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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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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. ...
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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?
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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 ...
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
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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 ...
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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 ...
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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: ...
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1answer
549 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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2answers
42k views

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
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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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 ...
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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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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 ...
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2answers
717 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 ...
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2answers
779 views

How to interpolate a variable with frequency of 5 years to annual data?

I have two time-series variables: each has 14 points with an interval of 5 years. The precise years are: ...
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1answer
883 views

Dickey-Fuller unit root test with no trend and supressed constant in Stata

I have seen in several papers that the $p$-value for the Dickey-Fuller (DF) test is reported for the test including trend and constant, then without the trend, and in the end in the absence of both. ...
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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 ...
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1answer
2k views

Unit roots and GMM estimation

I want to estimate panel models of the following structure: $y_{it} = \rho y_{i,t-1} + \beta_1 x_1 + \dots + \beta_k x_k + c_i + \gamma_t + \epsilon_{it}$, where $c_i$ are time constant country ...
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1answer
609 views

Heteroscedastic test does not solve the problem

As my previous questions I'm trying to solve a problem with my stocks tests. I tried Breusch-Pagan test for heteroscedasticity but some residuals still pass these tests. My procedure is: Get two ...
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1answer
172 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
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. ...
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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: ...
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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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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. ...
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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 ...
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1answer
811 views

ADF test for Unit Root, should you select a trend if the trend changes once?

Let's say you have a variable with a time series going back ten years. In the first 5 years, it clearly trends from 5 to 10. And, in the next 5 years, it trends downward from 10 back down to 5. ...
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2answers
2k views

ADF test, PP test, KPSS test: Which test to prefer?

If a time series is tested for Unit Root (by ADF, PP, KPSS,...) problem is detected with some tests and not found by others. Which one is preferred? For example if ADF says us that there is a Unit ...
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1answer
3k views

Problems with taking the first difference of a stationary series

Suppose you have sufficient observations for running a time-series regression, but you do not have sufficient observations to accurately test for the stationarity of the residuals. If you do take the ...
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1answer
2k views

Manual calculation of ARIMA(1,1,0) forecast

I have read the questions about the ARIMA and ARMA prediction here and here, and also here. I'd like to make an one-step ahead ...
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1answer
5k views

Interpretation of critical values of KPSS test

I am using the KPSS test from the R urca package. My result is the following: ...
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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?
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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 ...
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2answers
1k views

Unit root test specification with a structural break

I am puzzled as to what specification I should include in my unit root tests of the following data: . I will use ADF, KPSS and ZA tests. I can see there is a break in trend at observation 9. However, ...
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1answer
953 views

Structural-break unit-root test

My problem is the following: I have a model forecasting the sales of a certain brand. In period 4 a strike caused the sales to decrease. I want to know whether this strike has caused the sales to ...
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2answers
4k views

Which is the best criterion for DF-GLS lag selection?

When you have an output such as this in Stata for dfgls: ...
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0answers
230 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 ...
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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
54 views

Can a variable that is I(0) also be I(1)?

After applying the ADF test for nonstationarity, I find that for both the test at level and the test at first differences, all my variables are both I(0) and I(1). I.e. the p-value is below 0.05 in ...
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1answer
418 views

What do you think of this correlogram?

do you think this weekly data is stationary? Unit-root test indicates rejects null of non-stationary (rejects null of unit root). Thanks for your input. I just wanted to follow up that the ADF test ...
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1answer
2k views

Interpretation of ADF Test

I am doing the augumented Dickey-Fuller test to check if my series are stationary or not. ...
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0answers
333 views

Generating the ADF test distribution

I am trying to replicate the distributions for the Dickey-Fuller Unit Root test, but I had no success. I tried reading the original paper (but explains more of the 70's computing than about the ...
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1answer
342 views
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1answer
140 views

Differencing variables with unit roots

I want to regress my dependent variable on my independent variables in R. First for the level of the variables: lm(y~x+z+u). Now since my variables are non-...
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0answers
52 views

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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1answer
274 views

Cointegration between a variable of significant seasonality and one with no significant seasonality

After running programs of deseasonalization, I had an output in which one variable held significant seasonality, for which I corrected, and another that did not have. My main objective was to ...
0
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2answers
243 views

how does Augmented Dickey Fuller results help to make the data stationary?

I have done an Augmented Dickey Fuller test on a variable without differencing it (or without making any transformations). Attached is my output. Now my question is how will this result (considering ...