# 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 Unit Root test, Deterministic Terms

I'm learning about unit root tests and i'm trying to implement these tests in python. I have some doubts about the theory underlying the deterministic terms inside the regression. Some textbooks ( ...
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### Intuition behind unit roots in practice

One area where the application of unit roots to time series modelling seems very intuitive is in climate change: carbon dioxide stays in the air, so past shocks (size of flow) have a cumulative effect ...
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### Unit root stationarity and modelling AR(p) process

I'm reading through Introduction to Econometrics by Gary Koop. I'm a little confused on the process for modelling AR(p) processes. Hopefully someone can help clarify things for me. Let me set out my ...
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### How to derive the (partial) maximum likelihood estimator for a simple autoregressive model

I am trying to derive two maximum likelihood estimators which I have seen in a statistics book, but I am unable to derive them and would really like some help. It goes like this: Consider the simple ...
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### Multiple comparison problems for Unit Root testing

Lets say I have a multivariate time series and I will run unit root tests for each variable to figure out if the variable is stationary and how many differencing are necessary to make it stationary. ...
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### ADF & KPSS Test Reporting Series as I(19)

I am currently attempting to determine the order of integration for a nonstationary time series of the Federal Funds Rate (https://fred.stlouisfed.org/series/FEDFUNDS - Monthly, 1990 to 2004, 168 obs.)...
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### How to Handle a Trend-Stationary Dep. Variable and Stationary and Non-Stationary (Unit-Root) Ind. Variables?

I am trying to determine the best way to proceed when one has a mix of stationary, trend-stationary and non-stationary variables with unit roots. My dependent variable $Y_t$ is a trend-stationary ...
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### ARIMA(1, 1, 0) and explosive process

What is the difference between ARIMA(1, 1, 0) whose AR coefficient is smaller than 1 (e.g. 0.3) after being differenced and an explosive process whose AR coefficient is 1.3? Are these two identical? ...
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### Do monthly sales of a retail shop have a unit-root?

Simple question to understand if by nature monthly sales from a retail shop on the high street are likely to have a unit-root in its timeseries or not?
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### What happens if you difference a IMA?

When we over-difference a time serie, we are introducing units roots in its moving average component, hence obtaining an IMA. My question is: IMA is an integrated time serie, hence it has unit root ...
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### The difference of a variable has a unit root, but the variable itself doesn't

I am trying to build an ARDL model with the six following variables: lnNO2,lnP,lnGDP,...
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### Unit root test and cointegration

maybe someone can help me with my data. I analyse how macroeconomic indicators affect stock index. For this analysis I prefer VAR model.In my case data of all variables are non-stationary - I have ...
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### Unit root test on growth variable?

When constructing an ADF unit root test, is it Ok that input data is a growth variable? I was thinking about when you compute growth rate $\left(\frac{Y_t - Y_{t-1}}{Y_{t-1}}\right)$ and when ...
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### ARDL Unit root df

When applying ARDL I used Dickey-Fuller unit root test, and found variables integrated at I(1) and I(0). For running the ARDL model do I use my original data (not differenced) or do I use the ...
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### Augmented Dickey–Fuller test, Test Model

I don't understand how we obtain the model that we test for a unit root in the ADF test. Let me explain better. ADF test is used to test if a time series has a unit-root. We assume that the Data ...
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### Prove that OLS estimator of AR(1) coefficient for an AR(p) process with unit root converges to 1

Suppose that the DGP is an AR(p) with a unit root. When we fit, using OLS, an AR(1) model $x_t=\alpha x_{t-1}+u_t$ to the data, we get $\alpha=1$, indicating, correctly, that this is a unit root ...
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### Interpreting Phillips Perron Test results using R

I performed pptest in R for corn variables and am unsure how to decipher the p-value and what that means for the hypothesis.
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### Ng and Perron (2001) unit root test in R [closed]

I am looking for a function in R, which executes Ng and Perron (2001) unit-root test and computes all 4 test statistics like in eViews: So far I have read vignettes of packages bootUR and CADFtest, ...
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### Process is NOT integrated but autocorrelated. Can I use linear regression models?

I'm carrying out a stationarity analysis over a process Y that looks like this: From the autocorrelation function the process doesn't look strictly stationary since the decay is quite low, even if it ...
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### Understanding Dickey-Fuller-Result

I am currently looking into the dickey-fuller test but seem to not understand something fundamental. To understand the test better, I created 4 time series: cons, lin, r1 and r2. How these are ...
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### Deriving ADF unit root test form for the time series with quadratic deterministic trend

I have the following time series process $y_t$ $$\Delta y_t = \delta + \gamma t + \epsilon_t$$ where $e_t$ is white noise process with the variance of $\sigma^2$. I guess that whereas $\Delta y_t$ is ...
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### Unit root testing in AR(2) simulated data

I'm teaching a course in time series analysis, and using a lot of R simulation. I've come across the following situation. Consider an AR(2) process with $x_t = x_{t-1} - x_{t-2}+w_t$ where $w_t$ is ...
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### purtest and psacf: How to test it in R?

I am working with balanced panel data (annual country level data: 37 countries and 11 years) and would like to test stationarity. I am using fixed effects for both country and year. Now, I am checking ...
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### statsmodels.adfuller weird behaviour of usedlag value

I'm learning about time-series analysis and have two series on which I'm performing an Augmented Dickey-Fuller test in order to check for stationarity. I'm trying to understand why I get very ...
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