Nifty Index Determinants: Sensitivity Analysis through Artificial Neural Network

Introduction

The idea of an Artificial Neural Network (ANN) has gained widespread importance in the modern world due to the development of information technology. ANNs are now widely employed in the fields of medicine, research, technology, engineering, finance, etc. The biological neural networks present in the human brain served as the inspiration for ANNs. Neurons and intricate nerve networks make up the human brain. The axons and dendrites in this intricate nerve network are utilised to deliver and receive signals from other neurons, respectively. Researchers in the discipline of computer science use the human brain as a model to try and replicate how the brain performs computational processes (Chima & Duroha, 2019).

Review of Literature & Variable Theoretical Background

The neuron is the foundation of neural network theory. Non-linear boundaries are used for enclosed regions of a specific class and multilayer neural networks are used for these boundaries. The input from each neuron is merged linearly with varying weights in ANN. A non-linear activation unit, which can be a threshold unit in its most basic form, is then fed the outcome of this combination. Input-output mapping, fault tolerance and non-linearity are all features of neural networks. Strong fault tolerance is preferably provided by the network’s high connection, which ensures that the impact of error in a few terms will be minimised (Bhardwaj et al., 2015).

Since univariate time series predictions are what linear models like ARIMA do, they are unable to discover underlying dynamics in a variety of non-linear financial time series (Hiransha et al., 2018). The fact that the ANN model typically outperforms general linear and non-linear econometric models like OLS and GARCH is particularly fascinating. Statistical models are outperformed by ANN models due to significantly lower prediction errors (Kumar & Murugan, 2013).

One of the key characteristics of neural networks is their ability to handle both normal and non-normal data. Freitas et al. (2009) demonstrated that it is possible to obtain normal prediction errors with non-normal time series of stock returns, proving that prediction-based portfolio optimization took advantage of short-term opportunities, outperforming the Markowitz mean-variance model and beating the market benchmark.

Research Methodology & Hypotheses

The empirical dataset spans weekly time-series observations from November 5, 1995 to April 3, 2021 (totalling 1,379 observations). The dependent target variable is the NIFTY 50 Index, and the independent predictor variables are:

• WTI Crude Oil (in US dollars)
• Dow Jones Industrial Average (DJIA)
• US Dollar Index (USDX)
• US 10-Year Bond Rate
• Gold (in US dollars per ounce)

The computations were executed using SPSS 20 software utilizing Multilayer Perceptron (MLP) feed-forward architecture. The structural configuration of the model consists of:

• Input Layer: 5 predictor neurons (goldusa, wtioil, dollarindex, ustenyrbond, dowjones) plus 1 bias node.
• Hidden Layer: 3 hidden neurons [H(1:1), H(1:2), H(1:3)] plus 1 bias node, utilizing the Hyperbolic Tangent activation function.
• Output Layer: 1 target node (nifty), utilizing the Identity activation function.
• Partitioning & Cross-Validation: Data was partitioned into 70% training and 30% testing, verified across a 10-fold cross-validation scheme to prevent overfitting.

Empirical Data Analysis

Table 1: Descriptive Statistics & Non-Normality Test (Jarque-Bera)

Table 2: Bivariate Pearson Correlation with NIFTY 50

10-Fold Cross Validation & Error Convergence (Table 3 & 4)

Table 5: Sensitivity Analysis & Relative Normalized Importance

The sensitivity analysis was executed across the 10 neural network iterations to determine the normalized importance of each input neuron relative to the maximum predictor (Karaca et al., 2019):

Conclusion & Research Limitations

Sensitivity analysis demonstrates that the Dow Jones Industrial Average (DJIA) has the single largest impact on the Nifty Index (100% normalized importance), followed in descending rank order by:

1. Dow Jones Industrial Average (DJIA) – Rank 1 (100.0% Sensitivity, r = +0.9596)
2. Gold (USA) – Rank 2 (33.4% Sensitivity, r = +0.8679)
3. WTI Crude Oil – Rank 3 (17.1% Sensitivity, r = +0.4334)
4. US 10-Year Bond Yield – Rank 4 (11.0% Sensitivity, r = -0.7979)
5. US Dollar Index (USDX) – Rank 5 (5.7% Sensitivity, r = -0.1205)

The correlation findings reinforce this sensitivity hierarchy: the US Dollar Index and US 10-Year Bond Rate exhibit inverse (negative) relationships with the Nifty, while the Dow Jones, Gold, and Crude Oil are positively correlated.

References

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