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I am currently writing on my master thesis, therefore i have to find out if a specific moment had an impact on a time series. enter image description here

By just looking at the plot I would say that after the prize reached his maximum at observation 831, there was a shift in the trend... in other words i would say there is a structual break. I wanted to confirm my assumption by performing a chow test

enter image description here

on the first look i was very happy with the result.

p-value < 2.2e-16

which means that there is a structual break at observation 832

But then i replaced 832 with several different observation numbers and i noticed that the p-value declines if I run the chow test with lower observation numbers.

when i run the test on observation 1 there was a p-value of 0,23

pvalue at observation 200 = 0,19

pvalue at overvation 300 was 0,01

I can perform sctest on every single observation after 300 and it will always show a p-value < 0,01.

what am i doing wrong? is my formula Prize~Trend correct? (I am not that used to R or time series analysis in general)

I am very glad and grateful for your help

Regards

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(1) The Chow test is for a change in the coefficients of a regression model at a known time. If you don't know at which point in time the (hypothesized) structural change occurs, don't use a Chow test. A natural alternative is to use Andrew's sup$F$ test which formalizes your approach (conducting the Chow test for all possible timings) but appropriately adjusts the corresponding $p$-values. It rejects if the maximum of the $F$ (or Chow) statistics becomes to large. See vignette("strucchange-intro", package = "strucchange") for worked examples and more references. Also, citation("strucchange") gives you more pointers.

(2) The model Prize ~ Trend is surely not appropriate for your data. This would suggest that it is stationary around a deterministic linear trend. Even if you allow for structural breaks and relax it to a piecewise linear trend, you won't find a good model for the Prize time series. Probably it would make more sense to model the returns rather than the levels of this time series. But more context would be required for a better recommendation. I suggest you talk to your advisor and ask for more guidance and suitable references.

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