Update lectures for quantecon 0.13.1

lectures/arma.md

@@ -864,6 +864,8 @@ where `ma_poly` and `ar_poly` correspond to the polynomials in {eq}`arma_poly` -
 * `ma_poly` is the vector $(1, \theta_1, \theta_2, \ldots, \theta_q)$
 * `ar_poly` is the vector $(1, -\phi_1, -\phi_2, \ldots, - \phi_p)$
 
+Both vectors must have the same length, so the shorter one is padded with trailing zeros: `dimpulse` reads them as polynomials in positive powers of $z$, and an `ar_poly` longer than `ma_poly` would otherwise delay the response by the difference in their lengths.
+
 To this end, we also maintain the arrays `ma_poly` and `ar_poly` as instance data, with their values computed automatically from the values of `phi` and `theta` supplied by the user.
 
 If the user decides to change the value of either `theta` or `phi` ex-post by assignments

lectures/markov_jump_lq.md

@@ -240,10 +240,6 @@ The conditional expectation $\bar P_i$ appears inside the inverse.
 
 Averaging the quadratic forms $(\beta B_i' P_j A_i + W_i)' (Q_i + \beta B_i' P_j B_i)^{-1} (\beta B_i' P_j A_i + W_i)$ over $j$ instead gives a different and incorrect recursion, except when next period's Markov state is known with certainty or when $Q_i + \beta B_i' P_j B_i$ and $B_i' P_j A_i$ do not vary with $j$.
 
-At the time of writing, `quantecon.LQMarkov` implements that averaged recursion.
-
-In the examples below, its decision rules differ from those of the correct recursion by at most 2 percent.
-
 ## Applications
 
 We use the following imports.

lectures/policy_regimes.md

@@ -196,8 +196,6 @@ The decision rule in regime $i$ is $q_t = -F_i x_t$ with $F_i = (Q_i + \beta B'
 
 We code the iteration directly.
 
-At the time of writing, `quantecon.LQMarkov` averages over next-period Markov states outside the matrix inverse, which gives a different recursion when $\Pi$ has more than one nonzero element in a row.
-
 ```{code-cell} python3
 def solve_regimes(φs, Π, tol=1e-12, max_iter=20_000):
     "Decision rules F_i for regimes with feedback coefficients φs and transition matrix Π."