# What is spurious regression in time series?

## What is spurious regression in time series?

A “spurious regression” is one in which the time-series variables are non-stationary and. independent. It is well-known that in this context the OLS parameter estimates and the R. 2. converge.

How do you know if a regression is spurious?

Spurious regression happens when there are similar local trends. The solid line is y and dotted line is x. Sometimes their local trends are similar, giving rise to the spurious regression. In short, two series are cointegrated if they are nonstationary and related.

What is spurious regression explain?

Spurious regression is a statistical model that shows misleading statistical evidence of a linear relationship; in other words, a spurious correlation between independent non-stationary variables.

### How do you deal with spurious regression?

Spurious regression can be avoided by adding trend functions as explanatory variables. In the second case, the problem arises because we overlook the short range autocorrelation. We can use FGLS to remove the autocorrelation to a great extent. In the third case, the problem arises because we ignore structural breaks.

What is the role of stationarity in a spurious regression?

One of the reasons for testing for stationarity is to avoid spurious results, to show time series plots that determine the behaviour of random variables and to evaluate whether the properties of the series are not violated (Baumohl & Lyocsa, 2009 ).

What is relationship between spurious regression and cointegration?

Suprisingly, in finite samples, regressing a nonstationary series with another arbitrary nonstationary series usually results in significant coefficients with a high R^2. This gives a false impression that the series may be cointegrated, a phenomenon commonly known as spurious regression.

#### Is a regression involving non stationary variables always spurious?

In general, regression models for non-stationary variables give spurious results. Only exception is if the model eliminates the stochastic trends to produce stationary residuals: Cointegration.

Does time series need to be stationary for regression?

7.1 Introduction. For regression analysis to be performed, data has to be stationary. Or the equation has to be rewritten in such a form that indicates a relationship among stationary variables.

What is stationary series in regression?

Statistical stationarity: A stationary time series is one whose statistical properties such as mean, variance, autocorrelation, etc.

## Is stationarity required for regression?

A stationarity test of the variables is required because Granger and Newbold (1974) found that regression models for non-stationary variables give spurious results.

What happens if time series is not stationary?

The solution to the problem is to transform the time series data so that it becomes stationary. If the non-stationary process is a random walk with or without a drift, it is transformed to stationary process by differencing.