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POEstimating Parameters in R from a Weighted Sum of Lagged Variables
 

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  1. POEstimating Parameters in R from a Weighted Sum of Lagged Variables
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    <p>I am afraid I am stuck with an estimation problem.</p> <p>I have two variables, X and Y. Y is explained by the weighted sum of n lagged values of X. My aim is to estimate the two parameters c(alpha0,alpha1) in:</p> <p>Yt = Sum from j=1 to n of ( ( alpha0 + alpha1 * j ) * Xt-j )</p> <p><img src="https://i.stack.imgur.com/o1ypY.gif" alt="enter image description here"></p> <p>Where Xt-j denotes the jth lag of X. </p> <p>I came up with this approach because I thought it would be a good idea to estimate the slope of the weights rather than estimating one parameter for each lag of X added (I intent to set n very large).</p> <p>To the model noise ut is added, which is assumed to be <b>normally distributed</b> with mean zero and standard deviation sigma. </p> <p>Assuming I would like to set <b>n=510</b>, then I need the original series and 510 lagged series. In order to avoid any NAs in the series I transform the original data to "data_chopped", containing only the observations after the first 510 observations have been dropped, and the matrix "data_lagged" in which each column represents a lagged series:</p> <pre><code>library(stats) data&lt;-arima.sim(n=10000,list(ar=0.15,ma=0.1),mean=0.5) data_chopped&lt;-data[511:length(data)] data_lagged&lt;-matrix(nrow=length(data_chopped),ncol=510) for (i in 1:510){ data_lagged[,i]&lt;-head(data,-i)[(511-i):length(head(data,-i))] } #Check result: cbind(data_chopped,data_lagged[,1:3]) #data_lagged[,1] is the first lag of the original data, data_lagged[,2] is the second lag, and so on. No NAs whatsoever to deal with </code></pre> <p>To demonstrate the "working order" of my log-likelihood function and the generated series I first would like to fit an AR(3) model:</p> <pre><code>logl&lt;-function(sigma,alpha,beta,gamma){ -sum(log((1/(sqrt(2*pi)*sigma)) * exp(-(( data_chopped -alpha*data_lagged[,1] -beta*data_lagged[,2] -gamma*data_lagged[,3] )^2)/(2*sigma^2)))) } library(stats4) mle(logl,start=list(sigma=1,alpha=0,beta=0,gamma=0),method="L-BFGS-B") </code></pre> <p>When I now try to estimate my model in the same way it just does not work. I never got a loop within a log-likelihood function to work, this is why I just wrote out the above model. So,</p> <p>Yt = Sum from j=1 to n of ( ( alpha0 + alpha1 * j ) * Xt-j ) </p> <p>= (alpha+beta*1)*Xt-1 + (alpha+beta*2)*Xt-2 + (alpha+beta*3)*Xt-3 + ... + (alpha+beta*510)*Xt-510</p> <pre><code>logl&lt;-function(sigma,alpha,beta){ -sum(log((1/(sqrt(2*pi)*sigma)) * exp(-(( data_chopped -(alpha + beta*1)*data_lagged[,1] -(alpha + beta*2)*data_lagged[,2] -(alpha + beta*3)*data_lagged[,3] -(alpha + beta*4)*data_lagged[,4] -(alpha + beta*5)*data_lagged[,5] ... -(alpha + beta*510)*data_lagged[,510] )^2)/(2*sigma^2)))) } library(stats4) mle(logl,start=list(sigma=1,alpha=0.5,beta=0),method="L-BFGS-B") Error in optim(start, f, method = method, hessian = TRUE, ...) : L-BFGS-B needs finite values of 'fn' </code></pre> <p>I do not get the error if I try just a very few lines:</p> <pre><code>logl&lt;-function(sigma,alpha,beta){ -sum(log((1/(sqrt(2*pi)*sigma)) * exp(-(( data_chopped -(alpha + beta*1)*data_lagged[,1] -(alpha + beta*2)*data_lagged[,2] -(alpha + beta*3)*data_lagged[,3] -(alpha + beta*4)*data_lagged[,4] -(alpha + beta*5)*data_lagged[,5] )^2)/(2*sigma^2)))) } library(stats4) mle(logl,start=list(sigma=1,alpha=0.5,beta=0),method="L-BFGS-B") Call: mle(minuslogl = logl, start = list(sigma = 1, alpha = 0.5, beta = 0), method = "L-BFGS-B") Coefficients: sigma alpha beta 1.07797708 0.26178848 -0.04378526 </code></pre> <p>Can someone please help me out on this?</p>
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    1. USChris437
    1. USChris437
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    1. PO
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    1. COseems like you need to fit some `ARIMA` model or rather `MA` model...
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      1. POEstimating Parameters in R from a Weighted Sum of Lagged Variables
      1. USagstudy
    2. COYou probably need some noise in your model, `y[t] = ... + epsilon[t]`. Your log-likelihood should use the data, `y` and, if the noise is Gaussian, it should contain a sum of squares. Avoid the `lag` function: (unless you data are `xts` or `zoo` time series), it never does what you want. In your function, `logl` is `NULL`: you compute something inside the loop, but you do not do anything with the result, so it is discarded.
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      1. POEstimating Parameters in R from a Weighted Sum of Lagged Variables
      1. USVincent Zoonekynd
    3. COHi Vincent! Thank you lot for your reply. I actually do deal with ts data here, so I guess I may keep the lags? So you asked me to include the residuals into the function. Is the SSR then actually what is to be minimized by optim?
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      1. POEstimating Parameters in R from a Weighted Sum of Lagged Variables
      1. USChris437
 

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