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Questions tagged [unit-root]

A unit root is a property of a non-stationary time series which can lead to spurious regressions and wrong inference.

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Intuitive explanation of unit root

How would you explain intuitively what is a unit root, in the context of the unit root test? I'm thinking in ways of explaining much like I've founded in this question. The case with unit root is ...
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4answers
30k views

What is the difference between a stationary test and a unit root test?

What is the difference between the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test and the augmented Dickey-Fuller (ADF) test? Are they testing the same thing? Or do we need to use them in different ...
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3answers
2k views

Nice example where a series without a unit root is non stationary?

I've seen several times people reject the null in an augmented Dickey-Fuller test, and then claim that it shows their series is stationary (unfortunately, I cannot show the sources of these claims, ...
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3answers
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Which Dickey-Fuller test for a time series modelled with an intercept/drift and a linear trend?

Short version: I have a time series of climate data that I'm testing for stationarity. Based on previous research, I expect the model underlying (or "generating", so to speak) the data to have an ...
11
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1answer
41k views

Test for cointegration between two time series using Engle–Granger two-step method

I am seeking to test for cointegration between two time series. Both series have weekly data spanning ~3 years. I am trying to do the Engle-Granger Two Step Method. My order of operations follows. ...
11
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1answer
24k views

Difference between series with drift and series with trend

A series with drift can be modeled as $y_t = c + \phi y_{t-1} + \varepsilon_t$ where $c$ is the drift (constant), and $\phi=1$. A series with trend can be modeled as $y_t = c + \delta t + \phi y_{t-...
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2answers
13k views

What is the difference between serial correlation and having a unit root?

I may be mixing up my time series and non time series concepts, but what is the difference between a regression model that exhibits serial correlation and a model that exhibits a unit root? In ...
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4answers
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Interpreting R's ur.df (Dickey-Fuller unit root test) results

I am running the following unit root test (Dickey-Fuller) on a time series using the ur.df() function in the urca package. The ...
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3answers
119k views

How do you interpret results from unit root tests?

I have to do some unit root tests for a project, I'm just unsure on how to interpret the data (which is what I have been asked to do). Here is one of my results: ...
8
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3answers
3k views

What is the implication of unit root of MA?

A ARMA(p,q) process is weakly stationary, iff the root of its AR part is not on the unit circle. So its weak stationarity doesn't depend on its MA part. But what can the positions of the roots of its ...
7
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2answers
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R: Augmented Dickey Fuller (ADF) test

I'm having a problem with the Dickey-Fuller p-values and test statistic for unit root test in R. I tried using functions: ...
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3answers
6k views

Unit root tests for panel data in R

I have the plm package and would like to run unit root tests on some variables. I get the following error: ...
7
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1answer
3k views

Explosive processes, non-stationarity and unit roots, how to distinguish?

I understand that if we have a simple model such as: $$Y_t=\rho Y_{t-1}+\epsilon_t$$ where $\rho$ is less than one in absolute value then we have a stationary process. If $\rho$ equals one then we ...
7
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1answer
2k views

Best practice for ADF/KPSS unit root testing sequence?

I've been quite confused by the various unit root testing strategies recommended in the literature, so I was hoping others may have some advice on the best way to proceed using ADF and KPSS tests. ...
6
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1answer
4k views

How is the augmented Dickey–Fuller test (ADF) table of critical values calculated?

Could you please explain in simple terms how the table of critical values for the augmented Dickey–Fuller (ADF) test is created?
6
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1answer
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Why is the dickey fuller test different from a simple t-test

I am trying to understand why should there be different distribution for t-statistic, in case of AR model, Dickey-Fuller test For e.g. Say, the model is $Y_t = \beta_lY_{t-1} + \varepsilon_{t}$. ...
6
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2answers
2k views

Estimation of unit-root AR(1) model with OLS

Given a random walk $x_t$, $$x_t=x_{t-1}+\varepsilon_t,$$ consider estimating the slope coefficient $\beta$ in $$x_t=\beta x_{t-1}+\varepsilon_t$$ by OLS. This question and the following answer ...
6
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1answer
178 views

Time Series Stationarity

I am confused of why my Dickey-Fuller test is significant (which implies stationarity), while the time series clearly exhibits a deterministic trend?
6
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1answer
13k views

Dickey-Fuller augmented tests: how to choose lags?

