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Linear Trend Equation
Fri, 02/27/2009 - 13:11
Tim Altom wrote via contact form:
Hi, guys. I have a question about your display of the LTE.
The LTE I got on one dataset was Yt = 0.0210.000t This is not in a form I recognize, and it doesn’t conform to the equation form on your site/help either, which is Tt = a + b.Yt , which is a standard form without residuals.
The latter I recognize and could use. The first is isn’t. I’d think maybe the decimal points might be place indicators for the terms (.0210 would be a, for example) but the true value for an intercept of the data is .0207, so that doesn’t seem to work. Can you explain the calculated format, please?
__________________
Rizal Zaini Ahmad Fathony
Zaitun Time Series Developer Team
Fri, 02/27/2009 - 22:25
#2
Re: Linear Trend Equation
Tim Altom wrote via email:
So far as I know (not having practiced statistics anywhere but the United States) the usual linear trend equation is in the form y = ax + b, as you note. The coefficient of slope is a, and the intercept is b. But the equation in this form is general, and not specific to time series, so perhaps Yt = a + b(Xt) is a better way to show it for a time series. Either would be fine for me. I’m not at all sure about Tt = a + b(Yt), because the variable should probably be X, to show that it lies on the X axis, rather than Y.
As to the + or – signs, most conventions I’ve seen are that you omit the + if the slope is positive, but place the – if the slope is negative. This may need a setting, or an explanation.
Also, the practice of automatically rounding at the third digit can be a problem if the data itself is significant out to third place, as my data is in this case. I’m working with data that is generally around .0150, .0167, etc. Rounding to third place can give erroneous results in such cases, as it has here. It might be worthwhile to go out a bit further, or have a setting for it. I was attempting to forecast based on the linear regression line, and although it is zero to three places, it is some .00005 to five places. When a user has the kind of data I have, scientific notation (-5 E -05) might be best.
Otherwise, an outstanding program. Once I figured out the quirks of the data import, it’s been very helpful in my practice.
__________________
Rizal Zaini Ahmad Fathony
Zaitun Time Series Developer Team
Fri, 02/27/2009 - 22:28
#3
Re: Linear Trend Equation
Hi Tim
Thank you for your suggestion.
About the Tt = a + b.Yt equation format. We found it in one of our references. I think it is not a big problem about the differences in equation format, since it has the same meaning. But we will check again the general international format to write a Trend equation. Thank you. 
About the bug of Zaitun Time Series in viewing the trend equation which has small values in its slope or intercept. Zaitun Time Series round the slope and intercept values to 3 decimals only in the linear trend equation viewed in Model Summary tab. But in the calculation of forecasted, residual, predicted, values of the model, it uses the original slope and intercept values without any rounding process. So, the forecasted values, residual, and predicted values and the other criteria (such as R, MSE,etc) do not affected on the automatic rounding process, since they use the original slope and intersect values (without rounding process) in their calculation.
We will try to change the linear trend equation in Zaitun Time Series Trend Model Summary into a scientific notation, especially when it handle a variable with small values. Please wait the next revision of Zaitun Time Series (version 0.1.3) which includes the bug fix of the problem above. I will be released soon.
Thank you for your feedback.
__________________
Rizal Zaini Ahmad Fathony
Zaitun Time Series Developer Team
Sun, 03/01/2009 - 22:00
#4
Re: Linear Trend Equation
Hi Tim.
Zaitun Time Series v 0.1.3 which includes revision for this problem has been released.
Please visit http://www.zaitunsoftware.com/content/zaitun-time-series-v-013-released
for the further information.
You can download it in the download page on zaitun time series website.
Thank you for your report.
__________________
Rizal Zaini Ahmad Fathony
Zaitun Time Series Developer Team
Hi Tim.
Thank you for your feedback.
The format of LTE in Zaitun Time Series is Tt = a + b.Yt, as described in the manual. In the trend analysis result page, both slope and intercept values in the equation are rounded to 3 decimals, such as Yt = 90.560+2.597t .
In your case, the LTE in trend analysis result page was Yt = 0.0210.000t . it means the intercept value was 0.021 (rounded to 3 decimals) and the slope value was 0.000 (also rounded to 3 decimals). The "+" or "-" sign did not appear because the slope value is a negative value near with 0, may be was grater than -.00005 but less than 0. This case could happen because Zaitun Time Series automatically add the "+" sign in the LTE string if the slope value is a positive value (e. g. 0.458), but Zaitun Time Series doesn't add the "-" sign if the slope value is a negative (e. g. -0.458) value since the slope value is already have "-" sign. So there was a string format bug in Zaitun Time Series, in your case.
We will try to resolve this bug in Zaitun Time Series. May be we should change the format into a scientific format, e. g. Yt = -3.220E-07 + 4.916E-09*t
Or, may be, you have a suggestion.
We would be very happy if you give us a suggestion to improve Zaitun Time Series quality.
Thank you very much for your report.
Rizal Zaini Ahmad Fathony
Zaitun Time Series Developer Team