# Introduction¶

All tests expect a 1-d series as the first input. The input can be any array that can squeeze into a 1-d array, a pandas Series or a pandas DataFrame that contains a single variable.

All tests share a common structure. The key elements are:

• stat - Returns the test statistic

• pvalue - Returns the p-value of the test statistic

• lags - Sets or gets the number of lags used in the model. In most test, can be None to trigger automatic selection.

• trend - Sets or gets the trend used in the model. Supported trends vary by model, but include:

• ‘nc’: No constant

• ‘c’: Constant

• ‘ct’: Constant and time trend

• ‘ctt’: Constant, time trend and quadratic time trend

• summary() - Returns a summary object that can be printed to get a formatted table

## Basic Example¶

This basic example show the use of the Augmented-Dickey fuller to test whether the default premium, defined as the difference between the yields of large portfolios of BAA and AAA bonds. This example uses a constant and time trend.

import datetime as dt

start = dt.datetime(1919, 1, 1)
end = dt.datetime(2014, 1, 1)

df = web.DataReader(["AAA", "BAA"], "fred", start, end)
df['diff'] = df['BAA'] - df['AAA']



which yields

   Augmented Dickey-Fuller Results
=====================================
Test Statistic                 -3.448
P-value                         0.045
Lags                               21
-------------------------------------

Trend: Constant and Linear Time Trend
Critical Values: -3.97 (1%), -3.41 (5%), -3.13 (10%)
Null Hypothesis: The process contains a unit root.
Alternative Hypothesis: The process is weakly stationary.