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I have a time series of x:libor and y:money rates. using the following polynomial y=b0+b1(x)+b2(x)^2, i get values of y that exceed (or are sometimes negative) the coveriance/variance for large multiples of vector x. (i) Is my problem one of an asymptote? and (ii) is a regime switch appropriate?

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  • $\begingroup$ How did you optimize b? Maybe there is overfitting. $\endgroup$ – jeff Sep 20 '15 at 13:51
  • $\begingroup$ basically, i used a solver to minimize the error. $\endgroup$ – incus Sep 20 '15 at 14:32
  • $\begingroup$ If your x data is really 1-dimensional, it might be helpful to visualize the input and the estimations. But I'm sure there are analytical ways to determine overfitting as well. Also, the very choice of polynomial regression might be the cause of overfitting, maybe the underlying process was linear but you fitted a quadratic model so it behaves unexpectedly on test data, like this one: i.stack.imgur.com/0Q1jF.png $\endgroup$ – jeff Sep 20 '15 at 14:57
  • $\begingroup$ the polynomial regression parameters provide a relatively good fit on a historical back-testing perspective. between 2004 and 2010, 1M Libor looks like an upside U. The issue, however, is that implied forward rates are upward sloping and then begin to level off far out on the curve. For +200bps shifts in the implied, the values make sense on the long end. However, in +400bps shifts, the values of Y being to rise higher and higher. $\endgroup$ – incus Sep 20 '15 at 15:30
  • $\begingroup$ I'm not familiar with the terminology, but I suspect one thing (IIUC, you are referring to the libor, i.e. the input features by "+x bps shifts", right?) If so, maybe you are not using some parts of the input-output pairs when learning, for example, you are training the regressor with inputs around 200bps, but you are testing with samples around 400bps, so the model does not know how to behave there. Do you have the chance to include 400bps samples when training your system? $\endgroup$ – jeff Sep 20 '15 at 15:39
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My guess (without seeing your data) is model specification bias (error) . Try building a Transfer Function ( a.k.a. dynamic regression) incorporating memory structure as needed and possibly (probably !) both ARIMA structure and identifiable deterministic structure such as pulses,step/level shifts/local time trends

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  • $\begingroup$ he polynomial regression parameters provide a relatively good fit on a historical back-testing perspective. between 2004 and 2010, 1M Libor looks like an upside U. The issue, however, is that implied forward rates are upward sloping and then begin to level off far out on the curve. For +200bps shifts in the implied, the values make sense on the long end. However, in +400bps shifts, the values of Y being to rise higher and higher. $\endgroup$ – incus Sep 20 '15 at 15:32
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    $\begingroup$ You are in my opinion "wandering in the desert" BUT that's just my opinion. If you are trying to link your two variables in a model then your approach of fitting polynomials is doomed to failure. $\endgroup$ – IrishStat Sep 20 '15 at 19:26
  • $\begingroup$ thanks! actually the polynomial with error correction is very workable. appreciate your feedback nonetheless...was very helpful $\endgroup$ – incus Sep 20 '15 at 20:12

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