I’m trying to model a time series (log_consommation) in a ARIMA(p,d,q) using Stata. So I start by determining d by transforming my time series to make it ...
5
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2answers
1k views

Non-Stationary: Larger-than-unit root [duplicate]

I keep reading everywhere that a time series is non-stationary (e.g. http://en.wikipedia.org/wiki/Unit_root or http://en.wikipedia.org/wiki/Stationary_process) if there's a unit-root. But isn't a ...
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4answers
175 views

Can time series data have both unit root and structural break?

My data rejects unit root, but shows structural break, is this possible?
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3answers
651 views

Unit root tests ambiguous - is time series stationary?

I am testing a time series (quarterly) for stationarity. However, using the KPSS test, the ADF test and PP test, I get different results (ADF and PP reject non-stationarity, KPSS rejects stationarity, ...
5
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1answer
17k views

Fisher-type unit-root test for panel data. Results interpretation in Stata

As part of my master thesis, I'm performing several tests on panel data. One of these is a Fisher-type unit-root test, which works well with an unbalanced panel. I have performed the test, but I ...
5
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1answer
177 views

Why is cointegration found without unit root?

I'm working on the multiple price series data to look for the long run relationships. DF-GLS tests for unit root are rejected although the series show some trends and seem stationary after differenced....
5
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1answer
796 views

The ACF of a unit root process [duplicate]

If the correlogram of $Y_t$ displays slow decay (i.e., non-stationarity), is this indicative of a unit root? I reasoned that for the model $Y_t = Y_{t-1} + u_t$, the ACF is equal to 1 for all lags, ...
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3answers
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Difference between $y_t = \alpha + \beta t$ and $y_t = y_{t-1} + \beta$

Would someone mind walking me through the differences between: \begin{align} y_t &= \alpha + \beta t \\ &\& \\ y_t &= y_{t-1} + \beta \end{align} as well as between \begin{align} ...
4
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1answer
3k views

Difference between random walk and process integrated of order one?

I know that an $I(1)$ process becomes stationary after differencing once. However, I somehow always equated that to its being a random walk because say having a unit root process like \begin{eqnarray} ...
4
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2answers
8k views

Contradictory results of ADF and KPSS unit root tests

To check whether the data is stationary or not, I computed KPSS and ADF test and got the following results ...
4
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3answers
512 views

Bounded dependent variable: can it be unit-root non-stationary?

I have linear time series regression model where the dependent variable Y is bounded between 0 and 1. Using classical unit root tests (dickey-fuller and kpss), results would make you conclude that Y ...
4
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1answer
553 views

Must a time series be stationary if it has no unit root?

Must a time series be stationary if it has no unit root? I am not quite sure.
4
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1answer
1k views

What is an integrated time series?

In this question a commenter says that "differencing a series that is not integrated is certainty problematic from the statistical perspective". What is an integrated time series, and why is ...
4
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2answers
430 views

Are seasonal differencing and polynomial trends interchangeable?

Even though the title suggests just a simple question, it's a two-part. First, can a repeated seasonal differencing filter also remove a polynomial trend? In which conditions? I would guess only when ...
4
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1answer
1k views

Granger causality test for integrated time series

I have two time series that are both non-stationary at level. The ADF test says they have a unit root. When taking the first difference of each time series, they are now stationary. I guess this is ...
4
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0answers
659 views

What is the intuition for testing seasonal difference with OCSB test and its correct application?

