Estimate parameters of AR model for scalar time series
m = ar(y,n)
[m,ref1]
= ar(y,n,approach,window)
m= ar(y,n,Name,Value)
m= ar(y,n,___,opt)
Note:
Use for scalar time series only. For multivariate data, use 
returns
an m
= ar(y
,n
)idpoly
model m
.
[
returns
an m
,ref1
]
= ar(y
,n
,approach
,window
)idpoly
model m
and the variable refl
.
For the two latticebased approaches, 'burg'
and 'gl'
, refl
stores
the reflection coefficients in the first row, and the corresponding
loss function values in the second row. The first column of refl
is
the zerothorder model, and the (2,1)
element of refl
is
the norm of the time series itself.
specifies model structure attributes using one or more m
= ar(y
,n
,Name,Value
)Name,Value
pair
arguments.
specifies
the estimations options using m
= ar(y
,n
,___,opt
)opt
.



Scalar that specifies the order of the model you want to estimate (the number of A parameters in the AR model). 

Algorithm for computing the least squares AR model, specified as one of the following values:


Use of information about the data outside the measured time interval (past and future values), specified as one of the following values:


Estimation options.
Use 
Specify optional commaseparated pairs of Name,Value
arguments.
Name
is the argument
name and Value
is the corresponding
value. Name
must appear
inside single quotes (' '
).
You can specify several name and value pair
arguments in any order as Name1,Value1,...,NameN,ValueN
.

Positive scalar that specifies the sample time. Use when you
specify 

Boolean value that specifies whether the noise source contains an integrator or not. Use it to create "ARI" structure models: $$Ay=\frac{e}{(1{z}^{1})}$$ Default: false 

An 

An 2–by2 array. The first row stores the reflection
coefficients, and the second row stores the corresponding loss function
values. The first column of 
Given a sinusoidal signal with noise, compare the spectral estimates of Burg's method with those found from the forwardbackward approach and nowindowing method on a Bode plot.
y = sin([1:300]') + 0.5*randn(300,1); y = iddata(y); mb = ar(y,4,'burg'); mfb = ar(y,4); bode(mb,mfb)
Estimate an ARI model.
load iddata9 z9 Ts = z9.Ts; y = cumsum(z9.y); model = ar(y, 4, 'ls', 'Ts', Ts, 'IntegrateNoise', true) compare(y,model,5) % 5 step ahead prediction
Use option set to choose 'ls'
estimation
approach and to specify that covariance matrix should not be estimated.
y = rand(100,1); opt = arOptions('Approach', 'ls', 'EstCovar', false); model = ar(y, N, opt);
The AR model structure is given by the following equation:
$$A(q)y(t)=e(t)$$
AR model parameters are estimated using variants of the leastsquares
method. The following table summarizes the common names for methods
with a specific combination of approach
and window
argument
values.
Method  Approach and Windowing 

Modified Covariance Method  (Default) Forwardbackward approach and no windowing. 
Correlation Method  YuleWalker approach, which corresponds to least squares plus pre and postwindowing. 
Covariance Method  Least squares approach with no windowing. arx uses
this routine. 
Marple, Jr., S.L., Digital Spectral Analysis with Applications, Prentice Hall, Englewood Cliffs, 1987, Chapter 8.