MATLAB: Forcast using arma

?System Identification Toolbox

Hello!
I've just started to use matlab. What I have: a time series(some data from 1970 to 2010). What I want to do: make a forcast for 2030 and 2050 using ARMA based on the data I got. My first attempt was using the system identification tool. Unfotunately I'm not able to make forecasts. Does anybody know how to do so? Is the system identification tool the right way?

Best Answer

Hi Lukas, Rajiv Singh posted the following function for forecasting a number of time steps ahead, which is want you want.
function YP = forecast(model,data,K, Init)
%FORECAST Forecast a time series K steps into the future
%



% YF = FORECAST(MODEL,DATA,K)
%
% DATA: Existing data up to time N, an IDDATA object.
% MODEL: The model as any IDMODEL object, IDPOLY, IDSS, IDARX or IDGREY.
% K: The time horizon of forecasting, a positive integer with the number of 
samples
% YF: The forecasted output after time N, an IDDATA object with output
% only, covering the time span N+1:N+K.
%
%  YF = FORECAST(MODEL,DATA,K, INIT)
%  wehere INIT is 'z' or 'e' allows specification of initial conditions (at
%  time = Data.SamplingInstants(1)).
%
% See also idmodel/predict, which computes a fixed horizon prediction
% along the existing data record.
[N, ny] = size(data); % assume data is iddata
Mss = idss(model);
ord = size(pvget(Mss,'A'),1);
if ord>N
 error('Forecast:TooFewSamples','The data should contain at least %d 
samples.',ord)
end
if nargin<4, Init = 'e'; end
yp = zeros(K,ny);
mp = getPredictor(Mss);
[Ap,Bp,Cp] = ssdata(mp);
if Init=='z'
 xt = ltitr(Ap, Bp, data.y); % use zero init
 x0 = xt(end,:);
else % Init == 'e'
 [A1,B1,C1,D1,K1] = ssdata(Mss);
 x00 = 
x0est(data.y,A1,B1,C1,D1,K1,size(C1,1),size(B1,2),250e3,eye(size(C1,1)));
 x0 = ltitr(Ap,Bp,data.y,x00); x0 = x0(end,:);
end
u = [data.y(end,:); zeros(1,ny)];
for ct = 1:K
 xt = ltitr(Ap, Bp, u, x0);
 x0 = xt(end,:);
 yp(ct,:) = (Cp*x0.').';
 u = [yp(ct,:); zeros(1,ny)];
end
YP = data; YP.y = yp; YP.u = []; YP.Name = '';
YP.UserData = []; YP.Notes = '';
YP.Tstart = data.Ts*(N+1);
%------local function -----------------------------------
function mp = getPredictor(sysd)
[A,B,C,D,K] = ssdata(sysd);
Ts = sysd.Ts;
Ny = size(D,1);
mp = idss(A-K*C, [K B-K*D], C, [zeros(Ny), D], zeros(size(A,1),Ny), 'Ts', 
Ts);
mp.InputDelay = [zeros(Ny,1); sysd.InputDelay];
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