# Tag Info

### What is the difference between a stationary test and a unit root test?

The Concepts and examples of Unit-root tests and stationarity tests Concept of Unit-root tests: Null hypothesis: Unit-root Alternative hypothesis: Process has root outside the unit circle, which is ...
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Accepted

### How is the augmented Dickey–Fuller test (ADF) table of critical values calculated?

I am not sure an easy answer is possible here. As can be found in many textbooks, the limiting null distribution of the "Dickey-Fuller t-statistic" is that of a nonstandard random variable which may ...
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### What is the difference between a stationary test and a unit root test?

I don't totally agree with the accepted answer: the null hypothesis of the KPSS test is not stationarity, but trend stationarity, which is quite a different concept. To summarize: KPSS test: Null ...

### Why is the dickey fuller test different from a simple t-test

You are right that the test statistic is just a standard t-statistic. It, however, follows a different null distribution, i.e., using critical values from the t or normal distribution would lead to ...
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Please have a look at my answer to the following question. What is the difference between a stationary test and a unit root test? Here is the most important part of the answer: If you have a time ...
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Accepted

### OLS - Non stationary variables but stationary residuals - is this OK or not?

...the dependent variable (Y) and the independent variables (X1, X2, X3, ...) are non-stationary. But the residuals are found to be stationary. Does this mean my regression is OK?... This suggests ...
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### Unit root tests ambiguous - is time series stationary?

ADF and PP tests address a specific form of nonstationarity, i.e. unit-root nonstationarity. Apparently, you reject that form. However, unit-root nonstationarity it is not the only possible form of ...

### Must a time series be stationary if it has no unit root?

No, roots outside the unit circle gives asymptotic stationarity, not strict stationarity: For a standard ARMA time-series model, the recursive formula for a model locks in the autocorrelation of the ...
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### Roots within the unit circle and non-stationarity

Not restricted to time-series analysis, characteristic equations (CE) are used in many applications or problems, such as differential/difference equation solving, signal processing, control systems ...
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### Why, exactly, is a unit root a problem?

Adapting this from Bauwens & Lubrano (1999), the part of the statistical procedure that "breaks down" in the presence of unit roots is asymptotic normality of the (OLS) estimator. For a ...
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### Manual calculation of ARIMA(1,1,0) forecast

The ARIMA(1,1,0) model is defined as follows: $$(y_t - y_{t-1}) = \phi (y_{t-1} - y_{t-2}) + \varepsilon_t \,, \quad \varepsilon_t \sim NID(0, \sigma^2) \,.$$ The one-step ahead forecast is then (...
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Accepted

### what means to be outside unit circle?

The roots in this case are roots of a polynomial, and they can be (and often are) complex numbers. That means they have coordinates, in this case called the real part and the imaginary part. As an ...
Accepted

### Dickey-Fuller test significant => series stationary?

You are not misunderstanding anything as far as I can tell. You are presenting a solid story with logical supporting arguments. I could stop here and I think your question would be answered, but let ...

### Influence of Seasonality on Unit root tests

A few days after I posted this question, I attempted simulations to test my intuition that strong seasonality can hide the underlying stochastic trend in the usual ADF test. Consider the following ...
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Accepted

### Trend stationary data series

A linear trend term has no unit root. A unit root arises in models like $y_t=y_{t-1}+\epsilon_t$, where the characteristic polynomial $1-z=0$ has solution 1. A linear trend model correspondings to ...
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### Dickey-Fuller unit root test with no trend and supressed constant in Stata

As for your first question, yes, the applied researcher should think about the correct specification of the deterministic part. It is definitely not appropriate (something you did not suggest, to be ...
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### Criticism of augmented Dickey-Fuller test

There are various criticisms, some of which, in my opinion, are more pertinent than others: Lack of power: When testing $\rho=1$ against $|\rho|<1$, it is argued that many macroeconomic time ...
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### Choosing the maximum lag length in the augmented Dickey-Fuller test

This is can be a tricky one. These Zivot Notes discuss a slightly more advanced way to select lags for the ADF. That being said, it is good to remember that purpose of including lags is to control ...
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### Interpreting R's ur.df (Dickey-Fuller unit root test) results

I found Jeramy's answer pretty easy to follow, but constantly found myself trying to walk through the logic correctly and making mistakes. I coded up an R function that interprets each of the three ...

### Are seasonal differencing and polynomial trends interchangeable?

I do not have general answers, but here are some thoughts that will hopefully be helpful. First, can a repeated seasonal differencing filter also remove a polynomial trend? In which conditions? I ...

### Can Dickey-Fuller be used if the residuals are non-normal?

Yes, that is not a necessary condition. Recall that all we know about the null distribution of the Dickey-Fuller test is its asymptotic representation (although the literature of course considers many ...
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