Some papers written by Naylor, Lobell are using time variables as an independent variables. Let's say I obtain a model from observed data 1961-1990 such Y = a*time+a*time^2+c*temperature. Time and time^2 in this model are called time variables. To get this model I set time variable = time =1 for 1961, so in 1990 time=30.
If I want to estimate Y between 1991-2050, how do I set time variables ? shall I start time variable = 1 from 1991 ? or set time variable=31 from 1991 ?
Maybe you can replace t with
t=t0+dt
where t0 is the initial time and dt is the variation in time.
so you can use t0 as a parameter that depends on the period of your observations and dt will now be your independent variable measured comparatively to that parameter.
Since t0 is a parameter dependent on the period of observations you can now set t0=30 to estimate Y between 1991-2050 so you will get your new independent variable dt=1 in that period when t=1991
This is just my opinion, I am not sure it solves your problem.
Kind regards.
Fernando.
Here you are using the model which is estimated from the 30 observations i.e. from 1961-1990. Now if you want to estimate Y for subsequent values, then you have to perform your calculations starting from 31 for 1991. If you use 1 for 1991, it is mathematically wrong.
Hi All,
Based on observed data 1976-2011, I got a model to estimate crop productivity like: Y= 0.18*time - 0.005*time^2 + 0.15*temp + 2.33. and then I want to estimate the impacts of climate change (high temperature) by 2100. Please note that [0.18*time - 0.005*time^2] is called technological trend/progress.
The issue for me is [0.19*time - 0.005*time^2] will be negative when time=39. if I set time = since 1976, time=38 corresponds with 2015. Any suggestion to prevent negative values of [0.18*time - 0.005*time^2] ?
Please list any related papers
(Your further explanation clears up the question for me.) I raise a question whether your original model of crop productivity vs. time as a polynomial is correct. Of course, negative 'technological progress' is possible (outlawing various pesticides, water reduction regulations, etc.), but it sounds like you want to test a model equation increasing in time. Did technological progress really peak in 1996 (t=19)? Some possible suggestions are Y ~ sqrt(time), or Y ~ log(time). Good luck.
I agree with Davidsir. I would like to add further several comments:
1. Interpolation and Regression are the methods of curve fitting. If the data is accurate, then interpolation is used, otherwise regression. It can be used for forecasting. But your forecast will be far from reality if you extend the model in the future. The year 2100 is too far in the future.
2. Time is positive. The only term negative in your model is -0.005*time^2. Whenever the magnitude of this term exceeds the contribution of the sum of the other terms, Y will become negative. Moreover, thereafter it will remain negative. So, the model itself is not correct. In fact, your model is a parabola opening downwards. So, it is natural to happen.
3. So, what I suggest is to plot the points to get the idea which kind of curve is suitable to fit. Excel has good facility to try several models. By choosing a curve with higher R2 value, you can get an appropriate model. However, you have to be aware that the model actually represents the reality.
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