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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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Dickey-Fuller test interpretation (urca package)

I am having trouble with interpreting the Dickey-Fuller test on a time series using the ur.df() function in the urca package. I already read this thread but still need some advise. The command is: ...
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Unit Root Testing

I am having some troubles with the unit root test. The are some concepts that I do not fully understand. Could you please tell me if what I write in the following four passages is correct? I am new to ...
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Super confused about dfuller

I have a rather small dataset and just performed DFuller test for unit root. When testing with zero lags, it contains unit root. When using one lag, it does not contain unit root. However, when ...
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How Do I Interpret This Table When Testing For A Unit Root?

I'm testing data for unemployment in Poland for the presence of a unit root. I used NumXL (integrated into Excel) to perform an ADF test, which produced the table shown in the picture attached. How ...
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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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Are explosive ARMA(1, 1) processes stationary?

I was reviewing time series textbooks recently and have been left confused since. In particular I have looked into the book of Brockwell and Davis (Introduction to Time Series and Forecasting, Second ...
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85 views

Roots within the unit circle and non-stationarity

I am quite new to time series analysis and I am delving for the first time into stationary processes. I don't seem to understand the concepts of non-stationarity and the presence of roots within the ...
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21 views

Error Correction Model (ECM) procedure

I am getting familiar with ECM so I would like to ask for help in order to understand it. My goal is: performing a ECM in a multivariate context. I was reading ECM is part of a Cointegration analisis....
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27 views

Why do the Dickey-Fuller test and Lo-MacKinlay Variance Ratio test yield such different outcomes?

It is my belief that a unit root implies a random walk, but not vice versa. Therefore, would one not expect the Dickey-Fuller test to find non-stationarity in the same cases as the Lo-MacKinlay ...
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Q: Implications of autocorrelation in a Dickey-Fuller unit root test

I am conducting a Dickey-Fuller unit root test on the FEDFUNDS series from the FRED database. My estimation period is quarterly from 1955(1) to 2007(4) (taking the average of the monthly rates within ...
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12 views

Testing for (covariance) stationarity specifically (vs. testing for dependence)

I'm using Wooldridge's textbook as my guide for a time-series cross-sectional project. Wooldridge, unlike many, distinguishes between (covariance) stationarity and weak dependence. He says that both ...
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2answers
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Time series has unit root iff integrated of order 1

The wikipedia page for Unit Root says something like "..the stochastic process has a unit root or, alternatively, is integrated of order one..". Are these actually equivalent? Could someone point me ...
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What should I conclude if a Unit Root Test gives contradictory results with & without a trend?

I have a data set for a variable, for which I have run some unit-root tests: ADF (constant/without trend): t-stat=-1.0816, p-val=0.7218 - DNR ADF (constant & trend): t-stat=-4.5203, p-val=0.0021 -...
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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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21 views

Stationarity test for autocorrelation

can we use unit root test of residual to detect autocorrelation in a time series model? Are stationarity of the residual means there is no autocorrelation?
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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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Replicating Dickey Fuller? How did they know something was wrong? [cross posted on QF] [closed]

I am interested in testing if there is size distortion through simulations. I have recently been interested in replicating Dickey and Fuller (1979) and this source from another post helped a lot, here ...
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Should I test for sphericity and calculate statistical power before running and modelling any forecasting model?

I'm trying to model a regression for one dependent and five independent macroeconomic variables. I'm new to statistics but I've read lots of text books and articles about SEM, cointegration, ols, URT, ...
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R: interpreting ur.df ADF test results

I'm running ADF test on my data to test for unit root and stationarity, trend, and to find the optimal number of lags using urca package. my code is as follows: <...
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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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Model identification from Eviews Dickey-Fuller test output

So our econometrics professor gave us the following Eviews outputs. First, it asked if it was the right decision to differentiate twice, which, according to what I interpret from the Eviews display, ...
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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 ...
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Unit root in time series of log return of s&p 500. What to do? [closed]

I have 9500 closing prices of s&p500. I took daily return of the prices dailyreturn and then log return of the prices logreturn=log(1+dailyreturn). Now I checked the data using augmented Dickey-...
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1answer
53 views

Unit Root Test for Panel Data in R

I'm working with a unbalanced panel dataset of 18 countries with quarterly data from 1970 to 2014 of different characteristics per country (housing prices, education level, total population, GDP per ...
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1answer
108 views

Unit Root - Real Interest Rate

I want to find out whether the real interest rate of different countries are non-stationary. The real interest rate is defined as the difference between the nominal interest rate and the inflation ...
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148 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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Time series that is never stationary by differencing

When I was looking at time series I noticed that a common approach to time series modelling is the ARIMA model which basically does differencing until a stationary series is found and then fits the ...
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1answer
728 views

ADF test showing stationary for a non stationary series

I am running an ADF test in R on the following series: This to me is clearly non-stationary, but when I run the ADF test: ...
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1answer
42 views

Why is Dickey-Fuller test applied on the difference operator and not on the variable directly?

Why is not the Dickey-Fuller test applied directly on : $Y_t = \rho Y_{t-1} + u_t$ instead of : $\Delta Y_t = (\rho-1) Y_{t-1} + u_t$. Many papers apply the Dicker-Fuller on the first difference ...
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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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59 views

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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1answer
51 views

How to check if a process has constant variance?

I am using KPSS test to verify if my process has constant variance around the mean, but I am not sure if this is the correct test for my case. In KPSS the null hypothesis is that the process is ...
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How to implement fully modified vector autoregression (preferably in EViews)?

Do you know how to implement Peter Phillip's 1995 method [link to paper] for fully modified estimation of VARs in order to allow for valid inference in case of (co-)integrated time series variables?
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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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VAR/VEC and stationarity [duplicate]

Do VAR and VEC require no unit-roots? I have three variables where two are difference-stationary (unit roots) and one is trend-stationary (no unit root). The three of them are cointegrated. ...
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79 views

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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79 views

Normalization of time series data

What is best procedure to normalize the time series data. May I use a unit root test or simply proceed with $\frac{x-min}{max-min}$?
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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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1answer
52 views

Unit root tests and correlation coefficients

A linear regression is performed as part of some unit root tests such as ADF, ADF-GLS (ERS), and PP. Should I pay attention to the correlation coefficients (ordinary, adjusted) of the regression? ...
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1answer
609 views

Inverse AR/MA roots and near non-stationarity/invertibility

I computed an algorithm to find out the best ARMA (p,q) model via minimisation of the AIC. It turned out ARMA(5,5) is the best one with AIC=-2693.12. However, the inverse roots of the AR and MA ...
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Unit Roots For Dummies book?

After reading the intuitive explanation of unit roots by Whuber on this website, I am motivated to find out more about them. What book would people recommend that gives a clear explanation of all ...
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1answer
14 views

Different number of observations and testing order of integration [closed]

Suppose I have a time-series in which I know it to be I(1), but I need to model it with fewer observations. And due to the low power of ADF test, fewer observations means testing the series to be I(0)....
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1answer
173 views

ACF and PACF for a unit root process

Can someone please tell me how the acf and pacf look like for a unit root process?
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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.
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1answer
1k views

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 $Y_t = \beta_lY_{t-1} + \varepsilon_{t}$. ...
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1answer
252 views

Unit root test Unemployment

I want to analyze the unemployment rate in Austria from 1999 to 2017, quaterly data. Here's the code for the time series: ...
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1answer
46 views

Is covariance stationarity a sample property?

I apologize in advance if this proves to be a nonsensical question but it is something I have been struggling with. Is there a way to prove/discern that covariance stationarity is not an attribute of ...
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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 ...