# Tagged Questions

A stationary process (or time series) is one whose joint distribution is constant over time. A weakly stationary process or series is one whose mean and covariance function (variance and autocorrelation function) are constant over time.

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### Does correlation assume stationarity of data?

Inter-market analysis is a method of modeling market behavior by means of finding relationships between different markets. Often times, a correlation is computed between two markets, say S&P 500 ...
7k views

### Why does a time series have to be stationary?

I understand that a stationary time series is one whose mean and variance is constant over time. Can someone please explain why we have to make sure our data set is stationary before we can run ...
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### How to check if the volatility is stationary?

Please, take a look at the chart below. As you can see the first period the volatility is high and the second is low. How can I check if the volatility is stationary (homogeneous) during the ...
1k views

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

What is the difference between the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test and the augmented Dickey-Fuller (ADF) test? Are they testing the same thing? Or do we need to use them in different ...
201 views

### Testing two I(1) vectors for a relationship

Suppose I have two I(1) time series X and Y, and I want to know whether X and Y are "related" (for some definition of "related"). The standard cointegration approach defines relationship as ...
964 views

### Can I detrend and difference to make a series stationary?

I have a dataset that is clearly increasing as time goes on (exchange rate of a currency, monthly data over 20 years), my question is: Can I detrend the data and then difference it also to make it ...
389 views

### Conditions for Central Limit Theorem for dependent sequences

Cumbersome technical assumptions (e.g., mixing properties) are used in the literature to prove Central Limit Theorems for dependent sequences. I sketched a proof that does not require any of these ...
809 views

### Selecting regression type for Dickey-Fuller test

I have a time series and I want to check whether it has a unit root or not. I want to use the Dickey-Fuller test. How should I choose the regression equation from the three options: regression without ...
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### $R^2$ from a regression of two trend-stationary processes, $Y_t$ and $X_t$

In Estimation and Inference in Econometrics, by Davidson and MacKinnon, p.671, they claim that $R^2$ from a regression of $Y_t$ on $X_t$, where both time series are trend stationary, tends to 1 as $n$ ...
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### How to determine correlation between stationary and non-stationary time series

I have three time series of economic data based on quarterly observations; A, B and C, and I would like to ascertain the correlation (or not) between A and C as well as the correlation between B and ...
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### Putting stationary variables through Johansen procedure

Is it okay to feed $I(0)$ variables into the Johansen procedure? I've read three sources that seem to state that this is not what you're supposed to do. However, whenever I've done this, I notice that ...
I am confused on why a simple trend process is not stationary. Consider the following process: $Y_t = a + bt + \epsilon_t$ The variance is clearly constant. However, the mean $bt$ is dependent on ...