XLSTAT: Unit Root (Dickey-Fuller) and Stationarity Tests on Time Series in Excel

 

Background

A time series Yt is weakly stationary if its mean, variance, and autocorrelation do not change over time. White noise (e.g., Yt∼N(μ,σ2)) is a stationary example.

Non-stationary series can be stationary after differencing (integrated of order 1), like a random walk, or stationary in trend.

Stationarity tests verify if a series is stationary:

• KPSS test assumes stationarity as the null hypothesis (H₀).

• Unit root tests (Dickey-Fuller, augmented Dickey-Fuller, Phillips-Perron) assume a unit root (non-stationarity) as H₀.

XLSTAT offers these four tests: Dickey-Fuller, ADF, PP, and KPSS.

 

Dataset for Example

The data include:

• A random normal sample N(0,1) with 100 observations (series N),

• A stationary series with autocorrelation ρ=0.8,

• An autocorrelated series with ρ=1,

• An explosive series with ρ=1.1,

• A series varying linearly over time (N−0.1t).

 

Setting Up

• Open XLSTAT.

• Click on the Forecasting/ Time series analysis menu and select the Unit root and stationarity tests feature.

• After clicking the button, the dialog box appears.

In the General tab:

• Select the data from the Excel sheet and choose the first two time series in the “Time series” field.

• Keep the Series labels option activated since the first row contains variable headers.

• Select the Stationary option for the Augmented Dickey-Fuller test, as the series are non-explosive.

• Choose the Intercept model for the Phillips-Perron test, matching the data generation process.

• Select the Level option for the KPSS test.

 

In the Options tab:

• Select one method to estimate p-values and critical values for the unit root tests:

  • Surface regression (MacKinnon’s approach)

  • Monte Carlo simulation with a set number of runs.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

Example on Stationary Series

After the summary statistics, the results of the ADF, PP, and KPSS tests are shown for the first series, followed by the second (see sheet Dickey-Fuller|Phillips-Perron1).

The three tests agree: for the first series, ADF and PP reject the null of a unit root (r=1) and support stationarity, while KPSS retains the null that the series is stationary.

For the second series, the p-values are not as low (ADF test) or high (KPSS test) as it was with the first sample, but the same conclusions are retained.

 

Example on Non-stationary Series

We then applied the three tests to column E, where the data are known to have a unit root. All tests detected non-stationarity, with the PP test showing the strongest significance (see sheet Dickey-Fuller|Phillips-Perron2).

For the time series in column F (see sheet Dickey-Fuller|Phillips-Perron3), with the ADF test set to explosive and the KPSS to trend, the KPSS indicates non-stationarity, while both unit root tests reject the presence of a unit root.

 

Example on a Linear Trend Series

For the last series with a clear time trend, using the Stationary option (ADF), Intercept+Trend model (PP), and Trend version (KPSS), all tests agree the series is stationary after detrending.