# Questions tagged [spurious-correlation]

Nonzero correlation between variables $x$ and $y$ where neither $x$ causes $y$ nor $y$ causes $x$. May result from both variables having a common cause or the correlation being conditional upon a common effect of both $x$ and $y$. Use also for spurious regression.

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### If we include lags of the dependent variable on the RHS of our regression of Y_t on X_t, why we not have spurious regression

So, assuming X,Y are I(1), only (7) could be spurious right? Why can (8) and (9) not be spurious? Isn't there still a common stochastic trend shared between X_t and Y_t?
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### Spurious regression - are the coefficients biased or not?

Say that we are regressing a variable $Y_t$ on another variable $X_t$, and both series are non-stationary. Specifically, let's say that both are $I(1)$ and trend upwards over time. Now, say we ...
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### Non-Stationary Data with Lagged Dependent Variable?

I am currently dealing with non-stationary data and I am unsure of how to proceed. My data is stationary in first differences I(1), which I confirmed using a Dickey-Fuller unit root test. However, I ...
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### Spurious Regressions (Random Walk)

I have learned that the regression of a random walk process on another leads to seemingly statistically significant relationships, if you just use OLS. However, why do we get such large t-statistics? ...
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1 vote
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### Lagged dependent variable with non stationary time series

I'm doing a regression analysis with non stationary time series. If I run the regression the residuals are auto correlated and non stationary. If i add a lag of the dependent variable (the estimated ...
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### Regression of Stationary Time Series in Non-Stationary Time-Series

Let's suppose that I have a time series $Y_t$ with dimensions $T \times 1$ with monthly frequency, and a matrix of external variables $\boldsymbol{X_t}$ of dimensions $T \times p$ where $p$ also ...
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### Is spurious regression a problem for lasso and similar techniques?

I was toying with R to see how the number of variables might affect spurious regression. Suppose that we have an $I(1)$ vector $y$ and a matrix $X$ with $I(1)$ columns. If the two are not related then ...
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### Spurious regression for large T small N logistic regression?

My question is - Will there be problem of spurious regression for large T small N panel logistic regression (with individual fixed effects), if the dependent variable is binary (0 or 1), and ...
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### Technique to find spurious correlations among huge number of time series datasets?

I came across this tongue-in-cheek website that lists lots of spurious correlations. It's not lost on me that the author's main point is to discourage the brute-force-search of correlations, but his ...
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### Are predictions obtained with spuriously correlated predictors any useful?

Short version: How useful are predictions of a variable y that are obtained using theoretically unrelated variables X that happen by mere luck to predict y very well? Is there any paper out there ...
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### Teaching examples for internal validity: published experiments later shown to be confounded in an interesting way

There are some good examples of interesting/fun spurious correlations here (Examples for teaching: Correlation does not mean causation). Many/most of these are "funny" examples that aren't likely to ...
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### Term for baseline with randomly distributed classes over same data points

I have a dataset with few (20,000) data points and many (100) features ranging from 0 to 1. The dataset is divided into two classes with even distribution. I'm doing a classification task on this and ...
1 vote
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### Lower chance of type I error for A>B>C than for A>B?

Say I want to test the effect of two levels of my independent variable (IV) on some dependent variable (DV). For instance, administering a drug in a small vs large dosage, and then measuring reaction ...
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### How to prove that the probability of spurious correlation increases with random walk length?

Define a simple random walk $y_{t}$ as: $$y_{t} = y_{t-1} + \varepsilon_t\text{; where }\varepsilon_t \sim 2\times Bernoulli\left(0.5\right)-1,$$ so that at time $t$ the value of $y$ equals its ...
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### Is it possible to use time lagged variables in spurious regression?

Spurious regression is generated when we regress time series data that are non-stationary. So is it possible to time lag the variable to further find a higher correlation?
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### "Inflated" type I error rate for correlation test when a variable has repeated values

For a given variable Y, if we independently generate a random variable X and test the correlation between Y and X, we know that the histogram of the p-values of the correlation test should show a ...
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### What trends to remove in a time series to avoid spurious correlation

Do you remove the seasonal component, the trend component, or both, when adjusting a time series to avoid finding spurious correlations? I have two time series x and y with trends and yearly ...
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### Finding spurious regression based on Ferson et al and by detecting co-integration

After reading Ferson et al's (2003) paper on spurious regression, I understand that he uses extensive simulations to generate the true regressors and then compare them with those in the literature to ...
1 vote
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### Can series (A, B) be cointegrated if (A, B, C, D, E, F) are cointegrated?

If the result of series A and B shows cointegration, is this a spurious regression if series A,B,C,D,E,F were found cointegration as well? My explanation is that , if the stochastic trend series A ...
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### How can I determine the accuracy of correlation?

When I performed correlation analysis of C02 emission with around four-hundred attributes, i found out that C02 emission and cereal production has a correlation value of 0.98 where as the most obvious ...
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### Misunderstandings of "spurious correlation"?

I've heard people use the term spurious correlation in so many different instances and various ways, that I'm getting confused. Moreover, the Wikipedia page for Spurious relationship states: “In ...
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