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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?

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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 $\sigma^2$.

A real world example would be stock market returns, they are very much volatile and they exhibit near zero PACF at the monthly level.

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