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copied!<p>I show you the principle. I am not sure I used the correct equations, but since you wrote about 4 parameters, I think this is what you mean.</p> <p>I did not check for errors and leave that to you. You should also do the usual diagnostics that should be used when doing non-linear regression.</p> <pre><code>fitfun<-function(p,d,a,b,c,d1){ beta_1 <- 2-b-c beta_2 <- -(1-c)*(1-b) beta_3 <- c*d1 + b*a beta_4 <- -c*d1*(1-b) - b*a*(2-c) beta_5 <- b*a*(1-c) res <- as.numeric(filter(p,c(0,beta_1,beta_2),sides=1)) + #use filter to calculate lagged values as.numeric(filter(d,c(0,beta_3,beta_4,beta_5),sides=1)) + c res[-(1:3)] #to remove NAs } pfit<-df$p0[-(1:3)] fit<-nls(pfit ~ fitfun(p0,d1,a,b,c,d),data=df,start=list(a=2,b=1,c=1,d=1)) summary(fit) Formula: pfit ~ fitfun(p0, d1, a, b, c, d) Parameters: Estimate Std. Error t value Pr(>|t|) a 0.13858 0.62064 0.223 0.823 b 0.21101 0.01594 13.237 <2e-16 *** c 1.41492 0.03015 46.929 <2e-16 *** d 0.09838 0.09098 1.081 0.280 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 6.799 on 1043 degrees of freedom Number of iterations to convergence: 7 Achieved convergence tolerance: 5.107e-06 </code></pre> <h1>Edit</h1> <p>I show quickly how <code>filter</code> works.</p> <pre><code>x <- 1:10 #[1] 1 2 3 4 5 6 7 8 9 10 filter(x,c(0,1),sides=1) #1*x_{i-1} #[1] NA 1 2 3 4 5 6 7 8 9 filter(x,c(0,0,2),sides=1) #2*x_{i-2} #[1] NA NA 2 4 6 8 10 12 14 16 filter(x,c(1,2,3),sides=1) #1*x_i + 2*x_{i-1} + 3*x_{i-2} #[1] NA NA 10 16 22 28 34 40 46 52 </code></pre> <p><code>filter</code> is a time series function and thus pretty fast.</p>

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