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As a result, if θ θ is our vector of regression model parameters, we have Var(θ) =σ2(X′X)−1. Var ( θ) = σ 2 ( X ′ X) − 1. where I I is an n ×n n × n identity matrix. However, with time series data, it’s possible that the residuals are autocorrelated. We can check this by plotting the ACF of the residuals.
What should the residuals of a time series be?
In general, after fitting a time series model (at least you are using a standard model and not assuming a special individual model, where the residuals may behave differently) the residuals should be white noise. So they should have no autocorrelation.
Is there an AR ( 1 ) model for partial autocorrelation?
We next look at a plot of partial autocorrelations for the data: To obtain this in Minitab select Stat > Time Series > Partial Autocorrelation. Here we notice that there is a significant spike at a lag of 1 and much lower spikes for the subsequent lags. Thus, an AR (1) model would likely be feasible for this data set.
Which is the best way to test for autocorrelation?
The easiest way to assess if there is dependency is by producing a scatterplot of the residuals versus the time measurement for that observation (assuming you have the data arranged according to a time sequence order). If the data are independent, then the residuals should look randomly scattered about 0.
What causes serial autocorrelation in a VAR model?
Serial autocorrelation (“autocorrelarion for a high number of lags”) is usually a result of misspecification. Probably you used non-stationary time series. If this is the case, you could not make a VAR model but should make a vector error correction model.
How to estimate the parameters of a model?
Estimate the model parameters using a “working model” or “working covariance” matrix W −1 W − 1. This can be independence or something else. Compute a separate covariance matrix ^V V ^ for the errors. In this case, we may use something based on an estimated autocovariance function.