LEAST SQUARES Estimation code

Anybody know the code to estimate an ARMA model using LEAST SQUARES?

Thanks.

Answer 1

[Shashank Prasanna]

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.

[dav]

Thank you very much.

since I am still new to matlab I still have to understand the following:

does rng mean - random number generator? what does 5 do? what is inn and how do you get that equation?

It may be hard to answer all the above question. So would you please let me know of a good place to read on those functions.

Thanks.

Ps- I know MLe is the popular method. However, I have to do this using matlab.

[Shashank Prasanna]

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]

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)

Answer 2

[Azzi Abdelmalek]

Try my submission

http://www.mathworks.com/matlabcentral/fileexchange/37631-identification-by-least-square-method

[dav]

I am somewhat new to matlab. Is it possible for you to give me an example code so that I can understand it easily.

Suppose the order is (1 , 1). I want to estimate the parameters using least squares.

Thanks

[Azzi Abdelmalek]

the order is (1 , 1).? It's not clear, the order of your system is the order of your denominator

[Azzi Abdelmalek]

% 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]

hi i need to identify systems with 2 delays with least square algorithm anyhelp please