Analysis of Econometric and time series _ACF and PACF algorithm (PYTHON,TB (trading pioneer))

1 the ACF and PACF diagrams are very important two concepts in time series, if the time series are used to model, trade or predict. These two concepts are necessary.

2 ACF and PACF are: autocorrelation function (coefficient) and partial autocorrelation function (coefficient).

3 in many software such as eviews analysis software can call up a sequence of ACF and PACF diagram, as follows:

　　

3.1 Sometimes this picture is lying, but this is not important, anyway, the side is less than 0 negative range, one side is greater than 0 positive range, the mean (accurate is the coordinate Y axis is 0, some horizontal graph, will be the x-axis and the y-axis, the values are displayed near the x-axis).

3.2 Red box is the ACF diagram, the Cyan box is PACF map, which corresponds to the left of the autocorrelation is the full name of the English word autocorrelation ;Partial Correlation Is the full name of the English word.

3.3 We are going to calculate the values of these two columns.

3.4 in which the purple arrows are labeled twice times the standard error range, the following can be used to determine whether the value is beyond the range to judge the truncation, trailing and other information, and then determine which model to use.

3.5 Here is a special note of how these two lines are calculated by default:

Under large samples (T is very large, here T refers to the number of samples, in fact, the sample is exactly the same as the average of 0 is the distribution). So here for the ACF or PACF belong to a sub-site test, this thing in many Baidu can find a positive distribution map, and then left and right to draw the line will get 99%,90% ... , here are the two lines that refer to this. What we're going to do here is a two-sided symmetry test, so the top and bottom two lines distributed 0± the value of the sub-site. Sub-site = twice times xsqrt Radical (1/t), here the T refers to the number of samples, the number of samples refers to the original number of the sample, not the ACF or PACF calculation of the number of samples. If a value is greater than twice times the standard error, that is, greater than the normal distribution left/right 95% quantile, then, in the Reject field, the 0 hypothesis is rejected (that is, the hypothesis of rejecting the mean value of 0)

For example: A total of 10 samples, ACF or PACF after the calculation, their number is 9, which is divided into points: 2xsqrt (1/10) = 0.6324555320 ..., bilateral test edge value is: (0-0.6324555320,0+0.6324555320) =　　　　[ -0.6324555320,+0.6324555320] (this is the value of two dashed lines). (3.5.1)

4. implementation of the ACF and PACF algorithms :

(Continuous editing .....) ）

Econometric and Time series _ACF and PACF Algorithm analysis (PYTHON,TB (trading pioneer))