I am trying to fit a model to a time series that has a lower bound (at around -150). Using an ARIMA model, running simulations often leads to the time series hitting (and going underneath) this lower bound. How can I avoid this? Is there a better model I can use?
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3$\begingroup$ Could you explain why that lower bound exists, how you know its value, and what it means? Such information often can suggest effective solutions, such as transformations of the variable or generalized linear modeling approaches. $\endgroup$– whuber ♦Jun 29, 2015 at 14:43
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1$\begingroup$ Thank you for the reply. I am modelling the error in the weather forecast for wind speed. Since wind speed cannot be negative, there is a lower bound of the forecast error (the error cannot predict a wind speed less than zero). $\endgroup$– RPzJun 29, 2015 at 14:51
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1$\begingroup$ Have you considered separately modeling the forecast and the wind speed? In fact, if the forecast itself is obtained with a statistical model, then it already models the difference between its predictions and the true wind speeds--so you might not have to do any additional analysis. $\endgroup$– whuber ♦Jun 29, 2015 at 15:15
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1$\begingroup$ $logit(w)=\log(w/(1-w))$ where $0<w<1$. So if you know a reasonable upper bound say 250, then $logit(w)=\log(w/(250-w))$ where $0<w<250$. I agree that some transformation (not necessarily a logit transformation) is the simplest approach if you want to use an ARIMA model. One thing to keep in mind is that the standard ARIMA assumes normally distributed innovations. As the distribution of the innovations will be effected by the transformation you use, care should be taken in choosing the transformation and checking the residuals of the resulting ARIMA estimation. $\endgroup$– Zachary BlumenfeldJun 30, 2015 at 10:24
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2$\begingroup$ For example, it would be helpful to plot a histogram of wind speed. If wind speed appears to be log-normally distributed, then simply taking the log of wind speed will likely result in a close to normally distributed time series. Log series are nice because they are simple and offer a clear interpretations in respect to growth and percentage changes over time. $\endgroup$– Zachary BlumenfeldJun 30, 2015 at 10:37
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1 Answer
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The only way I can think of is to ignore values under 150
answered Jun 29, 2015 at 14:23
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$\begingroup$ What happens if the model produces values that are all under 150? In that situation, this approach would not work, I presume?! $\endgroup$ Jun 29, 2015 at 18:29
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$\begingroup$ i have seen sales data that can be small and the appropriate model might predict (slightly) negative numbers just because there is no restriction .Since negative sales numbers can't happen a logical override is to convert the negative number to 0 regardless of haw many periods you are forecasting. This is similar to modelling tire data as a result of mileage as negative tire wear is impossible, $\endgroup$ Jun 29, 2015 at 18:40
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$\begingroup$ That's fine, but the fact that the model produces numbers that are, in fact, impossible in reality is a defective property of the model. I would never bet on a horse that doesn't run in the race. - Nobody would! $\endgroup$ Jun 29, 2015 at 20:54
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$\begingroup$ The negative numbers are an artifact as was The Irish Derby . Up the Dubs ! $\endgroup$ Jun 29, 2015 at 21:28