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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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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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21 views

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
35 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
17 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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35 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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26 views

Divergent Dickey Fuller, KPSS, and Phillips-Perron tests

I'm fairly new to both CrossValidated/StackExchange and I'm no expert on Time Series Analysis, so please forgive any 'newbie' errors here. I've got an issue of divergent Unit Root tests results ...
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1answer
34 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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112 views

Discussion of a parameter in the python statsmodels augmented Dickey Fuller test

I would like to use the adfuller test from statsmodels.tsa.stattools, but I'm not sure when to change the parameter ...
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13 views

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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28 views

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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38 views

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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39 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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1answer
57 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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40 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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1answer
35 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
174 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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24 views

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
78 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
194 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
609 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
109 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
42 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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67 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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14 views

Unit roots in moving averages: distinguishing competing models

In «Introduction to Time Series and Forecasting» by Brockwell and Davis, it's stated that it's possible to distinguish between the competing models: $\nabla^kX_t=a+V_t$ and $X_t=c_0+c_1t+...+c_kt^...
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123 views

Dickey Fuller test statistic

Can Dickey Fuller test statistic be manually calculated? What is the equation for that?
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158 views

ARDL model assumptions

I am interested in using an ARDL model, instead of an error correction model, as my dependant variable appears to be I(2). I have understood that using an ARDL(2,1) model, I would be able to estimate ...
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81 views

Engle-Granger Two-Step Method and the significance of the found variables

After using the Engle-Granger 2-step method for testing whether two time series are cointegrated, may I use the regular T-statistics to see how significant the found alpha, beta and row are? If not, ...
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49 views

Unit root, stationary process

This is an extract from my lecture notes, and I am confused about how a process can be both unit root and stationary. This other question illustrates the unit rootness of a process implies it does ...
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53 views

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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472 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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17 views

What to do if data indicates possible unit root [closed]

I am trying to fit a model. I get an AR(2) like structure ( based off the pacf) But, when I solve for the reciprocal roots, I get one very close in modulus to 1. Few things, I calculate the roots ...
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91 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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73 views

How can Dickey fuller test give -ve value for t-stat?

I have been implementing dickey fuller test after gaining an understanding of its procedure ... The relevant equations are I have obtained the value for t-stat as +ve and hence when comparing ...
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36 views

What functional forms can I use to model a time series that is not stationary but has a unit root process?

I'm trying to choose the best forecast for this blue line (time series with 550 observations). Its not stationary but it does have a unit root. AR processes dont seem like the best choice. Could you ...
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172 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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14 views

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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29 views

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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1answer
644 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
370 views

How to prove nonstationarity of a random walk?

Given the AR(1) model $Y_t = ϕY_{t−1} + e_t$ . I want to show if |ϕ| = 1, the process cannot be stationary. I know to prove stationary it suffices to prove either mean function or autocovariance ...
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141 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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78 views

Testing first differenced time series - trend or not?

I have a question on testing for stationarity with the ADF test, in order to determine the order of integration. We do have a time series that looks in plot(df) obviously trending at level and has a ...
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236 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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1answer
65 views

Stationary dependent variable, integrated regressor: what to do?

Im running a univariate regression and the Y variable doesnt have a unit root, but the X does. The regression is: ...
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2answers
442 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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64 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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159 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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174 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. ...