Data Analysis Plan for quantitative Research – statswork

## Data Analysis Plan for Quantitative Research

To assess the serial correlation, Breusch Godfrey serial correlation test will be used. This test assumes about the independence of the disturbances from observation to observation. There is the problem of autocorrelation exists, if this assumption is violated the errors in one time period are correlated with their own values in other period. The auto correlated disturbances can occur due to following types of mis-specification

• Dynamic structure incorrect
• Functional form incorrect’
• Explanatory variables omitted

#### Null hypothesis: Errors are serially independent up to order p

Step 1: Run OLS model yt = β0+β1x1t + β2x2t + . . . .βkXkt + t

Step 2: Calculate predicted residuals

Step 3: Run auxiliary regression or with higher order lags—Bruesch-Godfrey test

Step 4: T-test on

#### Data Analysis Plan for Autoregressive conditional heteroskedasticity

This model was introduced by Engle (1982), in order to capture the behaviour of the volatility ARCH regression model tool has been used particularly when it is time varying in a high frequency. This model brings the difference between the conditional and the unconditional second order moments. In financial data in particular, traditional econometric models are unable to explain several typical features and using ARCH model, these typical features are treated in the present study.

First, the returns have leptokurtic distribution rather than normal distribution was indicated by Stenius (1991) from stock market data. The reason behind such distribution is due to the discontinuous trading resulted in asset prices jumps and continually markets are not opened, resulted in asset prices jumps which in turn result in returns of both positive and negative. All these features could result in fat tails and excess peakedness which is nothing but leptokurtic distribution (Watshman and Parramore, 2002). Further volatility clustering is the second features, which means that small returns expected to follow small returns and vice versa. In order to address these issues ARCH model, which assumes variance of errors is not constant or changes over time as a function of past errors which is known as heteroskedasticity.

#### Data Analysis Plan for General Autoregressive conditional Heteroskedasticity

As a function of past errors together with the lagged values of conditional variance, the GARCH specification allows the past conditional variance to change over time (Bollserslev, 1986). Several studies used GARCH models particularly for the variables such as foreign exchange rates, interest rates and inflation rate (Engle et al, 1987; Kendall and MacDonald, 1989)

#### Data Analysis Plan for TARCH

Traditionally, financial variables always tend to change over time and always smaller changes tend to follow the large changes and vice versa. In the dependent variables, episodes of volatility are generally characterized by large shocks. In order to mimic this phenomenon the conditional variance function is formulated. In the model of regression, from its conditional mean or equivalently a large positive or negative value of error term, a large deviation of dependent variable is represented through a large shock. An irrespective of the signs, the variance of the current error in the ARCH regression model shows an enhanced function of the lagged errors magnitude. Thus, a large error to either sign is followed through the smaller errors of either sign. And similarly, a small error to either sign is followed through the large error of either sign. In conditioning the variance of subsequent errors, the order of the lag q determines the length of time for which a shock persists. Further, if the value of Q tends to be larger, then the volatility will also tend to be larger.

The researcher has to exercise caution when distinguishing between good news and bad news in the financial markets. Bad news depresses asset prices and historically leads to these Foreign Portfolio Investors to exit the financial markets and conversely, good news leads to asset price appreciation attracting portfolio investors (Agarwal,R.N. 1997). (Kulwant Rai, N.R Bhanumurthy 2004) and (Kumar Sundaram 2009) (Chakrabarti Rajesh) have proved that the sensitivity with which these investors withdraw is greater than the sensitivity with which they invest. On account of being more risk averse in nature, their speed in investing is relatively slower than their speed in pulling out their investments from the markets. This leads to asymmetry between good and bad news. (Kulwant Rai, 2004)

• Descriptive Statistics
• Central Tendency (Mean, Median, etc.)
• Variability (Variance, Standard Error, Confidence Intervals, etc.)
• Sample Size and Power Calculation
• Categorical Analyses
• Chi-Square
• Contingency Tables
• Binomial Test
• Analysis of Variance (ANOVA)
• Basic
• Repeated Measures ANOVA
• MANOVA
• ANCOVA
• Correlation Analysis
• Regression Analysis
• Multiple Regression
• Non-Linear Regression
• Logistic Regression
• Multivariate Statistics
• Cluster Analysis
• Ordination/Principal Components Analysis
• Discriminant Analysis
• Canonical Correlation Analysis
• Factor Analysis
• Interim Analyses and Stopping Rules
• Survival Analysis
• Equivalence Testing
• Odds Ratios
• Log Likelihood Analysis
• SEM using AMOS
• PLS analysis
• Non-Parametric Analogs to the Methods Listed Above

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