Data generating process of a time-series data need to be identified before further estimation is carried out. Users can test whether the data is non-stationary or not using a unit root test. There are two unit-root tests provided by i-Regand, the augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests. Other unit root tests will be introduced in the coming version.

Specifying stationarity is a basis for further analysis. When the data are non-stationary, a regression is said spurious unless there exists cointegration. Alternatively, the data are differenced until stationarity is reached and then carry out regression analysis. Cointegration tests will be covered in the next topic.

## ADF unit-root test

ADF unit root test is carry out by regressing the first difference of the data on the lag of the series level, some deterministic and augmenting terms. The deterministic terms are constant, trend, quadratic trend or none of them. The augmenting terms are the lags of the first difference and have a purpose for wiping out ARMA terms. The optimal lag included in the test can be provided by the Apps when user choose automatic selection procedure either based on AIC, SIC or HQC. Alternatively, users can specify the lag length.

The steps to carry out ADF unit-root test are:

Step 1. Tap on the main menu and select ADF unit-root test

Step 2. Select the variable to be tested

Step 3. Specify the lag selection criteria and input the maximum lag

Step 4. Run and see the results

The output present test statistics from four models: NONE (no deterministic components), CONSTANT (model with constant), TREND (model with constant and trend), QUAD (model with constant, trend, and quadratic trend). Each of them is accompanied with 1%, 5%, and 10% critical values (negative). If the ADF statistic is less than the critical value, the data is stationary. There is also information about optimal lag chosen by the Apps.

## PP unit-root test

In contrast to the ADF test, Phillips-Perron unit root test soaks nuisance parameters by using kernels. The test is carried out on whitened residuals from Dickey-Fuller regression (not augmented). There are also four models: NONE , CONSTANT, TREND, QUAD.

The steps to carry out PP unit-root test are:

Step1. Tap on the main menu and select PP unit-root test

Step 2. Select the variable to be tested