La Ley de Defensa del consumidor

The following program can be used to estimate the value of β from a share series. The function shown in Equation (4.11) is constructed and minimised for the given share and dividend series.

betaest2.f_function(share,dividends=rep(0,length(share))){ N_length(share)

share2_share+dividends r_log(share2[-1])-log(share[-length(share)]) (1) m_length(r) ave_lowess(r,f=30/m) (2) r_r-ave$y r_r[21:(length(r)-20)] (3) share_share[21:(length(share)-21)] (4) assign("share",share,frame=1) (5) assign("r",r,frame=1) (6) result_nlmin(function(z){ length(r)*log(mean(r^2/(share^z)))+z*sum(log(share)) },0)[[1]] (7) list(beta=result+2,share=share,r=r) (8) }

The function has required argument _{St}, a series of closing share prices, and_{dt}, the series of dividends paid to holders of the share. The two series should be aligned so that element i of each series is for the same day. I have labelled eight lines of the program as follows (1), and will explain the function of these.

• Line (1) constructs the daily returns for the share series, where the return on day i is given by:

ri = ln µ Si+di Si−1 ¶ .

There are m observations in this series where there were N = m+ 1 observations in the share series.

• Line (2) estimates the mean levelµ(Yn) of the log return series, since E(lnSn+1−lnSn) =µ(Yn) is given by Equation (4.2). The Lowess filter is used for this purpose with a smoothing window of 30 observations.

• Lines (3) and (4) remove 20 observations from the ends of both the share price series, and the mean corrected log-returns. In order to es- timate µ(Yn) at the ends, the Lowess filter estimated observations to maintain a symmetric 30 observation window. By removing 20 obser- vations from each end of the series, the effects of this estimation will not affect the estimation ofβ.

• Lines (5) and (6) pass the data share and r to the minimisation procedure.

• Line (7) defines the function which must be minimised, g(β), and orders the minimisation procedurenlminto return the value ofβ which minimisesg(β). It will begin its search at β= 2 corresponding to z=0.

• Line (8) returns the estimated value for β, and the share price and mean corrected return series.

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