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I attached the graph of a time series below, which is a series of the probability of defaults.Time series, quarterly This is a quarterly time series. When I am using a regression model to forecast this time series, should I test the structural breaks? And if so, should I only use the coefficient of the most recent time window to forecast the time series?

But what if this is just a cycle or part of a cycle, that in the next few years, the trend is going up again. In this sense, should I keep using the coefficients after the break, or should I ignore the structural break?

The regression model I am using would be

$PD_t=\alpha+\beta Macro\ variable_t+\epsilon_t$

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  • $\begingroup$ structural breaks should not be just based on level shift (intercept) changes they can also be based upon trend changes or model parameter changes over time or model error variance changes over time or seasonal pulse changes over time._ $\endgroup$ – IrishStat Jun 24 at 16:50
  • $\begingroup$ In order to forecast the series you could use the Law of Total Expectation: $E(Y_{t+1}) = E(Y_{t+1} \mid B_{t+1}) P(B_{t+1}) + E(Y_{t+1} \mid B^\prime_{t+1}) P(B^\prime_{t+1})$, where $B_{t+1}$ is the prob of a structural break at time $t+1$. For the first term you would need to predict what the parameters would be after a change. For the second term you would use the most recent coefficient. In this case there is unlikely to be a multi-year seasonal trend - recessions don't arrive at regular intervals. $\endgroup$ – Alex Jun 24 at 20:53
  • $\begingroup$ The parameter $\beta$ in the regression might change suddenly, e.g. if there is a recession, so it might be worth looking for structural breaks. Also I mean $B_{t+1}$ is the event that there is a structural change, not the probability of one: $P(B_{t+1})$ gives the probability of a break. $\endgroup$ – Alex Jun 24 at 21:01
  • $\begingroup$ Your data ( at least from a univariate view) could habe 1 upeards trend and perhaps 2 or 3 downward trends . The inclusion of significant predictor series could possibly eliminate/account for those breakpoints $\endgroup$ – IrishStat Jun 25 at 19:59
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For forecasting you have two possibilities:

  1. You can test for structural breaks. It is complicated because you want to detect the breaks as fast as possible, but most tests (chow-breakpoint etc) need some observations after the occurrence of a break to discover it, a possible solution could be a fluctuation test.

  2. You could use a rolling forecasting method. Here you just use the last X observation for your model. With some time the model will automatically adapt the structural change. Of course, there will be an error at the breakpoint but it is very easy to implement and gives normally good results.

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