Forecasting with AR(1) model and fixed parameters

Hi guys. Allow me to share my issue with you. I have a variable with 150 observations and I want to generate forecasts with an AR(1) model. Also what I want is to estimate the AR(1) model first, using the initial 57 observations and then keeping my estimated parameters fixed, I want a loop generating 4-periods ahead forecasts by adding an extra observation every time. So estimate the model just one time, keep the estimates, and by expanding my sample by 1 obs each time I want to generate my forecasts.

Here I give you the script I wrote for estimating the AR(1) model. What I miss is the forecasting part.

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% load data

data=MatlabDataRealtimeandRevisedS1;

% construct complete Variables ,x1 is the lagged(-1).

y1=data(2:end,1);

x1=data(1:(end-1),1);

[Traw,col]=size(y1);

T_full=T_raw;

% data for initial estimation

T_estimation=57;

x2=x1(1:T_estimation,1);

Y=y1(1:T_estimation,1);

% Build regressors matrix and ones for the constant

X=[ones(length(x2),1),x2];

% Doing OLS

[Coef,CoefConfidInter,e]=regress(Y,X);

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Any help please??

Please let me know if you got question. Much appreciated