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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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Unsure about assumptions of linear model with time series variables, spurious regression and periodic patterns

Background I'm learning about time series in context of linear regression. The goal of this question is to understand how seasonality of either X or Y can affect the model. Linear model assumptions $...
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Spurious causation?

I am currently interested in the correlation v.s. causation discussion. I know that correlation might be spurious (see that spurious correlation website). However, as the causality is inferred from ...
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How do zero values affect the correlation between two twitter activity time series?

I have a time series of Twitter activities (lets call it time series 0) from which I extract two separate time series based on different sets of users (i.e. time series 1 contains the activity of a ...
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Lasso for non-stationary time series

Does it make sense to use Lasso to find an explanatory variable x to predict my variable y, assuming both y and x are non-stationary? (I'm using both variables as levels, not differences). If I find a ...
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Properties of OLS under non-stationary variables

I estimate the following equation using OLS: $y_{t} = a + b*x_{t} + u_t$. I performed ADF tests for both y and x series and found that H0 (the existence of unit root) can not be rejected. I also ...
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Correlation with a random walk

Correlation with a random walk: Thanks for kind explanations. But I am still confusing. A random walk repeats previous values plus stochastic fluctuations. Then, can exogenous factors influence a ...
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"Are All Correlations Spurious But Some Correlations Are More Spurious?" - Not George Orwell

(Sorry for the George Orwell/Animal Farm reference) I am an MBA student taking courses in Statistics. Over the Thanksgiving weekend, we have an informal assignment - we have to find publicly available ...
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Is non-stationarity an issue in this setting?

I am trying to model the development of European spot prices of gas. My purpose is to explain what has caused past movements in the gas price, rather than forecasting future gas prices. Naturally, ...
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Mechanical Relationship between two variables

Recently I attended a conference in which one of the authors was talking about the mechanical relationship between variables "X" and "Y" (I don't remember exactly the variables) ...
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Can spurious correlations exist in the (theoretical) population?

Is it possible that spurious correlations exist between two random variables X and Y in the (theoretical) population (here I mean purely by chance, not due to missing confounders in a model, etc.)?
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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 ...
Maximilian's user avatar
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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....
user10136297's user avatar
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1 answer
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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 ...
adrCoder's user avatar
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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 ...
Thorsten's user avatar
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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 ...
andrewH's user avatar
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7 votes
2 answers
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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 ...
Richard Hardy's user avatar
2 votes
1 answer
270 views

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 ...
Amy K's user avatar
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3 answers
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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 ...
ADI's user avatar
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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 ...
Rafael Silva Wagner's user avatar
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3 answers
818 views

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 ...
Yu Wang Dolby's user avatar
3 votes
1 answer
804 views

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 ...
Ryan Zotti's user avatar
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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 ...
Juan Martínez's user avatar
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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 ...
Nicholas Root's user avatar
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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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1 vote
1 answer
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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 ...
z8080's user avatar
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7 votes
2 answers
1k views

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?
chidori's user avatar
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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 ...
Randel's user avatar
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2 votes
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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 ...
StatisticianInStilettos's user avatar
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1 answer
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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 ...
quantuaryTsui's user avatar
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1 answer
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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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2 answers
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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 ...
jeffy abraham's user avatar
12 votes
5 answers
2k views

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 ...
lopta88's user avatar
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1 answer
277 views

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 $...
JVal's user avatar
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Why does the presence of cointegration solve the problem of spurious correlation?

This question was originally posted on Quantitative Finance Stack Exchange: https://quant.stackexchange.com/questions/31501/why-does-the-presence-of-cointegration-solve-the-problem-of-spurious-...
Paul's user avatar
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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 ...
Robert Grote's user avatar
3 votes
1 answer
191 views

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 ...
LiKao's user avatar
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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 ...
Curious Programmer's user avatar
1 vote
1 answer
2k views

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 ...
Jacob H's user avatar
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1 answer
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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 ...
kuppi's user avatar
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2 votes
0 answers
207 views

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 (...
chl111's user avatar
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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 ...
chl111's user avatar
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