What Is Autocorrelation?

Autocorrelation refers to the correlation between the expected values of random error terms. It is said that there is autocorrelation or serial correlation between random error terms. It was proposed in 1972.

Autocorrelation

For models

in case

How to tell if data is autocorrelated

a. Use related measurement software : E-VIEWS to check the distribution of residuals. If the residual distribution has a clear and rounded linear distribution image, it means that the possibility of autocorrelation exists. Conversely, the distribution images with large random fluctuations show weak correlation.

Autocorrelation judgment method 1 example

For example, in the above picture, the more rounded distribution on the left shows the existence of autocorrelation, and the opposite on the right with large fluctuations.

b. Durbin-Watson Statistics : Assuming that the time series model has autocorrelation, we assume that the error term can be expressed as Ut = * Ut-1 + . Use statistical testing to establish hypotheses. If = o. indicates no autocorrelation. The Durbin-Watson statistic (hereinafter referred to as the DW statistic) can be a tool for judging positive, negative, and zero (none) correlation. DW statistics: d = (Ut-Ut-1) ^ 2 / ut ^ 22 * (1-). If d = 2, there is almost no autocorrelation, and d is close to 0, there is a positive correlation. There is a negative correlation between d and 4. ^[1]

c . Q-Statistics takes (box-pierce) -Eviews (7th version seventh version) as an example: Many statistical measurement software software provides Q test to detect, here Eviews is used as an example. The test statistics for Q are Q = n * ^ 2. The null hypothesis H0 = 0 has the same meaning as Method 2. If the null hypothesis proves unsuccessful, then the opposite hypothesis 0 holds, meaning there is autocorrelation.

Q-test in the example picture shows the correlation.

How to weaken the autocorrelation of the model

Method 1 (GLS or FGLS): Assuming an autocorrelation model, the relationship between the error terms is: Ut = * Ut-i + ( is the error term except autocorrelation, iid ~ (0, ). The model for period t is yt = xt + Ut, and the period for period t-1 is * yt-1 = * xt-1 + * Ut-1. The period t-1 is subtracted from the period t-1. Yt-yt-1 = (xt-xt-1) + (Ut-Ut-1). Known Ut-Ut-1 = . After finishing the new model satisfies the assumption of Gauss-Makov and condition (homoscedasticity or equal dispersion), no autocorrelation.

Mitigation method 1

Method Two (HAC: Heteroscedasticity Autocorrelation consistent): Take Eviews as an example, select HAC when analyzing the model, and gradually add the number of time lags to the model to correct the DW statistics to normal values and reduce autocorrelation.