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).

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Augmented Dickey Fuller Test Procedure

So I am trying to understand the inner-workings of the Augmented Dickey Fuller Test. In the limited amount of novice information I could find, it seemed to be executed slightly differently. The best ...
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25 views

Time series regressions

I'm trying to make a basic scatter plot/regression to look at the relationship between two time series. Series a is volume of mentions of a product on a forum over time, series b is the sales of the ...
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Unit Root Test seems ambiguous - is my time series stationary?

I am testing the stationarity of my residuals through the ADF test (Augmented Dickey Fuller test) and the results imply stationarity of my time series. However, the time series do not really show ...
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25 views

ADF-Test indicates stationarity for a non-stationary time series

I have a minor issue and am not sure what to do. The link below leads to an image of two time series I plotted, the upper being the original, the bottom one obtained by taking the first differences. ...
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22 views

Augmented Dickey-Fuller test interpretation before and after log transform the data

I have apply the stationarity test to a stock's adjusted price by using the Augmented Dickey Fuller Test with the program R. That is the output from ...
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22 views

Which Method for making a time series stationary would work better?

If there is a possible multiplicative time series (seasonality increasing marginally over time) that has a large trend component and a smaller seasonal component, would a Lag 1 difference to remove ...
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12 views

Time series unfit for ARIMA

Time series has to be stationarized in order to be fit for application of ARIMA. We can either do this with additional order of integration or by differencing the series before making the model. But ...
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17 views

Is this data stationary ? I’m having issues with the correlogram

I have run the augmented dickey fuller test and the NGperron test , I have taken the first difference ,the data seems stationary however the correlogram is still exactly the same and the values as ...
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28 views

Contradictory result from adf.test and ndiffs in R

I want to check if a time series is stationary in R. For ndiffs, > ndiffs(GDPlst_t$GDP110000, test="adf") [1] 0 the ...
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1answer
20 views

How to conduct series of ADF tests on data in correct way?

I was trying to fit an ARMA model for some data. It was easy to spot that data is non-stationary, so I decided to conduct ADF test on it and it turns out that I was right. Then I took the first ...
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82 views

Trouble interpreting cointegration test results

I'm struggling with testing the cointegration of 2 time series (or rather interpreting the test results properly). So I got 2 time series x and ...
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51 views

What do we only care about $\alpha=1$ for unit roots?

https://www.machinelearningplus.com/time-series/augmented-dickey-fuller-test/ In 2), why do we only care about $\alpha=1$ to get a unit root. I guess if $\alpha<1$ we have some mean reversion, but ...
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Dickey-Fuller test significant => series stationary?

I recently came across the Dickey-Fuller test for existence of a unit root in an AR(1) series, definition on Wikipedia. If a unit root exists, the series is not stationary. Fine by me. Now looking ...
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51 views

Dickey-Fuller test for unit root

Why we subtract xt-1 from both sides of AR(1) equation to test if g1 = b1 - 1 is equal to 0, rather than test if b1 is equal to 1 in Dickey-Fuller test process?
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79 views

Augmented Dickey-Fuller Test and Lag Length

In R, using the package tseries, one uses the command adf.test for the Augmented Dickey-Fuller Test. However, this assumes a ...
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Should I use my residual's data to model if it has a lower p-value?

I ran the Dickey-Fuller Test on my original dataset and on my residual values. and got these results. As you can see, the p-value for both tests allowed me to reject my null hypothesis, which passed ...
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Augmented Dickey Fuller (ADF) test statistics GPU formulation

I have followed different sources of information and achieved the following formulation for the ADF $t$ test statistics. I implemented it to run several hundred thousands of ADFs $t$ statistics on GPU ...
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110 views

ADF test fail to reject while kpss and box say white noise and stationary

Why would Augmented Dickey-Fuller Test fail to reject in this case? (Which implies a unit root exists and non-stationary series) when Box-Ljung also fails to reject, which implies white noise? and, ...
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19 views

Bizarre simulation results with ADF test

I simulated the following processes \begin{align} y_{1,t} = \beta y_{2,t} + \epsilon_{1,t} \\ y_{2,t} = y_{2,t-1} + \epsilon_{2,t}, \; \; \; \epsilon_{2,t} \sim N(0,1) \\ \epsilon_{1,t-1} = \...
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148 views

When do you use the Dickey Fuller Test and the Ljung-Box Test?

