I am curious if an autoregressive process of order $k:$ $X_{t}= c+ \sum_{i=1}^{k}\phi_i X_{t-i} + \epsilon_i$ can be expressed as a $k$-step Markov chain with transition probability $$ P_{ij}^{k} = Pr(X_{n+k}=j|X_n = i).$$ How this vectorization would look like?
2026-02-22 23:10:46.1771801846
Can an autoregressive process of order $k$ be expressed as a $k$-step Markov chain?
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