Forecasting a "chaotic" time series

Question

Here are four graphs,

1, autocorrelation, autocovariance, partial-correlation and cross-correlation calculated from a time series are given.

2, The time series

I need to do some predictions on them.

My questions are 4 :

1, I do not quite understand what these four graphs can tell or show. Can anyone explain?

2, Does the four subplots tell if it is appropriate to do forecasting for the time series

3, If so, any method to do forecasting?

4, I am wondering if particle filter can be used.

I am a little clueless about this problem.

Answer 1

1) 1, I do not quite understand what these four graphs can tell or show. Can anyone explain?

The auto-correlation is the ratio of the co-variance to the variance. It tells you the unconditional impact of a lag on the observed series . The Partial Auto-correlation tells you the conditional importance/effect of a lag given all intermediate(lesser) lags much akin to a partial regression coefficient. The cross-correlation reflects the relationship between two series for different lags. It is totally meaningless when dealing with time series due to auto-correlation within the individual series.

2) it is not possible to answer your question until one forms either ARIMA models or ARMAX Models for causative problems

3)The method is called BOX-JENKINS

4)Which identifies the appropriate filter to separate observed data to signal and noise.