Statistical Tools Employed in the Analysis of Data

Descriptive Statistics

The summary statistics viz., mean, standard deviation, standard error, skewness, kurtosis, minimum, maximum, range, and coefficient of variation (CV) were used to study the behavior of major pest incidence and weather variables.

Correlation Analysis

Simple correlations were carried out to determine the degree of relationship between the two variables. The relationship between pest population and each of the weather parameters such as minimum temperature, maximum temperature, morning and evening relative humidity, rainfall, and sunshine hours were determined using Karl Pearson’s correlation coefficient.

INGARCHX Model

Generalized linear model (GLM) estimators are maximum likelihood estimators based on a density in the linear exponential family (LEF). These include Poisson and Negative Binomial for count data, Bernoulli for binary data, and Gamma for duration data.

Artificial Neural Network (ANNs) Model

ANNs are widely used in machine learning techniques. They resemble the structure of neurons in the brain and are non-linear, self-adaptive, and data-driven approaches.

Support Vector Regression (SVR)

SVR is a supervised learning algorithm used for predicting discrete values. It aims to locate the line of best fit while minimizing errors.

Extreme Learning Machine (ELM)

ELM offers a fast and efficient approach for training single-hidden-layer feedforward neural networks by randomly assigning weights and determining output weights analytically.

Proposed Two-Stage Modelling (Hybrid Models)

The proposed two-stage modelling considers time series as a combination of autocorrelated original time series and significant residuals. The approach follows Zhang’s hybrid methodology using models like INGARCH, ANN, SVR, ELM, and RFR.

BDS (Brock-Dechert-Scheinman) Test for Non-Linearity

The BDS test is a non-parametric test used to determine whether the data is independently and identically distributed (iid) or has nonlinear dependencies.

Model Comparison Criteria (MSE and RMSE)

MSE (Mean Squared Error) and RMSE (Root Mean Squared Error) are used to measure the accuracy of different models.

Statistical Significance Test (Diebold-Mariano Test)

The Diebold-Mariano test is used to compare the forecast accuracy of different models based on residual differences.

Statistical Software Used in this Study

• Google Colab: Used for fitting Random Forest Regression.
• R Package: Various R packages such as ggplot2, lmtest, tseries, forecast, and tidyverse were used for statistical modelling.

Table: List of R Packages Used

More details are available in the original document.