# Questions tagged [augmented-dickey-fuller]

A test of the [null] hypothesis that a time series has a unit root (ie, that it is non-stationary).

357 questions
Filter by
Sorted by
Tagged with
8 views

### Dickey Fuller test: confusion about the alternative hypothesis

I am rather confused about the alternative hypothesis of the Dickey-Fuller test (at least from a practical perspective). I understand the mathematical details behind the DF test, but I am struggling ...
• 431
12 views

### Confused about the stationarity and unit root concepts

Say that I consider a white noise process, which by definition is stationary. I'm confused by the fact that if I use the Dickey-Fuller test, technically speaking I should fail to reject the null ...
• 431
29 views

### 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 ( ...
• 107
21 views

### Stationary Check (ADF, KPSS and ACF PACF Plot) for SARIMAX model

I'm still confused about whether my data is stationary in terms of variance and mean or not, because based on the ADF test and KPSS test the data already shows stationary (because it rejects H0) but ...
14 views

### I don't understand the terms "constant and trend" in the case of the Dickey-Fuller test, where the difference $\Delta y_t$ is on the left hand side

Take Wikipedia https://en.wikipedia.org/wiki/Dickey%E2%80%93Fuller_test or the R documentation https://search.r-project.org/CRAN/refmans/aTSA/html/adf.test.html Type 3 Dickey-Fuller describes the ...
1 vote
21 views

### 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 ...
• 539
19 views

### In ADF test, how do I specify non-linearity?

I have a time series exhibiting a non-linear relationship, with dips during recessions. I want to perform an augmented dickey fuller test to test for a unit root/stationarity. I'm not sure how, or if, ...
86 views

### Unit-Root Asymptotics

I am using the book "Time-series-based econometrics" by Hatanaka to learn about asymptotic theory of unit roots. However, it is quite technical, so I am also using Hamilton's "Time ...
• 81
86 views

### Interpretation of ADF test output with R

I Run ADF test with R for 3 different models include,1.No deterministic terms, 2. with constant and 3.constant and trend based on the below code where all model specifications employ a lag-order of p =...
18 views

### ADF test output in R

I Run ADF test with R for 3 different models include, No deterministic terms, with constant and constant and trend based on the below code. However, I am unsure about which corresponding p-value (I ...
1 vote
28 views

### Choosing number of lag AND model form for Augmented Dickey-Fuller test

Before realising an Augmented Dickey-Fuller (ADF) test, one has to answer 2 questions, how many lags p to include in the model, AND which model to choose among the following: No constant, no trend ...
• 11
45 views

### How to choose the order of differencing?

I have a time series that looks like this I was asked to display the autocorrelation function and perform ADF test and based on that suggest a d for further analysis. I get plots like this and can ...
• 1
43 views

### OLS - Error term/Residuals failed the ADF/Stationary test, so what is the implication?

I have a simple liner regression model, and I tried validating if the model fit for purposes. One of the tests is Augmented-Dickey Fuller test on the residuals but the result of the test shows that ...
44 views

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 ...
119 views

### Understanding Dickey-Fuller test results on series with non-constant variance

My understanding is that a time series that does not appear to have constant variance over time is not stationary and that the Dickey Fuller test tests for stationarity (with the null hypothesis that ...
• 1,189
21 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.)...
1 vote
14 views

### A time series which doesn't look stationary but pass the ADF (augmented Dicky-Fuller) test [duplicate]

My time series look like this, but it passed the ADF test. Does it make any sense?
• 11
1 vote
50 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?
1 vote
89 views

### Discrepancies in ADF test results

I have several short (n=12) time series on which I am trying to conduct Augmented Dickey-Fuller tests, but I am getting very different/unexpected results: ...
• 161
1 vote
16 views

### For checking stationarity for applying Granger Causality Test, should the range of both the time series be same?

I have 2 time series - one is for scores of people in a survey and the other for the sales of a product for 10 distinct countries. The survey data is categorized into 3 categories for each country. So,...
33 views

### Rejection of ADF-test for log returns and AIC selected ARIMA(0,0,0) and ARIMA (0,0,0) with a drift?

I use monthly log returns for some stock portfolios and rejects the null of the ADF-test for both. Hereafter I use AIC to select best fitting models using auto.arima in R. The selected models are ...
1 vote
75 views

### First difference of logs of negative numbers causes trouble

I have the following problem: I have a timeseries with the prices for a few futures, which is non-stationary (according to ADF test). If I apply first difference of logs, ADF shows stationarity. But I ...
• 47
80 views

