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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12 views

Augmented Dickey-Fuller test with deterministic seasonality

I have several time series with monthly frequency which I need to test for the presence of unit roots. All of them clearly have a heavy seasonal component within the year. As such, the formulation of ...
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What would be an adequate test for a multivariate distribution to test for stationarity?

I have monthly returns of a certain portfolio with $d$ assets and I want to check it for stationarity; More precisely , I want to test whether the multivariate distribution of $$(X^t_{1}, \ldots, X^...
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what means to be outside unit circle?

I am trying to study time series without a great math background and I came across the next problem: When checking for stationarity I check the roots, and if they are not on the unit circle, then it ...
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Fitting the 'intercept only' regression model in Python

I am working on a project that includes time series forecasting and I decided to use ARIMA for this. Before determining p (AR order) and q (MA order), I need to run ADF test to determine the ...
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24 views

First difference or seasonal difference in VAR/VECM

I have monthly data on house price, rental price, wage index and interest rates. I want to use VAR to produce impulse response function. Is there any reason why I should use first difference, x(t)/x(...
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When should ADF, SPSS and LJUNG-BOX test be used?

I have several different time series data. I am using ARIMA for prediction provided that the data is stationary. To test for stationarity I am confused as to which test to use. Is there any guideline ...
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32 views

Does Augmented Dickey Fuller Test Capture both Trend and Seasonality?

When using ARIMA modeling to capture autocorrelation patterns, we remove trend by sequential differencing and seasonality by differencing at relevant lags prior to creating the ARMA model to capture ...
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13 views

Consequences of fitting Unit Root data directly in AR model

I feel it is useful to understand the consequence of violating the assumptions of a model. I check a couple textbooks, but most I can get about the consequence of fitting time series with unit root is ...
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31 views

OLS Time series regression with levels and first differences

I am currently working on my bachelors thesis and I am trying to perform an OLS time-series regression with the short-term interest rate as dependent and inflation expectations and an output-gap as ...
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Variable does not follow a normal distribution, can I trust its p-value from a Unit Root test? [closed]

If a variable does not follow a normal distribution, I should not trust in the p-value from a Unit Root test, right?
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Unit Roots in Short Horizon

I have a series that is stationary in the long run. However, in the model development sample - which is a short horizon - the same series is trending. Now, should I consider this series as non-...
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37 views

DF Test Rejects Non-Stationarity in a seemingly Non-Statioinary Series

Let $Y_t = \rho Y_{t-1} + \epsilon_t$ and $Y_0$ be some constant. I generated a time series data for the above model like this ...
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Detailed calculation of using Augmented Dickey Fuller test in AutoRegressive Model

In the wiki page of ADF test, its testing procedure is applied to the model $$\Delta y_t = \alpha+\beta t+\gamma y_{t-1} + \delta_1 \Delta y_{t-1} + \dots + \delta_{p-1} \Delta y_{t-p+1} + \epsilon_t$...
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Rationale of Augmented Dickey Fuller Test on lag difference

In the wiki page of ADF test, its testing procedure is applied to the model $$\Delta y_t = \alpha+\beta t+\gamma y_{t-1} + \delta_1 \Delta y_{t-1} + \dots + \delta_{p-1} \Delta y_{t-p+1} + \epsilon_t$...
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I want to use VECM, does that mean all my variables should be stationary in the first difference at trend and intercept?

All my variables are I(1) using none, and intercept models, but not stationary using trend and intercept models. Not sure if I can use these variables in VECM?
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When should one use breakpoint unit root test, e.g. Zivot-andrew unit root test

I have conducted the ADF unit root test, all my variables are I(1) in all the three models: intercept, trend and intercept, and none. But my reviewer suggested me to include a structural break unit ...
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KPSS test thinks that regression is spurious

It should be obvious that there is a relationship between the market price of black pepper and the market price of white pepper. ...
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21 views

Detecting spurious regression by testing the residuals

A linear regression between "Number of Australian Air Passengers" and "Rice Production in Guinea" reveals a "strong" but probably spurious relationship between the two time series. ...
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According to this table, can I say my variables are integrated of order 1?

I tested my variables in ADF unit root test , can I say they all integrated in order of 1?
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14 views

Cointegration, Error Correction, and ADF test with lags

I am fitting an error correction model (ECM) of two I(1) variables. I'm following the Engle-Granger approach of first finding the cointegrating relationship. So first, I regress one series against the ...
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R: Interpretation of p-value in urca Dickey-Fuller test?

I'm checking my variables for stationarity and can't figure out how to interpret the p-value listed in the output of the Dickey-Fuller test from the urca package. ...
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Testing for weak-form efficiency - are unit root tests redundant after autocorrelation test?

I am testing the variability of the market efficiency over the time and one of the methods I'm using is a quite simple estimation of correlation coefficients and their significance for different lags (...
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Unstable panel VAR / PVAR

Quick question on PVARs. I am using Stata's user-written pvar package. After running the unit root tests using xtunitroot, I ...
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71 views

How to use the Phillips-Perron and Dickey-Fuller unit root test to test for AR(1) or Ornstein-Uhlenbeck process

My question comes from this paper (p. 10), where the authors say: The $\ln(\hat{p_t}) - \ln(p_t) \sim AR(1)$ condition expresses that the LPPLS fitting residuals can be modeled by a mean-reversal ...
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How to apply VAR model for a I(1) and other I(0) variable? Objective is to forecast [duplicate]

I am modeling liquidity variable, real money growth with real asset price returns. The former is I(1) and the latter is I(0). The objective is to see the predictive power and forecast. However, can we ...
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phi2 interpretation in Dickey-Fuller Test (package urca)

I am testing a time series using ADF test in urca package: summary(ur.df(data, type = "trend", lags = 1, selectlags = "Fixed")) Value of test-statistic is: -9.774 31.8531 47.7796 Critical values ...
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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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272 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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41 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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67 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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70 views

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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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
42 views

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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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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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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434 views

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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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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825 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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100 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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196 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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239 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 ...