Exponential smoothing and WLS

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Exponential smoothing and WLS

riccardo visca
Hello all,

I am estimating a gaussian linear model

y_t+1 = X_t B + u_t

and I noticed that I can actually predict very well a transformation of y_t  
(R^2=0.82)
where yhat_t is in fact an exponential smoothed version of y_t with some
smoothing parameter H

y_t is stationary in mean, eteroschedastic and full of outliers daily returns
series
X_t are (optionally) smoothed values too

It is quite straightforward using weighted least squares to predict the trend
value Et( yhat_t+1 ) but apparently and quite obviously


y_t+1 = E(yhat_t+1)+N_t+1
N_t+1 = y_t+1 - E(yhat_t+1)

were the noise N_t is full of jumps, autocorrelated, nearly unit root and
eteroschedastic
 
Now my question is:

is there a way to estimate efficiently this family of models in one step and/or
can we forecast efficiently yt+1-E(yhat_t+1) ?
Other than Crane-Crotty model that uses exponential weights?

Maybe an obvious R implementation I missed?
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Re: Exponential smoothing and WLS

Eric Zivot
My understanding is that regression on exponentially weighted data and
one-step ahead prediction (sometimes called discounted least squares) is a
"poor man's" Kalman filtering technique in which the underlying state space
model is a related to an exponential smoothing model. The optimal way to do
estimation is to explicitly write the underlying state space model (e.g. use
the dlm package) and then estimate the parameters by the prediction error
decomposition of the log-likelihood, and then do prediction from the
estimated model. For example, you could write your regression model as a
time varying parameter model where the regression coefficient follow pure
random walk or stationary autoregressive processes.


-----Original Message-----
From: [hidden email]
[mailto:[hidden email]] On Behalf Of riccardo visca
Sent: Monday, May 09, 2011 10:47 AM
To: [hidden email]
Subject: [R-SIG-Finance] Exponential smoothing and WLS

Hello all,

I am estimating a gaussian linear model

y_t+1 = X_t B + u_t

and I noticed that I can actually predict very well a transformation of y_t

(R^2=0.82)
where yhat_t is in fact an exponential smoothed version of y_t with some
smoothing parameter H

y_t is stationary in mean, eteroschedastic and full of outliers daily
returns
series
X_t are (optionally) smoothed values too

It is quite straightforward using weighted least squares to predict the
trend
value Et( yhat_t+1 ) but apparently and quite obviously


y_t+1 = E(yhat_t+1)+N_t+1
N_t+1 = y_t+1 - E(yhat_t+1)

were the noise N_t is full of jumps, autocorrelated, nearly unit root and
eteroschedastic
 
Now my question is:

is there a way to estimate efficiently this family of models in one step
and/or
can we forecast efficiently yt+1-E(yhat_t+1) ?
Other than Crane-Crotty model that uses exponential weights?

Maybe an obvious R implementation I missed?
        [[alternative HTML version deleted]]

_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only. If you want to post, subscribe first.
-- Also note that this is not the r-help list where general R questions
should go.

_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only. If you want to post, subscribe first.
-- Also note that this is not the r-help list where general R questions should go.