What is the important of residual plot in modelling linear relationship- The first plot shows a random pattern, indicating a good fit for a linear model. The other plot patterns are non-random (U-shaped and inverted U), suggesting a better fit for a non-linear model.
What is constant variance of a time-series-
- The mean E(xt) is the same for all t.
- The variance of xt is the same for all t.
In other words, Mean of series x_t and x_t-h is same.
Standard deviation of series x_t is same as standard deviation of series x_t-h.
An interesting property of a stationary series is that theoretically it has the same structure forwards as it does backwards.
in the above image correlation with lag 1 is .6, with lag 2 is .36 and so on. Based on above graph we can say that it is AR(1) process where y=.6*yt-1 +constant +error.
If we have regression y= x1 and x2 so PACF between y and x2 will be-
For time series, PACF between yt and yt-2 is given by-
covariance (yt, yt-2/yt-1)/sd(yt,yt-1)* sd(yt-2.yt-1)
ACF is used to identify order of MA and PACF is used to identify order of AR terms in stationary time series.
know more about the relation between time-series and regression-
Regression and time series