Quote:
Originally Posted by itooam
I haven't read your book just doing the online course, I see this thread has been moved from the "general homework" forum to "Chapter 3" of the book forum. If "recency weightings" are explained in your book (please could you confirm?) then I will scour the earth for your book as this area is of much interest. Previously I looked for your book on Amazon.co.uk but couldn't find, maybe I can order internationally through .com or some other shop.

The book does not specifically cover weighted regression; but it does cover linear models in depth. And yes, you can find the book on amazon.com; unfortunately it is not available on amazon.co.uk.
With respect to your question though, you seem to be confusing two notions of recency:
Let's take a simple example of one stock, which can generalize to the multiple stocks example. Suppose the stock's price time series is
At time
for
you construct the input
and the target
. You would like to understand the relationship between
and
. If you know this relationship, you are can predict the future price from previous prices. So suppose you build a linear predictor
.
The learning task is to determine
. To do this you minimize
You will probably find that the weights in
are not uniform. For example the weight multiplying
might be the largest; this means that the most
recent price
is the most useful in predicting the next price
.
The notion of recency above should not be confused with
recency weighted regression which is catering to the fact that the weights
may be changing with time (that is in the stock example, the time series is nonstationary). To accomodate this fact you reweight the
data points giving more weight to the more recent data points. Thus you minimize the error function
The
enforce that the more recent data points will have more contribution to
and so you will choose a
that better predicts on the more recent data points; in this way older data points play some role, but more recent data points play the dominant role in determining how to predict tomorrow's price.
Thus in the example of time series prediction, there are these two notions of recency at play:
(i) more recent prices are more useful for predicting tomorrows price
(ii) the relationship between this more recent price and tomorrows price is changing with time (for example sometimes it is trend following, and sometimes reversion). In this case, more recent
data should be used to determine the
relationship between today's price and tomorrow's price.