This package performs a multiscale analysis of a single nonparametric time trends (Khismatullina and Vogt (2020)) or multiple nonparametric time trends (Khismatullina and Vogt (2022), Khismatullina and Vogt (2023)).
In case of a single nonparametric regression, the multiscale method to test qualitative hypotheses about the nonparametric time trend \(m\) in the model \(Y_t = m(t/T) + \epsilon_t\) with time series errors \(\epsilon_t\) is provided. The method was first proposed in Khismatullina and Vogt (2020). It allows to test for shape properties (areas of monotonic decrease or increase) of the trend \(m\).
This method require an estimator of the long-run error variance \(\sigma^2 = \sum_{l=-\infty}^{\infty} Cov(\epsilon_0, \epsilon_l)\). Hence, the package also provides the difference-based estimator for the case that the errors belong to the class of \(AR(\infty)\) processes. The estimator was also proposed in Khismatullina and Vogt (2020).
In case of multiple nonparametric regressions, we provide the multiscale method to test qualitative hypotheses about the nonparametric time trends in the context of epidemic modelling. Specifically, we assume that the we observe a sample of the count data \(\{\mathcal{X}_i = \{ X_{it}: 1 \le 1 \le T \}\}\), where \(X_{it}\) are quasi-Poisson distributed with time-varying intensity parameter \(\lambda_i(t/T)\). The multiscale method allows to test whether intenisty parameters are different or not, and if they are, it detects with a prespicified significance level the regions where these differences most probably occur. The method was introduced in Khismatullina and Vogt (2023) and can be used for comparing the rates of infection of COVID-19 across countries.
KhismatullinaVogt2020MSinference
KhismatullinaVogt2023MSinference