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print( ); # input placeholder
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print( ); # input placeholder
JSFH
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print( ); # input placeholder
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiI0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEkflE1RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdGNEYv
restart: with(linalg): read "Q5.m":
n := nops(X): Z := evalm((X-mu)/sigma):
with(plots):listplot(X);
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rho[0]:=1: k:=3:
solve({seq(rho[i]=add(alpha[j]*rho[abs(i-j)],j=1..k),i=1..k)},{seq(rho[i],i=1..k)}):
assign(%):
V:=factor(1/(1-add(rho[i]*alpha[i],i=1..k))):
A:=inverse(matrix([seq([seq(rho[abs(i-j)],i=1..k)],j=1..k)])*V):
LF:=expand(log(det(A))-2*n*log(sigma)-evalm([seq(Z[i],i=1..k)]&*A&*[seq(Z[i],i=1..k)])
-add((Z[i]-add(Z[i-j]*alpha[j],j=1..k))^2,i=k+1..n)):
LF1:=subs({sigma=1,mu=18},LF):
sol1 := fsolve({seq(diff(LF1,alpha[i]),i=1..k)}, {seq(alpha[i],i=1..k)});
PCUvJkkmYWxwaGFHNiI2IyIiIiQiK1lzN0leISM1LyZGJTYjIiIjJCIrUlciPVglRisvJkYlNiMiIiQkIStPdSw1P0Yr
LF2:=subs(sol1,LF):
sol2 := fsolve({ diff(LF2, sigma), diff(LF2,mu)}, {sigma=1,mu=20});
PCQvSSNtdUc2IiQiK3FIMFI9ISIpL0kmc2lnbWFHRiUkIityV2Y5TyEiKg==
LF1:=subs(sol2,LF): # now go back to 'sol1' and repeat till numbers no longer change
# (the convergence is rather slow)
# verify stability
solve(subs(sol1,x^k=add(alpha[i]*x^(k-i),i=1..k)),x):
seq(abs(%[i]),i=1..k);
NiUkIisvc0pLVCEjNSQiKz5pMSJcKEYlJCIreGhEJFwnRiU=
JSFH
JSFH
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