Application of ARIMA and GARCH Models in Financial Analysis

This report provides an overview of ARIMA (Autoregressive Integrated Moving Average) and GARCH (Generalized Autoregressive Conditional Heteroscedasticity) models, key statistical tools used in financial analysis and time series forecasting. The ARIMA model is introduced as a regression analysis technique that uses time series data to predict future trends, with its components of Autoregression, Integration, and Moving Average explained. The report highlights the application of the ARIMA model in financial markets and securities. The GARCH model, developed for estimating volatility in financial markets, is also discussed, emphasizing its preference among financial modeling experts for providing real-world contexts when predicting financial instrument rates and prices. The report covers the heteroscedasticity feature of GARCH, its use in analyzing financial data like macroeconomic data, and its application in estimating the volatility of stock returns, market indices, and bonds. Finally, the report outlines the three steps involved in the GARCH process: estimating the best autoregressive model, computing autocorrelations, and testing for significance. References to related research are included.

ARIMA AND GARCH MODELS 1
ARIMA and GARCH Models
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ARIMA MODEL
An autoregressive integrated moving average mainly denoted by the initials ARIMA is a
model of regression analysis in statistics that utilizes time series data to predict the future trends
of an event or simplify data set for easy understanding. The model gauges the power of
dependent variables relative to other independent variables (Cadenas et al, 2016, p.109). ARIMA
model has found its extensive application in the prediction of the future of financial markets and
securities. This is achieved through the examination of the differences realized when series
values are compared instead of the actual values. ARIMA model is composed of three
components which must be understood in order to understand how the model works. The three
components are Autoregression (AR), Integrated (I) and Moving average (MA).
The Autoregression shows the changing variables that regress on their own lagged values
while the Integrated component represents the differences in the raw observations to transform
time series into stationery. A lively example can be seen in calculations where data values are
replaced by the difference between the current data values and previous values. The last
component is the Moving average, which simplifies the dependency between observational and
residual errors from moving average models which are applied in lagged observations. Each of
the three components of the ARIMA model works as standard notation parameter (Kumar and
Vanajakshi, 2015, p.21). A standard notion in this model has p, d, and q, where the integers
substitute for parameters to denote the ARIMA model used. Each of the three parameters: p, d,
and q have their own definition. For instance, p denotes the number of lag observations in the
model while d denotes the number of times each raw observation is differenced. The last
parameter, q, denotes the size of a moving average window

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GARCH MODEL
The GARCH Model which in full refers to a generalized autoregressive conditional
heteroscedasticity is a statistical model which was developed in 1982 by Robert F. Engle. It was
developed as an approach to estimating volatility in the financial markets. GARCH modeling
exists in a number of forms. It’s a model which is highly preferred by most of the financial
modeling experts because of its ability to provide real-world contexts when predicting the rates
and prices of financial tools than any other form of modeling (Kristjanpoller and Minutolo, 2016,
p.240). The heteroscedasticity feature of this model describes the irregular patterns of variation
of error terms or variables in a statistical form. Essentially, the heteroscedasticity feature in this
model signifies that the observations do not conform to linear patterns but cluster patterns.
In consideration of that fact, the predictive values which are drawn from the model are
not reliable. GARCH model can be used to analyze different types of financial data such as
macroeconomic data. It is used in the financial markets to estimate the volatility of stock returns,
market indices, and bonds. The resulting information helps in judging and determining the assets
which can provide high returns (Narayan, Liu, and Westerlund, 2016, p.130). This can also be
used to forecast returns of current investments which help in making decisions on asset
allocation, risk management, hedging, and portfolio optimization GARCH process has three
steps. The first step entails the estimation of the best autoregressive model; the second step
entails the computation of autocorrelations while the final step is the test for significance.

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References
Cadenas, E., Rivera, W., Campos-Amezcua, R. and Heard, C., 2016. Wind speed prediction
using a univariate ARIMA model and a multivariate NARX model. Energies, 9(2), p.109.
Kumar, S.V. and Vanajakshi, L., 2015. Short-term traffic flow prediction using a seasonal
ARIMA model with limited input data. European Transport Research Review, 7(3), p.21.
Kristjanpoller, W. and Minutolo, M.C., 2016. Forecasting volatility of oil price using an artificial
neural network-GARCH model. Expert Systems with Applications, 65, pp.233-241.
Narayan, P.K., Liu, R. and Westerlund, J., 2016. A GARCH model for testing market
efficiency. Journal of International Financial Markets, Institutions, and Money, 41, pp.121-138.