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.
389
questions
0
votes
0
answers
25
views
Missleading ADF Results
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
1
vote
0
answers
11
views
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 ...
- 3,047
4
votes
1
answer
81
views
Rewriting the characteristic polynomial using that the inverse roots are invertible
I am looking at an I(1) process for an AR(3) model:
$$x_t=\theta_1x_{t-1}+\theta_2x_{t-2}+\theta_3x_{t-3}+\varepsilon_t$$
I rewrite it using the lag-operator:
$$(1-\theta_1L-\theta_2L^2-\theta_3L^3)...
- 65
0
votes
0
answers
15
views
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 ...
- 65
0
votes
0
answers
42
views
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.
...
- 1
0
votes
0
answers
19
views
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.)...
0
votes
0
answers
90
views
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 ...
1
vote
1
answer
26
views
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? ...
- 21
1
vote
1
answer
98
views
0
votes
0
answers
21
views
ADF tests: phi2 and phi3 explodes when differencing
ADF tests are used to inform on the order of integration of a time series. With the function ur.df, three different specifications can be used, called "trend&...
- 63
1
vote
1
answer
49
views
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?
0
votes
0
answers
15
views
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 ...
1
vote
0
answers
40
views
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,...
- 91
0
votes
1
answer
112
views
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 ...
0
votes
0
answers
113
views
Cross-sectional dependence and second generation unit root tests
Could someone explain me in simpler terms what a cross sectional dependence and panel unit root tests does in practice? How is panel unit root tests different from any other unit root tests such as ...
- 13
0
votes
0
answers
30
views
impact analysis and a unit root
In conducting an impact analysis, how can we deal with a target variable, if it contains a unit root? In this case, an impact is expected to change the level of the variable. But then the impact ...
- 21
0
votes
0
answers
17
views
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 ...
- 15
0
votes
0
answers
37
views
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 ...
- 15
2
votes
1
answer
66
views
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 ...
- 67
1
vote
0
answers
61
views
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 ...
- 211
0
votes
0
answers
97
views
ARIMA fit() summary() in Python's statsmodels not showing Roots of characteristic equation
I am using statsmodels version (0.13.5) to fit an ARIMA model. When the summary() is displayed I would like my results to include the Characteristic roots as show in the second set of results below ...
- 1,753
2
votes
0
answers
87
views
how to confirm a trend is deterministic or stochastic?
So I got this basic concept of deterministic and stochastic trend.
$$\begin{align*}\text{Deterministic trend (DT)} & : y_t = \beta t +\varepsilon_t\\
\text{Stochastic trend (ST)} & : y_t = \...
- 21
7
votes
2
answers
880
views
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) ...
- 211
0
votes
0
answers
34
views
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 ...
- 83
0
votes
0
answers
49
views
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 ...
- 211
3
votes
1
answer
80
views
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 ...
- 73
0
votes
1
answer
28
views
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. ...
0
votes
0
answers
92
views
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 ...
0
votes
0
answers
41
views
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, ...
- 33
0
votes
0
answers
37
views
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 ...
- 33
0
votes
1
answer
30
views
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 ...
- 113
1
vote
0
answers
23
views
Sign of first level differenced variable changes sign in regression
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 ...
- 11
0
votes
1
answer
48
views
Investigating the presence of unit root in the following $X_t$
I am given a model and need to calculate the unit-root of $X_t$ but it seems that there is no unit-root.
The model is given: $X_t = (x_{1t},x_{2t})'$
$$\Delta X_t = \alpha \beta ' X_{t-1} + \epsilon_t ...
user375678
0
votes
1
answer
470
views
Interpreting Phillips Perron Test results using R
I performed pptest in R for corn variables and am unsure how to decipher the p-value and what that means for the hypothesis.
- 1
2
votes
0
answers
155
views
Ng and Perron (2001) unit root test in R [closed]
I am looking for a function in R, which executes Ng and Perron (2001) unit-root test and computes all 4 test statistics like in eViews:
So far I have read vignettes of packages bootUR and CADFtest, ...
- 21
0
votes
0
answers
54
views
Process is NOT integrated but autocorrelated. Can I use linear regression models?
I'm carrying out a stationarity analysis over a process Y that looks like this:
From the autocorrelation function the process doesn't look strictly stationary since the decay is quite low, even if it ...
- 1
2
votes
1
answer
164
views
Understanding Dickey-Fuller-Result
I am currently looking into the dickey-fuller test but seem to not understand something fundamental. To understand the test better, I created 4 time series: cons, lin, r1 and r2. How these are ...
- 21
5
votes
1
answer
275
views
Deriving ADF unit root test form for the time series with quadratic deterministic trend
I have the following time series process $y_t $
$$\Delta y_t = \delta + \gamma t + \epsilon_t$$
where $e_t$ is white noise process with the variance of $\sigma^2$.
I guess that whereas $\Delta y_t$ is ...
- 1,060
1
vote
0
answers
141
views
Unit root testing in AR(2) simulated data
I'm teaching a course in time series analysis, and using a lot of R simulation. I've come across the following situation. Consider an AR(2) process with $x_t = x_{t-1} - x_{t-2}+w_t$ where $w_t$ is ...
- 267
0
votes
1
answer
74
views
Does the Augmented Dickey-Fuller test only consider first-order effects?
The original Dickey-Fuller test provides a test for the H0: no unit root, so $\gamma \neq 0$ in a simple AR(1) model:
$$X_t = \rho X_{t-1} + \varepsilon_t$$
$$ \Delta X_t = \gamma X_{t-1} + \...
- 695
0
votes
0
answers
21
views
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?
...
- 177
1
vote
1
answer
143
views
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 ...
- 13
1
vote
1
answer
272
views
Testing by using KPSS
When use KPSS to test the stationarity of data series I get this warning .Does it affect the final results?
...
- 177
4
votes
1
answer
56
views
The meaning of Test Unit Roots: unanswerable and answerable questions
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,...
- 997
2
votes
2
answers
81
views
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^...
user318514
1
vote
0
answers
420
views
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 ...
- 133
1
vote
1
answer
302
views
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 ...
- 113
1
vote
0
answers
53
views
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 ...
- 21
2
votes
0
answers
79
views
Does the Absence of a Unit Root Imply Wide Sense Stationarity?
I'm taking a course on time series currently and have been slightly confused about the interplay between unit roots and stationarity in a question I've been attempting to answer. The question set up ...
0
votes
0
answers
180
views
What to do when kpss contradicts ADF?
I'm testing to see if Inflation has a unit root and if it has a drift and trend, just drift or no drift and trend. My results from the ADF test looks like this:
...
- 177