What is Partial Autocorrelation?
In time series analysis, the partial autocorrelation function (PACF) gives the partial correlation of a stationary time series with its own lagged values, regressed the values of the time series at all shorter lags. It is different from the autocorrelation function, which does not control other lags.
Partial correlation quantifies the relationship between a specific observation and its lagged values. This helps us to examine the direct influence of past time point on the current time point, excluding the indirect influence through the other lagged values. It seeks to determine the unique correlation between a specific time point and another time point, accounting for the influence of the time points in between.
[Tex]PACF(T_i, k) = \frac{[Cov(T_i|T_{i-1}, T_{i-2}…T_{i-k+1}], [T_{i-k}|T_{i-1}, T_{i-2}…T_{i-k+1}]}{\sigma_{[T_i|T_{i-1}, T_{i-2}…T_{i-k+1}]} \cdot \sigma_{[T_{i-k}|T_{i-k}, T_{i-2}…T_{i-k+1}]}} [/Tex]
Here,
- [Tex]T_i| T_{i-1}, T_{i-2}…T_{i-k+1} [/Tex] is the time series of residuals obtained from fitting multivariate linear model to [Tex]T_{i-1}, T_{i-2}…T_{i-k+1} [/Tex] for predicting [Tex]T_i [/Tex].
- [Tex]T_{i-k}|T_{i-1}, T_{i-2}…T_{i-k+1} [/Tex]is the time series of the residuals obtained from fitting a multivariate linear model to [Tex] T_{i-1}, T_{i-2}…T_{i-k+1} [/Tex] for predicting [Tex]T_{i-k} [/Tex].
AutoCorrelation
Autocorrelation is a fundamental concept in time series analysis. Autocorrelation is a statistical concept that assesses the degree of correlation between the values of variable at different time points. The article aims to discuss the fundamentals and working of Autocorrelation.
Table of Content
- What is Autocorrelation?
- What is Partial Autocorrelation?
- Testing For Autocorrelation – Durbin-Watson Test
- Need For Autocorrelation in Time Series
- Autocorrelation Vs Correlation
- Difference Between Autocorrelation and Multicollinearity
- How to calculate Autocorrelation in Python?
- How to Handle Autocorrelation?
- Frequently Asked Questions (FAQs)