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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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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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330 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 (...
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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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157 views

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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60 views

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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807 views

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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339 views

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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111 views

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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360 views

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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190 views

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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3k views

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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3k views

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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518 views

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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187 views

Unit root test for ARIMA models

I have a slight confusion regarding seasonal models and which polynomial to use for conducting unit root tests. Given a model: $\phi(B)\Phi(B^s)\Delta^d\Delta^D_S X_t = \theta(B)\Theta(B^s)\epsilon ...
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339 views

Checking a panel unit root test in R done manually

I have spent much time looking for a special package that could run the Pesaran(2007) unit root test (which assumes cross-sectional dependence unlike most others) and I have found none. So, I decided ...
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Is detrending equivalent to differencing?

Given a non-stationary time series, there are many statistical tests (e.g. ADF, KPSS, etc.) to test whether the series has unit root or not. Equivalently, they test whether a trending time series has ...
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In Cointegration, adf test or for VAR models. What makes difference in having trend + Constant, Constant alone, and non

In Cointegration, adf test or for VAR models. What makes difference in having trend + Constant, Constant alone, and non. in below link http://www.econ.uiuc.edu/~econ508/R/e-ta8_R.html It said ...
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Unit-root and Johansen- lack of normal distribution

I have a question concerning unit-root data and normal distribution. As an assignment, I am checking the long-term relationship between unemployment rates and labor force participation rate. First I ...
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37 views

Unit root test with a dummy for an event

I'm currently working with financial time series that experience a crash towards the middle of the series. These series are returns. From the graph, these series clearly look stationary. However, due ...
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OLS with AutoRegressive Errors on Non-Stationarised Data

I'm working with some time series data (n=40) and trying to fit an OLS with AutoRegressive Errors to model the relationship between my dependent variable and a couple of predictors over time. I'm ...
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Tests for stationarity give contradicting results

I have a time series consisting of 192 data points (12 years of monthly data). A simple plot (in my opinion) clearly indicates that the data are not stationary: However, when I do an ADF test I get a ...
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110 views

What GARCH model to use when identifying structural breaks in exchange rate?

I'm trying to test if a specific country's president's unexpected statements create a structural break in the exchange rate series (dollar). I decided on what to do in what order but I'm having a ...
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Raw data is I(1) yet is I(0) in logs. Why?

I'm curious how this is possible. The data in question, based on the ADF, we strongly fail to reject the null of a unit root. Yet in natural logs, the series is stationary apparently (ie, reject the ...
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136 views

Confusion about stationarity because of contradiction in unit root test and graphical analysis

I am confused about the output of a unit root test I performed. After taking data with a seasonal effect in seasonal differences, the time-plot and the correlogram (shown below) both suggest non-...
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Nonlinear methods for detecting and measuring the strength of a trend in the context of unit roots

I am looking for statistical methods to detect the presence and strength of a trend in the context of unit root testing. We could for instance use a trend-stationarity ADF test: Here the t-statistic ...
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206 views

CADFtest critical values?

I just came across the CADF test package and have a question related to the critical values. As I understand this source, the CADF test allows to test with the modified AIC (MAIC) by Ng and Perron (...
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403 views

Augmented Dickey Fuller Test: Always lag=1?

I do have a question related to the ur.df test in R with the (urca package). The data comprises a monthly time series over a span of 48 months. When testing my variables for a unit root, my results ...
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77 views

Unit root test with different trend types

Basic unit root tests include only constant and linear trend case. So, what should I do if I want to test hypothesis about quadratic trend stationarity asumption, for example? What test should I use? ...
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249 views

Quantile Kolmogorov-Smirnov based on Koenker and Xiao (2004) for a QAR(1)

my goal is to investigate if a process has a unit root at different quantiles, hence, I use a QAR(1) model. I checked the PACF and only the first lag seems to be relevant. All my coding is done in R ...
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344 views

Confidence intervals for ARIMA parameter estimates and unit roots

Given the following simulation, I estimate a correctly specified ARIMA model and obtain the point estimate and confidence interval for the MA parameter. ...
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270 views

Dickey-Fuller test and Monte Carlo method

The Dickey-Fuller test aims to test the presence of unit roots in a process. If I've the following process: $$y_t = a_1y_{t-1} +\epsilon_t$$ it tests $H_0\colon \ a_1=1$. If I specify $\theta =a_1-...
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158 views

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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475 views

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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452 views

Do the dependent variable in a ARDL model have to be I(1) or can it be I(0)?

I`m 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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842 views

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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483 views

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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70 views

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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110 views

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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40 views

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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290 views

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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156 views

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 aren`t rejected ?
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311 views

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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0answers
479 views

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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460 views

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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537 views

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 ...
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121 views

General question regarding unit-root tests on panel-data

I am running FE and RE regressions and my Prof. suggested that I run unit-root tests. I have been trying to do that with R but am not able to find a library that will handle unbalanced panels with ...
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232 views

R: Calculating Unit Root for unbalanced data with gaps

I have panel data that I need to calculate a unit-root test on. The data is unbalanced and has gaps. Does anyone know of a library that handles unbalanced panel-data with gaps? I have tried the ...