diff --git a/matlab/ols/common_parsing.m b/matlab/ols/common_parsing.m
index e5a06f59b..3fc3d459c 100644
--- a/matlab/ols/common_parsing.m
+++ b/matlab/ols/common_parsing.m
@@ -62,7 +62,9 @@ if overlapping_dates
     minlp = min([enddates{:}]);
     for i = 1:neqs
         Y{i} = Y{i}(maxfp:minlp);
-        X{i} = X{i}(maxfp:minlp);
+        if ~isempty(X{i})
+            X{i} = X{i}(maxfp:minlp);
+        end
         if ~isempty(lhssub{i})
             lhssub{i} = lhssub{i}(maxfp:minlp);
         end
diff --git a/matlab/ols/parse_ols_style_equation.m b/matlab/ols/parse_ols_style_equation.m
index 10c7cc040..b623a1a65 100644
--- a/matlab/ols/parse_ols_style_equation.m
+++ b/matlab/ols/parse_ols_style_equation.m
@@ -153,8 +153,13 @@ end
 Y = Y - lhssub;
 
 %% Set start and end dates
-fp = max(Y.firstobservedperiod, X.firstobservedperiod);
-lp = min(Y.lastobservedperiod, X.lastobservedperiod);
+fp = Y.firstobservedperiod;
+lp = Y.lastobservedperiod;
+if ~isempty(X)
+    % X is empty when AR(1) without parameter is encountered
+    fp = max(fp, X.firstobservedperiod);
+    lp = min(lp, X.lastobservedperiod);
+end
 if ~isempty(lhssub)
     fp = max(fp, lhssub.firstobservedperiod);
     lp = min(lp, lhssub.lastobservedperiod);
@@ -182,7 +187,9 @@ if isfield(jsonmodel, 'tags') ...
 end
 
 Y = Y(fp:lp);
-X = X(fp:lp);
+if ~isempty(X)
+    X = X(fp:lp);
+end
 if ~isempty(lhssub)
     lhssub = lhssub(fp:lp);
 end
diff --git a/matlab/ols/put_in_sur_form.m b/matlab/ols/put_in_sur_form.m
index 87efa6665..0afe6f6af 100644
--- a/matlab/ols/put_in_sur_form.m
+++ b/matlab/ols/put_in_sur_form.m
@@ -40,10 +40,13 @@ if isempty(Y) || ~iscell(Y) || isempty(X) || ~iscell(X) || length(Y) ~= length(X
 end
 
 %% Organize output
-neqs = length(X);
+neqs = length(Y);
 nobs = zeros(neqs, 1);
 for i = 1:neqs
-    assert(size(X{i}, 1) == size(Y{i}, 1), 'Y{i} and X{i} must have the same nuber of observations');
+    if ~isempty(X{i})
+        % X{i} is empty for AR(1) equations
+        assert(size(X{i}, 1) == size(Y{i}, 1), 'Y{i} and X{i} must have the same nuber of observations');
+    end
     nobs(i) = size(X{i}, 1);
 end
 nrows = sum(nobs);
@@ -51,23 +54,28 @@ Xmat = dseries([X{1}.data; zeros(nrows-nobs(1), size(X{1}, 2))], X{1}.firstdate,
 Yvec = Y{1};
 constrained = {};
 for i = 2:neqs
-    to_remove = [];
-    nr = sum(nobs(1:i-1));
-    nxcol = size(X{i}, 2);
-    Xtmp = dseries([zeros(nr, nxcol); X{i}.data; zeros(nrows-nr-nobs(i), nxcol)], X{1}.firstdate, X{i}.name);
-    for j = 1:length(X{i}.name)
-        idx = find(strcmp(Xmat.name, X{i}.name{j}));
-        if ~isempty(idx)
-            Xmat.(Xmat.name{idx}) = Xmat{idx} + Xtmp{j};
-            to_remove = [to_remove j];
-            constrained{end+1} = Xmat.name{idx}; 
+    if isempty(X{i})
+        data = [Xmat.data;zeros(size(Y{i},1), size(Xmat.data, 2))];
+        Xmat = dseries(data, X{1}.firstdate, Xmat.name);
+    else
+        to_remove = [];
+        nr = sum(nobs(1:i-1));
+        nxcol = size(X{i}, 2);
+        Xtmp = dseries([zeros(nr, nxcol); X{i}.data; zeros(nrows-nr-nobs(i), nxcol)], X{1}.firstdate, X{i}.name);
+        for j = 1:length(X{i}.name)
+            idx = find(strcmp(Xmat.name, X{i}.name{j}));
+            if ~isempty(idx)
+                Xmat.(Xmat.name{idx}) = Xmat{idx} + Xtmp{j};
+                to_remove = [to_remove j];
+                constrained{end+1} = Xmat.name{idx};
+            end
+        end
+        for j = length(to_remove):-1:1
+            Xtmp = Xtmp.remove(Xtmp.name{j});
+        end
+        if ~isempty(Xtmp)
+            Xmat = [Xmat Xtmp];
         end
-    end
-    for j = length(to_remove):-1:1
-        Xtmp = Xtmp.remove(Xtmp.name{j});
-    end
-    if ~isempty(Xtmp)
-        Xmat = [Xmat Xtmp];
     end
     Yvec = dseries([Yvec.data; Y{i}.data], Yvec.firstdate);
 end
diff --git a/matlab/ols/sur.m b/matlab/ols/sur.m
index af5bb77c1..6c69b45ec 100644
--- a/matlab/ols/sur.m
+++ b/matlab/ols/sur.m
@@ -54,6 +54,11 @@ neqs = length(jsonmodel);
 [Y, ~, X] = common_parsing(ds, ast, jsonmodel, true);
 clear ast jsonmodel;
 nobs = Y{1}.nobs;
+
+
+
+
+
 [Y, X, constrained] = put_in_sur_form(Y, X);
 
 if nargin == 1 && size(X, 2) ~= M_.param_nbr