Journal of Data Science

Earthquake in recent years has increased tremendously. This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) charting technique to determine if the frequency of earthquake in the world is unusual. The frequency of earthquake in the world is considered from the period 1973 to 2016. As our data is auto correlated we cannot use the regular control chart like Shewhart control chart to detect unusual earthquake frequency. An approach that has proved useful in dealing with auto correlated data is to directly model time series model such as Autoregressive Integrated Moving Average (ARIMA), and apply control charts to the residuals. The EWMA control chart and the CUSUM control chart have detected unusual frequencies of earthquake in the year 2012 and 2013 which are state of statistically out of control.

Time series modelling is very popular technique used in data science. Main motive of time series modelling is to know the data generating process and also get its parameters which depend on all the observations. There may be few observations which misinterpret the data and also influence the parameters, such type of observations are called Outlier. The present study dealt the handling of outlier in context of ARIMA time series and proposed an alternative approach for the replacement of outlier. In usual process two ways of handling the outlier is popular, in first remove the outliers from the data and second replace it by the nearby values. Removal concept cannot work in the auto-correlated data like time series and similarly replacement of outlier through just previous/after value is also not much appropriate method because of dependency structure. Therefore, we are proposing an alternative approach, in which outlier is replaced by estimated values through best model. Detailed methodology is discussed and then an empirical analysis on the time series of National Pension Scheme (NPS) is carried out. Most of the series are modelled perfectly and few series were not due to non-stationary nature of the series. After getting an outlier free series, forecasting is also done. The realization of the series also performed on proposed methodology to get generalized view of proposed methodology and get similar result.