|
|
Hi,
I've got a simple question about predicting temperature readings. I got
a couple of responses yesterday... but I'm still not too clear about a
few things...
Say I record temperature readings of a place every minute. I do this
for 10 minutes, i.e. I've got 10 readings (T1 to T10). I then make a
prediction of the temperature for the 11th minute, P11. I then get a
reading for the 11th minute as well, T11.
Now in the 12th minute, I make my prediction (P12) based on *only* the
past 10 temperature readings, i.e. T2 to T11.
So basically, every prediction can ONLY be made based on the last 10
readings.
In addition, I also need to state the accuracy of the predicted
reading, e.g. there is a 95% chance that the predicted temperature at
the 12th minute, i.e. P12, is within +/-0.5C.
Another important point is that I need to use a technique that is VERY
computationally simple. So I definitely don't want to deal with complex
computations. In fact, I'd prefer a simple method, even if that means
giving up some accuracy.
Now it seems to me that there could be two ways of doing this:
1. Using Time Series Forecasting
2. Using Linear Regression
Let me first state some things about Time Series Forecasting:
=============================================
Since I'm only considering a very small time frame, there won't be any
seasonal components. Only a trend. I guess I can use something like
AR(4) (i.e. p=4) for example. I make the assumption that q=0. But then
I understand that I need to compute some coefficients, and the way to
do that could be using say the durbin-levinson algorithm. Am I right in
saying this? It seems to me that it's computationally quite difficult?
I can't really find any examples of this using actual numbers, e.g.:
20,21,20.5,22.4,23.8, 24.6,26,27.3,27.9,28.5,29.....what next? what are
the precise steps?
Now for Linear Regression
===================
I could do a simple linear regression and use that to make the
predictions. Also, since the trend of the temperature may change
suddenly, I'm thinking of using weights, so that more recent
temperature readings have a greater impact on the line of best fit. By
the way, I plan to use the least squares method to work out the model.
Questions:
========
1. Why is it I can't find any examples where linear regression is used
to make predictions where time is the factor used to make the
prediction of the measured variable? All the examples seem to be say
between two measured parameters, e.g. temperature and humidity. Is it
wrong to use linear regression?
2. Can I add weights to the AR model to give priority to more recent
readings? Couldn't seem to find any info on that in the book I'm
referring to. Or are the coefficients the weights?
3. What's the main difference between Linear Regression (LR) and Time
Series Forecasting (TSF)? How do I know when to use LR and when to use
TSF? Can't find any info on this anywhere...
Thanks a lot for your comments in advance...
and Happy New Year!!
Cheers,
Sam
|
|