# Understanding partial autocorrelation (PACF) and variability

A strong positive partial autocorrelation of lag 1 means that an observation is highly correlated with its previous observation whereas a near zero PACF indicates no correlation.

Does that mean that a near zero PACF suggests no variability within the observations while a positive PACF suggests increasing variability?

Take a person's sleep duration over a period of one month as an example. If he or she sleeps consistently close to 8 hours a day, the day-to-day variability is low and the PACF is near zero.

Are these 2 concepts similar or am I understanding them incorrectly?

They are slightly different, by variability I am guessing you refer to the variance. You can have a noise process $$\epsilon_t \sim N(0, \sigma^2)$$ that is independent across time and that can be highly variable depending on the variance $$\sigma^2$$.