Stability tests with kalman filter

[Aktar]

ok so if the gap between the straight line and the cumulated sum of square is big, it say that the parameters are stable ? and if the cusum are below the line paramters are not stable ?

"If they're generally small, then get larger, it will drop well below the line early in the data set". i don't understand sorry (my english is poor)

i have a graph where the the cumulated sum of square is above of the line with a big gap, and in the end of the sample the gap narrowed and the the cumulated sum of square is very near of the line.

Thank you and sorry for questions im a rookie in econométrics

[TomDoan]

ok so if the gap between the straight line and the cumulated sum of square is big, it say that the parameters are stable ? and if the cusum are below the line paramters are not stable ?

"If they're generally small, then get larger, it will drop well below the line early in the data set". i don't understand sorry (my english is poor)

i have a graph where the the cumulated sum of square is above of the line with a big gap, and in the end of the sample the gap narrowed and the the cumulated sum of square is very near of the line.

Thank you and sorry for questions im a rookie in econométrics

A CUSUMQ test is mainly testing whether the variance is constant over the interval, though it can pick up other forms of instability. It, by construction, has a zero gap at each end. If the CUSUMQ graph lies well below the line at the maximum gap, it means that the smaller (squared) residuals cluster near the start of the data set, and if it lies well above the line, it means that they cluster near the end. If the maximum gap is relatively small, there is no evidence of instability of the variance at least in terms of the time sequencing.

[Aktar]

ok so if the cusumq is above the line with a relatively big gap, the variance is no stable at the end of the sample and inversly, if the cusum are below the line, the variance is no stable (clustering) at the start of the sample, wathever where the gap is ( the gap is always small at the end and start of the sample ?)

it is right ?

In my case i have a big gap for CUCUMQ above the line but when i make CUSUM test the recursive residuals are in the corridor from beginning to end. there is no contradiction ? (the cusum rise at the start and decrease after up to the end for cusum test)

sorry for disturbing you for little things, i don't understand very well english.

thank you very much

[TomDoan]

The two are testing different things so there's no reason to expect them to give similar results. The CUSUM test isn't very good at picking up a structural break near the start of the sample - that's a known problem, and, in fact, it's possible to run a reversed CUSUM to try to detect that. However, you also have to consider that the early residuals in a state space model can be very poorly estimated. You might want to try running the tests starting a few data points higher into the data set.

[Aktar]

thank you !

a last question : i have cusumQ graph where the recursive residuales are bellow the line and cut the line in the middle of the sample, and after it stay above.

how i can interprete it ?

[TomDoan]

Small (squared) at both ends, larger in the middle.