kenlitsanchez asked . 2022-04-22

Autoregressive model with lags

Pt = β1Pt−24+β2Pt−48+β3Pt−72+β4Pt−96+β5Pt−120+β6Pt−144+β7Pt−168+β8Lt+β9Rt+β10Et+β11Nt I was able to do the first part how to i find the other variables β8Lt+β9Rt+β10Et+β11Nt My code for the first part ar_X(:,1) = y(145:end-24); ar_X(:,2) = y(121:end-48); ar_X(:,3) = y(97:end-72); ar_X(:,4) = y(73:end-96); ar_X(:,5) = y(49:end-120); ar_X(:,6) = y(25:end-144); ar_X(:,7) = y(1:end-168); ar_Y = y(169:end);

autoregression using lags

Expert Answer

Kshitij Singh answered . 2025-03-25 17:52:13

Great job on setting up the autoregressive terms for your model! Now, let's incorporate the additional variables β8Lt\beta_8 L_t, β9Rt\beta_9 R_t, β10Et\beta_{10} E_t, and β11Nt\beta_{11} N_t.

Assuming you have vectors L, R, E, and N corresponding to the variables LtL_t, RtR_t, EtE_t, and NtN_t over time, you can add these variables to your design matrix ar_X.

Here's how you can extend your code:

matlab

% Given additional variables
L = ...; % Define your L_t vector here
R = ...; % Define your R_t vector here
E = ...; % Define your E_t vector here
N = ...; % Define your N_t vector here

% Ensure these variables are the same length as y
L = L(:); % Ensure L is a column vector
R = R(:); % Ensure R is a column vector
E = E(:); % Ensure E is a column vector
N = N(:); % Ensure N is a column vector

% Incorporate additional variables into ar_X matrix
ar_X(:,8) = L(169:end); % Adding L_t
ar_X(:,9) = R(169:end); % Adding R_t
ar_X(:,10) = E(169:end); % Adding E_t
ar_X(:,11) = N(169:end); % Adding N_t

Full Code

Here’s the complete code incorporating both the autoregressive terms and the additional variables:

matlab

% Autoregressive terms
ar_X(:,1) = y(145:end-24);
ar_X(:,2) = y(121:end-48);
ar_X(:,3) = y(97:end-72);
ar_X(:,4) = y(73:end-96);
ar_X(:,5) = y(49:end-120);
ar_X(:,6) = y(25:end-144);
ar_X(:,7) = y(1:end-168);

% Given additional variables
L = ...; % Define your L_t vector here
R = ...; % Define your R_t vector here
E = ...; % Define your E_t vector here
N = ...; % Define your N_t vector here

% Ensure these variables are the same length as y
L = L(:); % Ensure L is a column vector
R = R(:); % Ensure R is a column vector
E = E(:); % Ensure E is a column vector
N = N(:); % Ensure N is a column vector

% Incorporate additional variables into ar_X matrix
ar_X(:,8) = L(169:end); % Adding L_t
ar_X(:,9) = R(169:end); % Adding R_t
ar_X(:,10) = E(169:end); % Adding E_t
ar_X(:,11) = N(169:end); % Adding N_t

% Dependent variable
ar_Y = y(169:end);

By incorporating these additional variables into your design matrix ar_X, you will be able to account for their effects in your autoregressive model. If you have any further questions or need additional assistance, feel free to ask!

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