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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Variance and empirical distribution

We know that regressing two I(1) time series that are not cointegrated might give rise to spurious results. Indeed, we might have an excess of rejection of the null hypothesis due to the fact that as ...
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Sample-size-dependent magnitude of spurious correlation?

In my recent research, my computations involve sample-based covariance estimates. As you might know, with an insufficient sample-size, we will encounter spurious correlations: cross-covariances which ...
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Does it really matter if a correlation is spurious?

Let’s say you are trying to find if there is a correlation between two stock prices, where both are likely non stationary series. You have no concern as it relates to a potentially causal relationship....
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Non stationarity and forecasting

Let's assume we have estimated a linear regression model on a dataset from 2000 to 2017. The data were stationary. What happens if the data are no longer stationary in the next years? Do the forecasts ...
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ARDL model as remedy for spurious regression?

Suppose there are two non-stationary time series of integrated order 1. The two time series are not cointegrated. According to conventional econometric theory, "In general, regression models for ...
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What to do about spurious regression

Say you have two variables with trends in them. It is often said that this leads to spurious regression. My question is, when will regression with ARIMA error (which may involve differencing) ...
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Spurious regression

I am using regression with ARIMA error which modifies the error terms to generate correct results for time series regression. I know that if two variables have a trend in it then you may get spurious ...
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Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one)

I'm a rookie with statistics, and I'm struggling to understand this: it is well known that a confounding factor can cause a spurious association, leading to rejecting a true null hypothesis (i.e. due ...
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Will the coefficients of an error correction or lasso-penalized model usually reveal spurious correlation?

As time goes by I have learned of more and more ways that correlations can be spurious and more and more tests and correction procedures intended to avoid taking such correlations as meaningful. My ...
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Spurious relationships: flavours, terminology

The following types of relationships come to my mind when I think of the term "spurious" (as in "spurious regression" or "spurious correlation"): A statistical ...
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Interpretation of ECM coefficients

Say that we are regressing consumption $C_t$ on time $Y_t$. Furthermore, suppose that both series are $I(1)$ and are co-integrated. Given this, we set up the error correction model (ECM) as follows: $...
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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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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 ...
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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 ...
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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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11 votes
5 answers
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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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Ratio of correlated vectors is uncorrelated?

Having an issue wrapping my head around a problem today. I have 4 vectors: $A, B, X$ and $Y$. $A$ is linearly correlated to $X$ with an $R^2$ of ~0.93, and $B$ is linearly correlated to $Y$ with an $...
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Why does the presence of cointegration solve the problem of spurious correlation?

This question was originally posted on quantstackexchange: https://quant.stackexchange.com/questions/31501/why-does-the-presence-of-cointegration-solve-the-problem-of-spurious-correlation Many of us ...
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Question about Spurious Relationships of Trending Variables

Why is the answer to this question 'false?' If both X and Y exhibit trending behavior, then regression of Y on X and a trend variable will always generate spurious relationship. What are some ...
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3 votes
1 answer
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Impossible effects in a logistic regression. What causes them, and what to do about them

I am currently analysing some data from a psychological experiment. In this experiment participants have to decide between two options based on some information. I can derive a variable indicating ...
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Avoiding inflated DF - spurious results computational modelling

I have a computer model comparing a number of paired groups of data (reaction time & accuracy for 1 'subject' go together for a number of categories) But since the program runs 500+ subjects for ...
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Is a High R squared a Sufficient condition for a spurious regression?

I know that a necessary condition for spurious regression is a R squared approaching 1. However, is a R squared approaching unity a sufficient condition? Said another way, if two non-stationary ...
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Correlation between two time series of sales data

I have two time-series of 2 different products x & y. They belong to the same main category, e.g.: Iphone 6 and Iphone 5. Maybe one product is the predecessor ...
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Does ARMAX solve the autocorrelated errors and avoid spurious regression?

I have a OLS model looks like this: However, the residuals have auto-correlation like this: It doesn't seem a strong autocorrelation, and the model passes the Engle-Granger cointegration test (...
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Model residuals pass stationarity test, but Durbin–Watson test fails

I have a OLS model that I try to prove it has cointegration between two regressors and the dependent variable. The model fits well, with a very high $R^2$. The residuals don't seem to be ...
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2 answers
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How to "statistically adjust" for variables? [duplicate]

I've been trying to understand what means "statistically adjusted" when comparing two variables. For example, when computing the odds ratio for a death after surgery in two hospitals, we compute the ...
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Can negative relationship between X and Y be spurious

Let's assume I have X and Y and both X and Y have positive relationship. In such case in which both series trend in the same direction, we need to test for cointegration to be sure that relationship ...
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Is this "strong correlation" definition valid?

This page defines a a "strong correlation" using a formula that combines a standard correlation measure with lag-1 autocorrelation measures. I've never seen a definition of correlation like this ...
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spurious regression?

I am regressing one variable on 1,500 features. I have 30,000 rows of data. I know some of my features are correlated, but a Ridge regression where I select the ridge parameter $\lambda$ by cross ...
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Correction methods for spurious correlation

I'm investigating the relationship between A/B and A*. I've found that higher A/B scores lead to lower A scores. Obviously however there is spurious correlation between A/B and A, and if that spurious ...
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Testing a single time-series for changing variance structure (Heteroscedasticity and Volatility Clustering)

I would like to assess a single time-series for a changing variance structure that might be leading to spurious variance estimates when that time-series is used in regression. In my head two terms ...
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Avoiding spurious correlation in time series

I am investigating the relationship between monthly macro-economic variables, and monthly indicators of a company's performance and workload. I am doing this for predictive purposes, and I am ...
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Do we have to model spurious auto-correlation in time series?

I am analyzing a data set of power consumption with the aim of forecasting. The times when there is consumption are rather sparse. If there is consumption then there is likely one in the next time ...
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Are these nonstationary variables?

If I have understood correctly, computing the correlation of two nonstationary variables can lead to spurious results. For example, computing the correlation of two stock price time series would lead ...
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Nonstationary panel data, spurious regression

I would like a more detailed explanation of this quote: "Unlike the single time series spurious regression literature, the panel data spurious regression estimates give a consistent estimate of ...
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