tag:blogger.com,1999:blog-7729093380675162051.post7874891033573081212..comments2022-09-27T06:36:53.309+10:00Comments on moyhu: Significant trend differencesNick Stokeshttp://www.blogger.com/profile/06377413236983002873noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-7729093380675162051.post-75817965902296844492016-04-18T21:57:34.006+10:002016-04-18T21:57:34.006+10:00How can you be modeling the residuals if you don&#...How can you be modeling the residuals if you don't even have a model for ENSO?<br /><br />Its a good thing that I am asking these pointed questions. Like I mentioned, you ought to look closely at how I characterize mean SLH from tidal gauge readings at Sydney and Aukland here -- <a href="http://contextearth.com/2016/04/13/seasonal-aliasing-of-tidal-forcing-in-mean-sea-level-height/" rel="nofollow">http://contextearth.com/2016/04/13/seasonal-aliasing-of-tidal-forcing-in-mean-sea-level-height/</a><br /><br />The goal is to decompose the time series until the residual is white noise.<br /><br />@whuthttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-55755012610945090082016-04-18T14:26:00.702+10:002016-04-18T14:26:00.702+10:00"Otherwise it will just bounce around the mea...<i>"Otherwise it will just bounce around the mean without any kind of trend appearing"</i><br />AR(1) isn't modelling the trend; it is modelling the residuals. And the only use made of it here is to see how much it increases uncertainty of trend.<br /><br />In <a href="http://www.moyhu.blogspot.com.au/2013/09/uncertainty-of-temperature-trends.html" rel="nofollow">this post</a> I show how it interacts with oscillations that do appear in the acf, which I think are related to ENSO. <br />Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-83175928942058803532016-04-18T14:08:02.628+10:002016-04-18T14:08:02.628+10:00Yet the Ornstein-Uhlenbeck process has a strong re...Yet the Ornstein-Uhlenbeck process has a strong reversion to the mean, which means that the only way you will see any kind of large low-frequency fluctuations is if the diffusion and potential parameter is somehow set to give that. Otherwise it will just bounce around the mean without any kind of trend appearing. So to get the low-frequency movements means that you probably won't be able to pick up the faster ENSO fluctuations.<br /><br />Bottom-line is that essentially what you are saying is that you keep the AR(1) model around so you can laugh at how bad it works to explain anything like ENSO. That's the only way I will use it for these climate time series. <br /><br />Taking the Auckland tidal gauge SLH data to extract SOI<br />http://contextearth.com/2016/04/13/seasonal-aliasing-of-tidal-forcing-in-mean-sea-level-height/#comment-177421<br /><br />@whuthttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-85067782047519208752016-04-18T03:01:04.341+10:002016-04-18T03:01:04.341+10:00The trend may be deterministic, but we have to cal...The trend may be deterministic, but we have to calculate it in the presence of variation that we can't predict, and that affects the outcome. So we'd like to know, if that variation had worked out differently, how would that affect our answer for trend. Ar(1) is our model for how it might have worked out differently. It isn't a perfect model; it's a matter of finding the best you can.<br />Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-58500261465652060892016-04-18T00:22:07.137+10:002016-04-18T00:22:07.137+10:00"Could you state what regression model is use...<i>"Could you state what regression model is used for linear trends? AR(1), AR(2) ARMA(1,1)...?"</i><br /><br />Why would you use any of these when the global trend is deterministic and not stochastic? <br /><br />That said, I do agree that if any physics-based stochastic model is used it should be the Ornstein-Uhlenbeck process, which statisticians refer to as AR(1)<br /><br /><a href="http://math.stackexchange.com/questions/345773/how-the-ornstein-uhlenbeck-process-can-be-considered-as-the-continuous-time-anal" rel="nofollow"> How the Ornsteinâ€“Uhlenbeck process can be considered as the continuous-time analogue of the discrete-time AR(1) process?</a><br /><br /><br />My question is exactly what is the random walk element that you are trying to extract? The only thing I see that is close to random is volcanic activity. <br /><br /><br /><br /> <br /><br /><br /><br /><br /><br />@whuthttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-35777636891993457722016-04-17T16:35:06.250+10:002016-04-17T16:35:06.250+10:00Barry,
I'm using Ar(1). I've written about...Barry,<br />I'm using Ar(1). I've written about the issues <a href="http://moyhu.blogspot.com.au/2013/09/adjusting-temperature-series-stats-for.html" rel="nofollow">here</a>, <a href="http://moyhu.blogspot.com.au/2012/03/autocorrelation-regression-and.html" rel="nofollow">here</a>, and <a href="http://www.moyhu.blogspot.com.au/2013/09/uncertainty-of-temperature-trends.html" rel="nofollow">here</a>. In the last, I'm specifically looking at Ar(1) and alternatives, and giving the case for Ar(1).<br />Nick Stokeshttps://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-17443411221820765812016-04-17T13:46:05.095+10:002016-04-17T13:46:05.095+10:00Hey Nick,
Could you state what regression model i...Hey Nick,<br /><br />Could you state what regression model is used for linear trends? AR(1), AR(2) ARMA(1,1)...?barryhttps://www.blogger.com/profile/12419101193566520809noreply@blogger.com