### Differencing, taking logs or squaring does not fix nonstationarity. What to do?

I want to test for correlation in a time series model. However, all four independent variables and the dependent variable are non-stationary. I tried taking first, second and third differences but my ...
177 views

### Stationarity in an interrupted time series

I am using proc autoreg in SAS to conduct an ITS analysis and I have a question about stationarity. Proc autoreg is able to ...
• 75
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 ...
• 25
98 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 ...
• 107
92 views

below is my ADF test for regression residuals. I use alpha=5% My interpretation is : my residuals are non-stationary as my model does not take into account the 4 lags suggested by ADF. In other words, ...
• 337
114 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 ...
4k views

### Johansen Cointegration test in Python (statsmodels)

I have three time series df['a'], df['b'] and df['c'] which I want to test for cointegration ...
294 views

### Python statmodel coint doesn't give the same p-value as adfuller on OLS residual

According to Eagle and Granger (1987), if I have 2 time series y1 and y2, we can test their cointegration with the p-value of an ADF stationarity test performed on the OLS residual. Though, when ...
1 vote
247 views

### Understanding different versions of Augmented Dickey Fuller tests

I am new to statistics and I have been struggling to understand the three different versions of (A)DF test. For simplicity I will use the naming conventions from https://en.wikipedia.org/wiki/Dickey%...
• 11
48 views

### Why are tsplot and ADF test results inconsistent?

I have airline time series. Here is the tsplot The data clearly seems non-stationary to me. However, ADF test produces a p value of 0.01, indicating that the data is stationary. Any idea why?
• 951
170 views

### ADF and KPSS test both conclude stationarity but the time series has trend?

I am trying to implement time series stationarity tests on my data. When I carry out ADF (Augmented Dickey-Fuller) and KPSS tests on my data the p values suggest time series stationarity. However, ...
184 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
951 views

### Is the Dickey Fuller test one-sided or two-sided?

The Dickey Fuller test tests whether a unit root is present in an AR model. Specifically, we have $$X_t = \phi X_{t-1} + \varepsilon_t$$ where $\varepsilon_t$ is a Gaussian noise term. Now the ...
• 715
331 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 ...
• 1,140
1 vote
167 views

### Stationary time series with drift

I have a question regarding the ADF test. I ran a ADF test with drift with the urca library in R. The result implies a stationary series with drift, which is not ...
• 31
163 views

### Applying the Engle-Granger and the Johansen test to univariate multiple regression

I have want to test the cointegration of interest rates in three time series: a group of small open economies, US, and Erozone. I use daily data, and assume that the small open economy has no impact ...
• 63
173 views

### Dickey Fuller Test for Stationarity

I have a data with 4 columns, all has clear downward trend from 2020 to 2022. Except second column dickey fuller declare them stationary data.I believe due to clear trend all columns are non ...
1 vote
162 views

### How to use MC simulation to calculate Supremum ADF test critical values

I am replicating some techniques from Advances in Financial Machine Learning by Marcos López de Prado. In Chap 17, I am doing the Supremum ADF test and Quantile ADF test. It seems that they do not ...
1 vote
279 views

### Non-stationary time-series on visual analysis passes all Stationarity tests?

I have a time-series data (Fig 1) that clearly look non-stationary on visual analysis. There is a clear trend and seasonality in the time series as shown in the Final figure below. But the ADF test ...
• 544
283 views

### Can a timeseries with a clear trend be considered stationary?

I performed a augmented Dickey-Fuller test on a timeseries (that clearly has a trend) and, from the results, it suggests it is stationary (p-value = 0.01). Is this possible? ...
• 91
1 vote
213 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
721 views

### Why does the order of the pair of series passed to a cointegration test matter?

Update 2022-07-13 My question could be rephrased as Why do I get a different result for cointegration test when I swap the independent and dependent variables? The link leads you to a thread on this ...
• 51
114 views

### Cointegration between 2 Stocks. - confirming Times Series Stationarity using ADF & KPSS Test

I had created a google sheet with the help of online resources, - to conduct cointegration test on 2 stocks time series. It checks null hypothesis, to see that a unit root is present on the residual ...
32 views

### determine if series is non-stationary or stationery

I have series and I need to determine if the series is stationary or non-stationary. According to this web page Link, is prefer to use the ADF and KPSS and then judge on the series. My result of ADF ...
• 177
880 views

### Should I difference my data before run a ADF test?

I plot my data as shown in the following screenshot: Clearly the series contains a trend. A first order difference of my data will eliminate the trend, which I plot as follows: Now I would like to ...
• 125
1 vote
84 views

### How powerful is cointegration test?

I am performing Engle-Granger cointegration test on my data as below ...
• 65
1 vote
364 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