Testing the dispersion structure of count time series using Pearson residuals

Abstract

Pearson residuals are a widely used tool for model diagnostics of count time series. Despite their popularity, little is known about their distribution such that statistical inference is problematic. Squared Pearson residuals are considered for testing the conditional dispersion structure of the given count time series. For two popular types of Markov count processes, an asymptotic approximation for the distribution of the test statistics is derived. The performance of the novel tests is analyzed and compared to relevant competitors. Illustrative data examples are presented, and possible extensions of our approach are discussed.

Goodness‐of‐fit tests for Poisson count time series based on the Stein–Chen identity

“…These residuals might be used for diagnostic model checking in analogy to Zhu and Wang (2010). The choice f (x) ≡ 1 in (15) results in the ordinary (standardized) Pearson residuals, see Aleksandrov and Weiß (2020b) for a recent investigation, but we conjecture that nonconstant Stein-Chen functions will lead to an improved performance for some types of alternatives.…”

Goodness–of–Fit Tests for Bivariate Time Series of Counts

“…Various GOF tests have been suggested in the literature for the aforementioned two classes of models. Neumann (2011) and Fokianos and Neumann (2013) considered GOF tests for the regression function r in a Poisson INGARCH(1,1); see model ( 1) with p = q = 1 and Poisson F. A slightly less formal assessment of model adequacy is explored in Aleksandrov and Weiss (2020) for a PAR(1) model as well as for a Poisson INAR(1). GOF tests based on the sample index of dispersion were considered in Schweer and Weiss (2014) and Weiss et al (2019) for a Poisson INAR(1), and by Weiss and Schweer (2015) for a PAR(1).…”

Multivariate control charts for monitoring a bivariate correlated count process with application to meningococcal disease

“…15 ). The maximum likelihood estimation results of these models are shown in Table 1, with the corresponding log-likelihood function values, Akaike information criterion (AIC), and root mean square (RMS) value. The RMS denotes the root mean squares of differences between observed values and one-step predicted values (Aleksandrov and Weiß 29 ). where T = 84 , E false( X j , t | X j , t − 1 , bold-italicθ ^ false) , j = 1 , 2 is the conditional expectation of X j , t under known parameter estimation results bold-italicθ ^.…”