nonseasonal difference of a time series. The time series is quarterly U.S. GDP measured from 1947 to 2005.

Load the GDP data set included with the toolbox.

load Data_GDP
Y = Data;
N = length(Y);

figure
plot(Y)
xlim([0,N])
title('U.S. GDP')

The time series has a clear upward trend.

Take a first difference of the series to remove the trend,

$$\Delta y_t = (1-L)y_t = y_t - y_{t-1}.$$

First create a differencing lag operator polynomial object, and then use it to filter the observed series.

D1 = LagOp({1,-1},'Lags',[0,1]);
dY = filter(D1,Y);

figure
plot(2:N,dY)
xlim([0,N])
title('First Differenced GDP Series')

The series still has some remaining upward trend after taking first differences.

Take a second difference of the series,

$$\Delta^2 y_t = (1-L)^2y_t = y_t - 2 y_{t-1} + y_{t-2}.$$

D2 = D1*D1;
ddY = filter(D2,Y);

figure
plot(3:N,ddY)
xlim([0,N])
title('Second Differenced GDP Series')

The second-differenced series appears more stationary.

See Also

|

Related Examples

More About

Was this topic helpful?