# Monitoring Sparse and Attributed Network Streams with MultiLevel and Dynamic Structures

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Overview of the Proposed Methodology

#### 2.1. Zero-Inflated Generalized Linear Mixed Models

#### 2.2. State Space Models and the Extended Kalman Filter

#### 2.3. Monitoring of Dynamic and Multilevel Sparse Network Streams

## 3. Performance Evaluation Using Simulation

#### Simulation Results

## 4. Case Study: Change Detection in the Interbank Market during the Financial Crisis

- Overnight (OVN) transactions. Unsecured (U) loans, i.e., without collateral. (OVNU).
- Overnight (OVN) transactions. Secured (S) loans, i.e., with collateral. (OVNS).
- Short-term (ST) transactions, namely those with maturity up to 12 months, excluding overnight. Unsecured (U) loans, i.e., without collateral. (STU).
- Short-term (ST) transaction, namely those with maturity up to 12 months, excluding overnight. Secured (S) loans, i.e., with collateral. (STS).
- Long-term (LT) transactions, namely those with the maturity of more than 12 months of consideration. We distinguish collateralization. Unsecured (U) loans, i.e., without collateral. (LTU).
- Long-term (LT) transactions, namely those with the maturity of more than 12 months of consideration.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Comparison of average run length (ARL) using simulation data in the performances of different scenarios. Smaller ARL values indicate better performances.

**Figure 2.**Schematic representations of multilevel interbank networks. Each node is a bank, and links represent credit relations. The network in black is the total interbank market, obtained by aggregating all layers.

**Figure 3.**EWMA charts for Pearson’s residuals from the zero-inflated generalized linear mixed model to detect the onset of Crisis 1. Red dots are considered as out of control data.

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**MDPI and ACS Style**

Mostafapour, M.; Movahedi Sobhani, F.; Saghaei, A.
Monitoring Sparse and Attributed Network Streams with MultiLevel and Dynamic Structures. *Mathematics* **2022**, *10*, 4483.
https://doi.org/10.3390/math10234483

**AMA Style**

Mostafapour M, Movahedi Sobhani F, Saghaei A.
Monitoring Sparse and Attributed Network Streams with MultiLevel and Dynamic Structures. *Mathematics*. 2022; 10(23):4483.
https://doi.org/10.3390/math10234483

**Chicago/Turabian Style**

Mostafapour, Mostafa, Farzad Movahedi Sobhani, and Abbas Saghaei.
2022. "Monitoring Sparse and Attributed Network Streams with MultiLevel and Dynamic Structures" *Mathematics* 10, no. 23: 4483.
https://doi.org/10.3390/math10234483