KPSS test
Encyclopedia
In econometrics
, Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests are used for testing a null hypothesis
that an observable time series
is stationary
around a deterministic trend. Such models were proposed in 1982 by Alok Bhargava
in his Ph.D. thesis where several John von Neumann
or Durbin–Watson type finite sample tests for unit root
s were developed (see Bhargava, 1986). Later, Denis Kwiatkowski, Peter C.B. Phillips, Peter Schmidt and Yongcheol Shin
(1992) proposed a test of the null hypothesis that an observable series is trend stationary (stationary around a deterministic trend). The series is expressed as the sum of deterministic trend, random walk, and stationary error, and the test is the LM test of the hypothesis that the random walk has zero
variance. KPSS type tests are intended to complement unit root test
s, such as the Dickey–Fuller tests. By testing both the unit root hypothesis and the stationarity hypothesis, one can distinguish series that appear to be stationary, series that appear to have a unit root, and series for which the data (or the tests) are not sufficiently informative to be sure whether they are stationary or integrated.
Econometrics
Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...
, Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests are used for testing a null hypothesis
Null hypothesis
The practice of science involves formulating and testing hypotheses, assertions that are capable of being proven false using a test of observed data. The null hypothesis typically corresponds to a general or default position...
that an observable time series
Time series
In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
is stationary
Stationary process
In the mathematical sciences, a stationary process is a stochastic process whose joint probability distribution does not change when shifted in time or space...
around a deterministic trend. Such models were proposed in 1982 by Alok Bhargava
Alok Bhargava
Alok Bhargava is an Indian econometrician. He studied mathematics at Delhi University and economics and econometrics at the London School of Economics. He is currently a full professor of economics at the University of Houston....
in his Ph.D. thesis where several John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
or Durbin–Watson type finite sample tests for unit root
Unit root
In time series models in econometrics , a unit root is a feature of processes that evolve through time that can cause problems in statistical inference if it is not adequately dealt with....
s were developed (see Bhargava, 1986). Later, Denis Kwiatkowski, Peter C.B. Phillips, Peter Schmidt and Yongcheol Shin
Yongcheol Shin
Professor Yongcheol Shin is a British-Korean economist. He has held positions at leading academic institutions such as University of Cambridge, University of Edinburgh and University of Leeds...
(1992) proposed a test of the null hypothesis that an observable series is trend stationary (stationary around a deterministic trend). The series is expressed as the sum of deterministic trend, random walk, and stationary error, and the test is the LM test of the hypothesis that the random walk has zero
variance. KPSS type tests are intended to complement unit root test
Unit root test
In statistics, a unit root test tests whether a time series variable is non-stationary using an autoregressive model. A well-known test that is valid in large samples is the augmented Dickey–Fuller test. The optimal finite sample tests for a unit root in autoregressive models were developed by John...
s, such as the Dickey–Fuller tests. By testing both the unit root hypothesis and the stationarity hypothesis, one can distinguish series that appear to be stationary, series that appear to have a unit root, and series for which the data (or the tests) are not sufficiently informative to be sure whether they are stationary or integrated.