INAR(1) simulation in R [closed]

How do we simulate values of $$Y_t$$ for a maximum value of $$t=60$$ when we have an INAR(1) process as follows:
$$Y_t=ρ^*Y_{(t-1)}+R_t$$ where
$$t$$ takes values from 1 to 60,
$$ρ=0.3,0.8$$,
$$ρ^*$$ is the thinning,
$$R_t$$ is assumed to follow Poisson distribution with rate

$$λ_t$$ = $$exp(β_0 +β_1x_{1t})$$ where $$β_0=β_1=1$$
We are required to simulate values for a 100 Monte Carlo experiments.

closed as off-topic by Robert Long, Peter Flom♦Apr 23 at 11:06

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The definition of the INAR(1) process leads to a straightforward simulation implementation: if $$𝑌_𝑡=ρ\circ 𝑌_{𝑡−1}+𝑅_𝑡$$ this means that$$𝑌_𝑡=\sum_{i=1}^{Y_{𝑡−1}}\zeta_{it}+𝑅_𝑡$$where $$\zeta_{it}\stackrel{\text{iid}}{\sim} \mathcal B(1,\rho)\qquad R_t\sim\cal P(\lambda_t)$$i.e.$$ρ\circ 𝑌_{𝑡−1}\sim\mathcal B\text{in}(𝑌_{𝑡−1},\rho)$$Hence the R code for simulating $$Y_t$$ given $$Y_{t-1}$$ and $$\lambda_t$$ could be
Y[t]=rbinom(1,Y[t-1],rho)+rpois(1,lambda[t])

where blue stands for the $$y_t$$'s and gold for the $$x_t$$'s
• Is it mandatory to create a function for the variable $Y[t]$? – Shifa Apr 23 at 10:31