LEAST SQUARES Estimation code

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dav
dav 2013-2-7
评论： yem 2014-12-16
Anybody know the code to estimate an ARMA model using LEAST SQUARES?
Thanks.

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Shashank Prasanna
编辑：Shashank Prasanna 2013-2-8
To show you an example I am going to generate some data from the following ARMA model. I am generating this using the ARIMA function in the econometrics toolbox. If you don't have it don't worry because I am using this data to demonstrate how to estimate the coefficients using least squares. How ever I would like to inform you that that a more popular approach is to use MLE.
Generate some data to simulate.
Here AR lag 1, coeff 0.3
MA lag 1, coeff 0.2
rng(5);
simModel = arima('AR',0.3,'MA',0.2,'Constant',0,'Variance',1);
% simModel = arima('AR',0.4,'Constant',0,'Variance',1);
Y = simulate(simModel,500);
The following code will estimate the coefficients using least squares using MATLAB's \ operator.
>> rng(5);
inn=randn(500,1);
[Y -[0;Y(1:end-1)] -[0;inn(1:end-1)]]\inn
ans =
1.0000
0.3000
0.2000
The first number is for y(t) which is 1. the AR is 0.3 and MA is 0.2.
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Shashank Prasanna
Shashank Prasanna 2013-2-8
RNG is used to set the random number generator seed, it could be anything, i just used 5. Notice that I reuse it again while I estimate so that I use the exact same random numbers during estimation that I used during data generation.
inn is commonly known as innovations or error terms, and it is assumed to be white noise or normally distributed with 0 mean 1 var, but could be something else. i use the randn function to generate some inn. The equation I used is just the solution to a linear system Ax=b which can be solved in MATLAB for x by performing A\b.
I would suggest any starting with MATLAB documentation: http://www.mathworks.com/help/matlab/ref/rng.html http://www.mathworks.com/help/econ/specification-1-1.html
Lastly, MLE is indeed a popular mathod and MATLAB is capable to solving MLEs as long as you formulate you problem that way. search documentation for MLE
hth
dav
dav 2013-2-16
Thanks alot. what I really have to do is as follows. I used the following R code to estimate ARMA model. Note that first, I have generated a garch data set. Now, according to a theory I know epsi^2 has an ARMA model. So when when I estimate epsi^2 using LEAST SQUARES, I should get parameter estimates close to the same parameter values of the GARCH model. I have to have an additional condition that constraint that parameter estimates are greater than zero. I am actually trying to write a code to do step 1 of the paper titled " computationally efficient bootstrap prediction intervals for arch and garch processes " by Bei Cheng.
If you could help me with this, it is greatly appreciated.
R CODE: a0 = 0.05; a1 = 0.1; b1 = 0.85
nu = rnorm(2300)
epsi = rep(0, 2300)
h = rep(0, 2300)
for (i in 2: 2300) { h[i] = a0 + a1 * epsi[i-1]^2 + b1 * h[i-1] ; epsi[i] = nu[i] * sqrt(h[i])}
epsi = epsi[2001:2300]
epsi=epsi*epsi
arma(epsi,order=c(1,1))
(my problem with using R is that it doent have enough memory to do the entire process)

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Azzi Abdelmalek
Azzi Abdelmalek 2013-2-7
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Azzi Abdelmalek
Azzi Abdelmalek 2013-2-7
编辑：Azzi Abdelmalek 2013-2-7
% n: is the order of your system
% u: input signal
% y : output signal
k1=5 % k1 >n
k2=30
teta=least_square(u,y,n,k1,k2)
yem
yem 2014-12-16
hi i need to identify systems with 2 delays with least square algorithm anyhelp please

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