# 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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I am trying to use the adfuller test to determine whether the following timeseries is mean reverting (stationary) From the chart we can see that its obviously (at least my non-expert eye) non ...
1 vote
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### How to deal with different orders of integration between explained and explaining variables?

Is there a standard, or at least a valid, regression approach if you are trying to regress a dependent variable with a unit root against a set of stationary independent variables? I know I could ...
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### Why, exactly, is a unit root a problem?

Suppose that we have observations $x_1,\dots,x_n$ for some process. We want to fit an AR(k) model to these observations. I do not understand why the naïve OLS approach to estimate our AR(k) ...
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### Trying to understand stationary series: How is this TS stationary?

I'm studying the cointegration of the prices of 2 assets. The time series that you see here is the first integration of the log prices of these assets. If I only look at the graph I would say that the ...
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### Can a process with a unit root still be stationary?

It is quite clear, by expanding the inverse lag polynomial, that a process without unit roots will be weak-stationary. However, I'm not finding anywhere a proof of the other implication: to be weak ...
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### Trend stationary data series

I have a trend stationary data series that does not have a unit root. The data are hourly with about five years of data. I have controlled for the apparent trend in the data using a series of binary ...
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### Need help in panel data tests and steps

Greetings! I am analyzing the impact of climate change of wheat crop across 4 districts for the last 30 years. It is imperative to check the stationarity of the panels. I performed LLC and IPS tests. ...
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### ADF test in R and Gretl - Why are the results different?

I am working on a time series-based study on the Czech Republic. I have macroeconomic data from 1993 to 2021. I tested my time series for stationarity using both R (function ...
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### ECM long-run elasticity with one I(2) variable

I am estimating a 2SLS using a time series simultaneous equation ECM. The purpose is to estimate the price elasticity of electricity demand. Assume that both price and demand are I(1) variables, ...
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### ADF-test. Contrary results at different lag lengths

I have a time series of weekly household electricity consumption, which I'm using as the dependent variable in an ECM. An Augmented Dickey Fuller (ADF) test reveals that the variable (LNO1_Con) has a ...
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### Does the AR-parameters sum to 1 violate stationarity?

Use AR(2) model as an example of my question: $$x_t = \phi_1 X_{t-1} + \phi_2 X_{t-2} + \varepsilon_t$$ if $\phi_1 = 0.5$ and $\phi_2 = 0.5$, then sum of AR-parameters equals to 1. Does it violate the ...
1 vote
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I have first level differenced an independent variable in order to combat unit root in panel data. My panel data consists of N = 487 and T = 1491. When comparing the coefficient of the original ...
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### How to interpret the results of mean and variance to determine the stationarity of time series

After breaking the series into 3 parts and then compute mean and variance for each part. I need to understand what is the acceptable difference between the 3 parts to say this series is stationary? ...
1 vote
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### Order of integration for a time series with constant mean and increasing variance

I am trying to find the order of integration of a time series. I checked for stationarity using the ADF and KPSS tests. Both the tests indicated non-stationarity, so I differenced the series once and ...
1 vote
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### Testing by using KPSS

When use KPSS to test the stationarity of data series I get this warning .Does it affect the final results? ...
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In the section 15.4 of Hamilton's book Time Series Analysis ( 15.4: The meaning of Test Unit Roots) the author says: Although it might be very interesting to know whether a time series has a unit root,...
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### Is it possible to describe a AR(1) process as stable in terms of a stability triangle?

Is it possible to describe AR(1) as stable in terms of a unit triangle as in the explanation below or not because a lack of a second degree characteristic polynomial? Consider the equation  \lambda^... 1 vote
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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 ...
1 vote
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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 ...
1 vote
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### Examining stationarity, mean and variance of time series

Hi guys, I encounter this question for a Business Forecasting module and I am very confused by it. Firstly, this looks like an autoregressive model of order 1. From the looks of it, the φ coefficient ...