Generalized Random Environment INAR Models of Higher Order

On generalized random environment INAR models of higher order: Estimation of random environment states

“…Beside the marginal distribution parameter, authors assumed here that Simulated R2NGINAR(1) time series-exact environment states States estimated by the application of standard K-means method the order of the model is also determined by the environment state in particular moment. Another step ahead was made by [9]. Beside all the assumptions mentioned above, authors additionally assumed that the thinning parameter value α z n in moment n depends on the environment state z n in the same moment.…”

“…Beside all the assumptions mentioned above, authors additionally assumed that the thinning parameter value α z n in moment n depends on the environment state z n in the same moment. According to [9], {X n (z n )} ∞ n=1 is called a generalized random environment INAR model of higher order with geometric marginals and negative binomial thinning operator (abbrev. RrNGINAR(M, A, P)) if its element X n (z n ) at moment n ∈ N is determined by the recursive relation…”

“…Beside the shortcomings mentioned above, we detected another difficulty when applying K-means to a generalized random environment INAR process of higher order, as it was done in [9]. To explain the difficulty, consider the simplest case with r = 2 environment states and suppose similarity between mean values within states, µ 1 ≈ µ 2 .…”

“…Finally, the K-means algorithm will be applied on such obtained three-dimensional data sequence. It is possible to apply RENES method to any other generalized random environment INAR model of higher order (to those that have different marginal distribution and thinning operator), but we focus on RrNGINAR(M, A, P) models, as it was the case in [9]. In order to confirm the efficiency of RENES, corresponding simulated data sequences are created.…”

Estimation for random coefficient integer-valued autoregressive model under random environment

“…On the other hand, the introduction of random environment in the INAR models has greatly improved the adaptability of the model. Nastić et al [13] and Laketa et al [14] studied integer-valued autoregressive models based on the negative binomial thinning operator with different geometric marginal under random environment. For a more detailed and profound introduction to random environment models, see Laketa [15].…”