# 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.

111 questions
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### 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 ...
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### 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 (...
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### Result of an ADF-Test compared with an estimated AR (p) model

I am currently investigating the inflation persistence for different countries by using R. I took data from the OECD for Sweden (1993-2017) and checked first if the series is stationary with the ur....
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### While selecting model order for VAR models is it sound to stop increasing when a root outside the unit circle is found?

Basic question I guess. I'm fitting VAR models (and derivatives), and I've tried my hand on model order selection based on regularization but now I'm back to informative criteria (IC). Thing is my ...
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### AIC comparison vs. unit root test for model selection in forecasting

Rob J. Hyndman once wrote in "Why I don't like statistical tests" (emphasis is mine): In forecasting, the only place in which I find testing useful is in determining the order of integration of a ...
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### How to relate roots of AR and MA to unit circle

I'm working on these problems and think I figured out most of the steps, but am stuck near the end as I don't understand how to relate my roots back to the unit circle in order to determine ...
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### Clarifying Elder & Kennedy 2001 Case 3, how to test for the presence of intercept?

I am attempting to follow the unit root testing strategy for Case 3 as per [Elder & Kennedy 2001]. After failing to reject there is no unit root, I wish to test for the presence of an intercept. ...
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### Should I test for heteroskedasticity when I run unit root tests?

"The Phillips-Perron (PP) unit root tests differ from the ADF tests mainly in how they deal with serial correlation and heteroskedasticity in the errors." Zivot (2005) Modelling Financial Time Series ...
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### Interpreting Phillips-Perron Unit Root Tests

I would like to make sure that I'm properly understanding how to interpret the Phillips-Perron Unit Root Tests available in SAS. The best resource that I've been able to find was this page: https://...
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### Unit root testing with two structural breaks

I'm investigating two possibly cointegrating time series and need to test for stationarity. Both series have structural breaks, possibly more than one. My procedure is as follows: Clemente Montanes ...
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### Time trend in DF unit root test

I have a couple of questions concerning the time trend (βt) in an augmented Dickey-Fuller test for panel data: 1) From what I understand there is no clear rule/standard or test as to when to include ...
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### R: Stationarity/non-Stationarity: implementing a solution

I have an Augmented Dickey Fuller Test in R on leg_totalbills that shows I can not reject the null hypothesis: Unit Root. The ...
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### Which panel unit root tests should I use? Panel of 7 countries and 7 years

I have a balanced data of 7 years and looking into 7 countries. There are many panel unit root tests to be used. I am looking at using the Fisher-type and IPS tests but there are more than that and I ...
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### How to deal with unit roots in panel regression with fixed effects?

I am trying to figure out how to alter my panel regression in a case where fixed effects exists and one (or both) of the variables are I(1) processes (or in other words contain unit root). This is ...
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### Confusion about the term “stochastic drift”

After reading lots of material about the subject, I believe that the term "stochastic drift" is defined in a two different ways. These two different definitions make the term unambiguous and I assume ...
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### About 2 unit root tests and null hypothesis

I have been looking at unit root testing. Specifically 2 tests: The ADF test. The ADF (augmented Dickey Fuller) test has the null hypothesis that "the time series has a unit root" (meaning that the ...
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### Stochastic or deterministic trend

Having run panel unit root tests, we cannot reject the null of individual unit root (Im, Pesaran), suggesting a non-stationary series. Question 1 At this point, how do we know if we have a ...
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### Second Difference in Unit Root Test

If variables are stationary at second difference. Is it possible to proceed to next test with variables stationary at second difference or need to transform the variables to make them stationary at ...
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### Do the dependent variable in a ARDL model have to be I(1) or can it be I(0)?

Im trying to make a ARDL model and have 6 variables were the dependent variable are I(0), stationary at level, with 6 lags and the 5 remaining independent variables are I(1), stationary at first ...
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### Manual calculation of ARIMA(p,d,q) forecast

I have obtained the answer on my own question Manual calculation of ARIMA(1,1,0) forecast, then I have seen the question and answer Forecasting with ARMA models. I'd like to write the formula to the ...
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### Interpretting Ng perron Unit Root Statistics

i have applied NG Perron's modified tests to my timer series data. But when I tried to interpret test statistics I saw that, decision given by MZa and MAzt contradicts with MSB and MPT. Is there an ...
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### Contradiction between results of ERS point optimal and ADF Uni Root Tests

I have a hypothetical time series data which is derived from following . equation y =0.10 + 0.75 Trend+ 1.00 𝑦𝑡−1_ + ε When I apply standard ADF procedure to data, I see that y has a unit root ...
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### Relationship between I(0) variables in the presence of structural breaks

Consider the following hipothetical data. $A_t$ is a time-series tested to be I(0) with one known structural break and $B_t$ is another time-series on the same data set also tested to be I(0) with a ...
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### Model a structural VAR using I(0) and I(I) variables

Is it correct to run a structural VAR using I(0) and I(1) variables if the I(1) variables are cointegrated?
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### For system GMM, do we need stationarity in levels or first-differences?

I'm trying to decide whether I should use a difference GMM or a system GMM. I have a panel of 50 states over 19 years. I know that system GMM has better finite sample properties when the series is ...
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### Common unit root or individual unit root

Is it acceptable to estimate panel equation with fixed effects when the common unit root is rejected, but individual unit root tests arent rejected ?
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### ARDL time series steps

I want to confirm that regarding Auto-Regressive Distributed Lag model used for time series all variables must be stationary at level or at 1st difference and no variable should be at 2nd difference. ...
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### ADF and KPSS test both rejected

When testing the stationarity of residuals after OLS estimation, the ADF and KPSS test have opposing conclusions when it comes to rejecting the null: ADF: Rejection of null concludes evidence of ...
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### Dickey Fuller and deterministic regressors

Can somebody help me with how I can determine what deterministic regressors(trend, drift and intercept) I shall include in the Dickey Fuller test. A Stata help file outlines four cases: 1 Random ...
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### Does this series have a unit root?

I am trying to figure out whether my time series is stationary or not. In order to do so I run four different tests: the three test from the Dickey-Fuller test (standard, drift and trend) given by the ...