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iwan2no@xxxxxxxxxxx wrote:
> 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.
If you really think there is a (linear) trend, straight moving-averages
of type you propose will be biased. In forecasting things like sales
figures, etc., a very common method is to use "exponential smoothing",
which is a kind of weighted moving average, with late points receiving
more weight than very old points. For a trendless series (possibly
having random errors) the exponentially-smoothed series is A(t) =
a*D(t) + (1-a)*A(t-1), where D(t) = data at t and A(t) = best estimate
of the value at t. The smoothing constant is 0 < a < 1. Higher values
of a emphasize recent data more, while smaller values emphasize all
data more evenly. (Note: youy need an A(0) to get started; often, one
just uses a straight moving average as a value of A(0).)
However, if your series has a linear trend, exponential smoothing is
biased; to get good smoothing (and good forecasting), you need to go
to so-called "double exponential smoothing". You can Google this term
to find more details. Similar ways of fixing moving averages for trend
are available, but they are less commonly used.
R.G. Vickson
>
> 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
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