Argumented Dickey Fuller Test. Essay

While in the Dickey Fuller test it was assumed that the ut was uncorrelated. Therefore Argumented Dickey Fuller Test was developed. This test conducts by argumenting the three equations by adding the lagged values of the dependent variable. This test consists of estimating the following regression
Yt = 1 2t  Yt1 m Yt1 +t
t is a pure white noise error term. The number of lagged differences terms to include so that the error term is serially uncorrelated (Gujrati & Poter, 2004).
3.6.5 Normality Test
Normal distribution has Skewness of 0 and kurtosis of 3 and we know that financial series tend to be fat tailed Solution. The Jarque Bera test is a goodness of fit test which tells us that either the sample data has the skewness and kurtosis matching with the normal distribution. The test is named after Carlos Jarque and Anil K. Bera. Normality can be checked by using histogram and J B test. Jarque Bera Test is defined as
JB = n/6 + [Skew2 + (Kurtosis3)2/4]
3.6.6 The box jenkins (ARIMA) method
Auto Regressive (AR) models were first introduced by Yule in 1926. They were consequently implemented by Slutsky who in 1937 presented Moving Average (MA) schemes. It was Almgrist & Wiksell Stockholm (1938) combined both AR and MA schemes and showed that ARMA processes can be used to model all stationary time series as long as the appropriate order of p the number of AR terms, and q the number of MA terms, was appropriately specified.
The model is mentioned below
Yt=  +1Yt1+out+1ut1
Box Jenkins Analysis refers to a systematic method of identifying, fitting, checking, and using integrated autoregressive, moving average (ARIMA) time series models. The method is relevant for time series of medium to long length. This model is also used for univariate time series data. ARIMA is a forecasting technique that projects the future values of a series based totally on its own inertia. Its main application is in the area of short term forecasting requiring at least 40 historical data points. It works best when your data exhibits a stable or consistent pattern over time with a minimum amount of outliers. ARIMA is usually superior to exponential smoothing techniques when the data is reasonably long and the correlation between past observations is stable. If the data is short or it is highly volatile, then some other regular method may perform better. If you do not have at least 38 data points, you should consider something other method than ARIMA model. ARIMA models are fundamentally ?backward looking. As such, they on a broader scale are poor at predicting turning points, unless the turning point represents a return to a longrun equilibrium. BoxJenkins forecasting models is based on statistical concepts and principles. It has a wide range of class of models to choose from and a systematic avenue for identifying the correct model form. It has both statistical tests for verifying model validity as well as statistical measures of forecast uncertainty.