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<iwan2no@xxxxxxxxxxx> wrote in message
news:1167589111.940345.138320@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> 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...
>
Your question seems a no-brainer.
After all, whatever you call it your series is a time series because it
relates to time.
From memory (30 years ago) and searching on Google, much of time-series
forecasting uses linear regression. I think that greater dependence is based
on the most recent readings than earlier ones - possibly autocorrelation.
See
http://socserv.mcmaster.ca/jfox/Books/Companion/appendix-timeseries-regression.pdf
Chris Chatfield was an author that is very good on time-series - indeed, I
attended a seminar given by him when I was at university.
Nick
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