Autocorrelation
Is Cross Correlation but the two functions are the same so a cross correlation with itself. How is this interpretetd? Same goes here for time series is this interpreted? Because it is slid across it is basically the correlation with the lagged version of it self. so each point is correlation of the series with the x lag of itself.
Partial Auto Correltion
a, b, c. a with b are correlated and b with c, to measure true influence of c on a need to take out the influence b had on a. Taking out inluence of other timespots on current.
AR model or MA model https://medium.com/@vaibhav1403/ar-model-vs-ma-model-427ee28587a#:~:text=How%20they%20differ%3A,white%20noise%20or%20error%20terms (opens in a new tab).
1 lag differencing is a way to detrend. subtract lag 1 values.
first order AR model is if lag 1 is used, second order if lag 2 etc. How many points are taken = order, simpler models prefered. Significance threhsold, how to get?
AR model uses partial AC, MA model uses full AC https://www.youtube.com/watch?v=5Q5p6eVM7zM (opens in a new tab)
Also known as Conditional correlation. Take out all intermediate effects.
correlogram with Confidence intervals are drawn as a cone. By default, this is set to a 95% confidence interval, suggesting that correlation values outside of this code are very likely a correlation and not a statistical fluke.
The partial autocorrelation at lag k is the correlation that results after removing the effect of any correlations due to the terms at shorter lags.
The autocorrelation for an observation and an observation at a prior time step is comprised of both the direct correlation and indirect correlations. These indirect correlations are a linear function of the correlation of the observation, with observations at intervening time steps.
It is these indirect correlations that the partial autocorrelation function seeks to remove. Without going into the math, this is the intuition for the partial autocorrelation
how it is calcualted: https://timeseriesreasoning.com/contents/partial-auto-correlation/ (opens in a new tab)