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:

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[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?

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