I have daily time series data of a shop's revenue. Now I would like to test for seasonal differencing with the OCSB test originally intrduced in (Osborn et al. (1988): Seasonality and the Order of ...
4
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0answers
329 views

Regressing nonstationary on stationary variable

I am trying to empirically estimate the coefficient for the Okun's law as a relationship between output growth and unemployment. I am using the simple gap version, where I regress real output growth (...
4
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1answer
922 views

Is a trend-stationary variable I(1) or I(0)?

I am trying to do cointegration analysis between two variables. I first used the standard Dickey-Fuller and Phillips-Perron tests; they concluded my variables were I(1). I then did cointegration and ...
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2answers
1k views

About the stationarity of a sine wave

I generated two sine wave time series and want to check the stationarity of them. (1) The first time series is short. kpss.test() thinks it is stationary. ...
3
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2answers
740 views

How to show the inconsistency of the OLS estimator for unit-root AR(1) processes by simulation?

From what I understand, OLS gives consistent estimates for stationary AR(1) time series but not for unit-root ones. I am trying to illustrate this phenomenon with a small simulation in R but the OLS ...
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4answers
10k views

Unit root tests, stationarity, and the null hypothesis

I was reading about unit root test, when I started to get slightly confused about the setting for the Null hypothesis vs Alternative hypothesis, and so I thought of asking the experts opinion. In the ...
3
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2answers
382 views

Eviews : How to test for cointegration in the right way

I am studying ECM alone using a book and some parts are not explained. First, the book advise to test for a unit and for the order of integration of the series. In eviews options are not pretty clear ...
3
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1answer
4k views

Trend stationary and difference stationary simultaneously

Can a time series be both trend stationary and difference stationary at the same time? In this situation how do we approach the problem?
3
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4answers
11k views

Unit root tests: how to decide if to include a trend and/or a constant

Applying a test to univariate time series data for checking if the series has a unit root or not, one is faced with a decision if one would like to test if the series is stationary around a constant ...
3
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1answer
3k views

Random Walk with Drift: Why is the change in a trending variable also a function of a random variable when $E(\epsilon_t) = 0$?

I came across Pearson’s companion site of Murray, M. P. (2005). Econometrics: A modern introduction. Pearson Higher Education. While skimming through the related lecture slides here http://wps.aw.com/...
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2answers
3k views

Unit root near unit circle or near 1?

According to slide 6 of Bartlett's Introduction to Time Series Analysis, Lecture 6 (with emphasis on slide 6), an autoregressive time series model is stationary if the autoregressive polynomial has a ...
3
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2answers
718 views

What is the best way to proof your time series has a deterministic linear trend

In case you suspect your time series has a linear trend, what is the best way to prove it? If you just regress it against time, you ignore the auto correlation of the time series so I assume that is a ...
3
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2answers
791 views

Removing Unit Roots

If I have the following AR(p) process \begin{align} y_t=a_1 y_{t-1} + a_2 y_{t-2} + ... + a_p y_{t-p}+u_t, \end{align}where $ u_t $ is white noise, and I suppose the AR polynomial has 2 unit roots, ...
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1answer
325 views

Autoregressive model for time series with structural breaks

I'm using a structural break model (threshold model or regime switching model) to examine the dynamics of a time series. The ADF test shows that the series has a unit root. Right now I'm regressing $y$...
3
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1answer
9k views

Connection of t-statistic and p-value in augmented Dickey-Fuller test

My project is about purchasing power parity (PPP). I am checking whether the real exchange rate of Canadian dollar(CAD)/US dollar(USD), Japanese Yen(JPY)/USD and Great Britain Pound(GBP)/USD has a ...
3
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1answer
958 views

Interpretation of Canova and Hansen test for seasonal unit-root with R uroot package

I want to fit a SARIMA model and have daily sales data with a weekly seasonal pattern (frequency = 7) with this auto correlation function (ACF): Clearly, there are seasonal effects as the spikes of ...
3
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1answer
539 views

Phillips-Perron Unit Root Test with exogenous breaks

I would need to do a Philips-Perron test in R, while controlling for an exogenous break. I found the Philips-Perron test in the package tseries (PP.test), but can't find (contrary to the CADF test) ...