When do you use the Dickey Fuller Test and the Ljung-Box Test? They seem to serve the same purpose? I think that the Durbin-Watson statistics just checks for autocorrelation at lag 1.
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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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32 views

Can a ratio variable be trend stationary?

Can a ratio variable, e.g. the wage share of factor incomes, really be trend stationary? It is bounded between 0 and 1 and moves in between during long periods, acting like a non-stationary variable. ...
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71 views

Can adf test and kpss test contradict?

I have a time series data for 18 months. To check for stationary I conducted adf test, to which my p value is 0.8. And kpss test has a p value of 0.1 , so at 95% confidence level I fail to reject null ...
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80 views

Can a time series be stationary and still have seasonality?

Would there be a case that a time series does have seasonality but, ADF test fails to point it out. I want to be sure of it being stationary so that I can use it in a regression and be sure that the ...
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53 views

Interpreting Dickey-Fuller test vs Autocorrelation

I have time series dataset and I have run the Augmented Dickey–Fuller test using statsmodels and got the below statistic ...
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44 views

Dickey-Fuller Test Terms

Why do we distinguish between the terms "constant", "intercept" and "drift" in the ADF test? I understand them to be analogous yet the literature seems to define "intercept" separately? For example, ...
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Different cointegration results for pairwise time-series

I have two time-series Y and X, they are both univariate and integrated of order one. I want to observe the cointegration relationship between them and I use Engle-Granger method. Each time when I ...
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53 views

Johansen Cointegration and ADF Example

I'm trying to reproduce the Example 3.2 from "Likelihood-based Inference in Cointegrated Vector Autoregressive Models" by Søren Johansen. The example proposes the following processes: $X_{1t} = \sum_{...
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Help with understanding tau1, tau2 and tau3 from ADF test?

I'm new to Time Series and could need some help! I'm trying to do a ARIMA forecast for (differentiated) consumption expenditures ("dkonsumtionsutgifter" is the variable called in my data. I'm running ...
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18 views

Why does a trended series and a random series give low p values on ADF test?

Why do the following two series both produce p-values below 0.05, given that one is trending and the other not? What does this test really mean given this? ...
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67 views

Statsmodel ADF interpretation

I'm regressing two time-series against one another, and I'm struggling with how to interpret an ADF test: does a low value indicate that a series, once detrended, would be stationary; or does it show ...
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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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38 views

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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What's the intuition behind re-parameterization in the Dickey-Fuller test?

In text books and lecture slides, people often explain that the normal t-test of, say, the AR(1) parameter in the Dickey-Fuller test does not follow the usual distribution. It also explain that after ...
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1answer
53 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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Multivariate stationarity/cointegration test

Am I right to say that for multivariate time series, we can't use normal stationary test like Dickey–Fuller test and we need to use cointegration Test like Johansen? Or this is not true in general?
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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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137 views

How to interpret the the results of augmented Dickey-Fuller test to make conclusions about the order of integration

I am following Pfaff 2011 chapter 3 and 5.1 to find the order of integration of a time series $y_t$ by augmented Dickey-Fuller (ADF). Basically what we do here is testing whether $y$ has a unit root ...
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29 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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53 views

Is my interpretation of ADF and KPSS correct?

I am new to time series analysis, and I am trying to interpret the ADF and KPSS results. Is my interpretation of stationary correct? ...
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69 views

Augmented dickey fuller test

Why augmented dickey fuller test gives me less p-value i.e. less than 0.05 despite of having seasonality my data. My data's plot: Code for adf test : from pandas import Series from statsmodels.tsa....
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120 views

How many lags to use for ADF test if several values reject null hypothesis?

I'm still a novice with time series so I'm sorry if this is a little basic.When performing an Augmented Dickey Fuller test on my data I found that lag values from 1-4 all lead me to reject the null ...
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217 views

Is my Data stationary? KPSS, ADF Tests and ACF

I already differenced my Data by 1 and i am not sure whether my Data is now stationary or not. I perfomed an KPSS and ADF test in order to help me decide if it is. I think it is stationary but im not ...
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96 views

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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Augmented Dickey-Full Test Standard Error

I am currently reading Introduction to Time Series and Forecasting (Brockwell & Davis 2016) and am struggling to understand the following (pg 170 for those with the book). The unit root test for ...
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36 views

How to interpret Dickey-Fuller Results

I want to prove that my data is non-stationary at level, but stationary after first differencing. I am trying to do this with the ur.df() function in R, but I am a ...
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154 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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