Several ways can detect autocorrelation, including Durbin Watson test, Lagrange multiplier test, Breusch Godfrey test, and rank test. In comparison, cross-section data does not need to be tested for autocorrelation. One thing that needs to be considered by researchers is that the autocorrelation test is conducted on time series data. The autocorrelation test must be conducted to obtain the best linear unbiased estimator.
If there is a correlation, then it is called an autocorrelation problem.
The autocorrelation test aims to test whether there is a correlation between residuals in the t period and the previous period (t-1) in the linear regression model. One of the assumption tests required in the regression is the autocorrelation test.Īutocorrelation tests can be done in both simple and multiple linear regression. And for the PACF, there is a sistem of equations that connect the ACF correlations to it, known as the Levinson recursion (which also is explained in that answer).Researchers who use time series data in linear regression analysis with the OLS method need to conduct some of the required assumption tests. Then, you can get $\gamma_j$ and $\rho_j$ by the formula present in the most upvoted answer in ACF and PACF Formula. Obs: This is a more formal thing about statistics, ideally you should try to learn what exactly those things mean and how to see when you can make that assumption and when you can't, but it's best to ask that in another post. $$\bar + u_t$.įor using the data of your time series to calculate the amostral counterpart of those statistics (without having to set a model as what i presented untill now), first you need to assume that your series is at least weakly stationary and ergodic, which in loose terms is like saying that the series "will not change its statistical properties with time", so that the values of the series that you observe can be meaningful to the process behind it.
Well if you mean how to estimate the ACF and PACF, here is how it's done:
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