**1. Introduction**

Time series is a series of observation collected with respect to time. The time could be in minutes, hours, daily, weekly, monthly, yearly etc. Time series data can be seen and applied in all fields of endeavors such as engineering, geophysics, business, economics, finance, agriculture, medical sciences, social sciences, meteorology, quality control etc. [1] but this chapter focused on financial time series analysis.

In the field of time series analysis, Autoregressive Moving Average (ARMA) and Autoregressive Integrated Moving Average (ARIMA) models are popular and excellent for modeling and forecasting univariate time series data as proposed by Box and Jenkins in 1970 but many times these models failed in analyzing and

forecasting financial time series [2], this is because the ARMA and ARIMA models are used to model conditional expectation of a process but in ARMA model, the conditional variance is constant. This means that ARMA model cannot capture process with time-varying conditional variance (volatility) which is mostly common with economic and financial time series data [3].

Adigwe, et al. [7], examined the effect of stock market development on Nigeria's

Yaya, et al. [8] examined the application of nonlinear Smooth Transition- Generalized Autoregressive Conditional Heteroscedasticity (ST-GARCH) model of Hagerud on prices of banks'shares in Nigeria. The methodology was informed by the failure of the conventional GARCH model to capture the asymmetric properties of the banks' daily share prices. The asymmetry and non-linearity in the model dynamics make it useful for generating nonlinear conditional variance series. From the empirical analysis, we obtained the conditional volatility of each bank's share price return. The highest volatility persistence was observed in Bank 6, while Bank 12 had the least volatility. Evidently, about 25% of the investigated banks exhibited linear volatility behavior, while the remaining banks showed nonlinear volatility specifications. Given the level of risk associated with investment in stocks, investors and financial analysts could consider volatility modeling of bank share prices with variants of the ST-GARCH models. The impact of news is an important feature that relevant agencies could study so as to be guided while addressing underlying issues

Emenike and Aleke [9] studied the daily closing prices of the Nigerian stocks from January 1996 to December 2011 used the asymmetric GARCH variants. Their result showed strong evidence of asymmetric effects in the stock returns and there-

Arowolo [10] examined the forecasting properties of linear GARCH model for daily closing stocks prices of Zenith bank Plc in the Nigerian Stock Exchange. The Akaike and Bayesian Information Criteria (AIC and BIC) techniques were used to obtain the order of the GARCH (p,q) that best fit the Zenith Bank return series. The information criteria identified GARCH (1,2) as the appropriate model. His result

Emenike and Ani [11], examined the nature of volatility of stock returns in the Nigerian banking sector using GARCH models. Individual bank indices and the Allshare Index of the Nigerian Stock Exchange were evaluated for evidence of volatility persistence, volatility asymmetry and fat tails using data from 3 January 2006 to 31 December 2012. Results obtained from GARCH models suggest that stock returns volatility of the Nigerian banking sector move in cluster and that volatility persistence is high for the sample period. The results also indicate that stock returns distribution of the banking sector is leptokurtic and that sign of the innovations have insignificant influence on the volatility of stock returns of the banks. Finally, the findings of this study show that the degree of volatility persistence is higher for

Abubakar and Gani [12] re-examined the long run relationship between finan-

cial development indicators and economic growth in Nigeria over the period 1970–2010. The study employed the Johansen and Juselius (1990) approach to cointegration and Vector Error Correction Modeling (VECM). Their findings

fore proposed EGARCH as performing better than other asymmetric rivals.

further supported the claim that financial data are leptokurtic.

the All Share Index than for most of the banks.

economic growth. The objective of the study was to determine if stock market development significantly impact on the country's economic growth. Secondary data were employed for the study covering 1985 to 2014. Ordinary Least Square (OLS) econometric technique was used for the time series analysis in which variations in economic growth was regressed on market capitalisation ratio to GDP, value of stock traded ratio to GDP, trade openness and inflation rate. The analysis revealed that stock market has the potentials of growth inducing, but has not contributed meaningfully to Nigerian economic growth, since only 26.5% of variations in economic growth were explained by the stock market development variables. Based on this, they suggested for an encouragement of more investors in the market, improvement in the settlement system and ensuring investors' confidence

*Financial Time Series Analysis via Backtesting Approach*

*DOI: http://dx.doi.org/10.5772/intechopen.94112*

in the market.

in the banking system.

**101**

In economic and financial time series literatures, time-varying is more common than constant volatility, and accurate modeling of time volatility is of great importance in financial time series analysis by financial econometricians [4]. In practice, financial time series contains uncertainty, volatility, excess kurtosis, high standard deviation, high skewness and sometimes non normality [3]. Therefore, to model and capture properly the characteristics of financial time series models such as Auto-Regressive Conditional Heteroscedastic (ARCH), Generalized Auto-Regressive Conditional Heteroscedastic (GARCH), multivariate GARCH, Stochastic volatitlity (SV) and various variants of the models have been proposed to handle these characteristics of financial time series [5]. This chapter would focus on univariate GARCH models. In practice, the backtesting approach compliment the estimated GARCH model, in order to select a reliable GARCH model useful for real life application.

This book chapter aimed at obtaining reliable GARCH model via backtesting approach using daily Zenith bank Nigeria plc stock returns.
