MGMT90239 Business Analytics for Decision Making

Introduction

The Time series is a sequence of data point successive times spaced at a uniform time interval. It is a statistical technique used to analyze time-series data or trend analysis is called time series analysis (Brockwell et al., 2016).  The series of intervals or particular periods is known as Time series analysis. The dataset named Burglaries in England and Wales, Sales by the Gas and public electricity supply systems, Births Marriages & Deaths are taken for time series analysis. The Burglaries dataset contains quarterly data from 2007 to 2012.  The Fuel is a quarterly dataset containing gas sales in domestic and electricity sales in commercial and domestic. The birth marriage and death dataset contains the quarterly birth rate, marriage and deaths in the UK from 2007 to 2012.  Those data set are taken for analysis and forecast the future quarterly values.

Time series analysis

It is the forecast of a future event based on a past event. For time series analysis need the past and present data to forecast the future. The two types of time series forecast are Exponential smoothing forecast and Linear forecast(Hamilton, 2020). When the forecasting time series data are based on historical data with seasonal cycles is called an Exponential smoothing forecast. Linear forecast is using linear regression to predict the future. In time series date, time sequentially observed at a regular interval, and the numeric values are predicted for future dates (Schäfer, 2016). In time series, it is important to have equal intervals between each data points. This analysis report tries to forecast the next year's data based on historical data.

In the Burglaries dataset, the first column is the years from 2007 to 2012 and the second column is the quarters, and the third column is the values in thousands. To plot the exponential forecast plot, select both the values and quarter column and click on the Data tab forecast.

The Exponential forecast graph shows that in 2007 the value is in between 250 to 300. In 2008 it was decreased to 250. From 2008 to 2012 it is gradually decreased to 200. In 2013 the value was between 150 to 200. The graph shows that the rate of Burglaries gradually decreases and it is noticed that there is a decrease in rate if compared with 2007. The upper and lower line shows the range of the value (Appendix 1). The linear forecast chart shows that in 2007 first quarter the Burglaries rate is in between 300 and 350. The actual value shows that it is between 200 and 250. The predicted line shows that in the fourth quarter of 2011 gradually increase in rate. In the first quarter of 2012, the predicted line touches 250. The burglaries rate gradually decreases, and the actual and predicted value is equal in the last quarter of 2012. (Appendix 2)

The Fuel dataset is the quarterly Gas and electricity sales from 2007 to 2012. The units of the Gas column is in gigawatt hours. The Electricity sales in commercial and domestic column are in terawatt hours. One gigawatt is 0.001 terawatt. To convert the units of Gas sales, multiply the domestic gas with 0.001. The total column is the sum of all gas and domestic sales. The Fuel Exponential forecast chart shows that in 2007 the fuel sales are between 120 and 140. It is gradually increased to 140 in 2008 first, after that slightly decrease and stable in 2013. So the chart shows that the total sales in 2012 and 2013 are 140 (Appendix 3).

The linear fuel forecast shows that the sales in the first quarter of 2007 are 200, but it gradually decreases till the third quarter of 2007, after that again it increases till 2008 first quarter. So the graph shows that every year from the first quarter to third quarter the sales gradually decrease and from the third quarter to first quarter of next year it increases. It shows that it is a seasonal time series data (Appendix 4).

The third dataset is the quarterly birth, marriage and death rate in the UK. The number of births in 2007 is between 180 to 185, but it is gradually decreasing. In 2012 the birth rate was in between 165 to 170. In 2013, it was decreasing, and the line is in between 165 to 160. So the graph shows that gradually the birth rate in the UK decreases (Appendix 5). The exponential forecast chart shows that the marriage rate in 2007 is 78, then the marriage rate decreases slowly till 2009, then slowly increase till 2010 then again decrease. It is forecast that the marriage rate decrease to 68 (Appendix 6). The death rate is 157 in 2007, it is gradually decreasing, in 2009, it is close to 158, but after 2009 it decreases largely. In 2012 the death rate is 152. The forecast line shows that the death rate decreased in the UK (Appendix 7).

The linear birth plot shows that there is a cyclic change in the birth rate in the UK. The predicted line shows that the death rate in 2012 is 175 (Appendix 8). The linear forecast model shows that there is cyclic change. The predicted line shows that the marriage rate in 2012 is between 80 to 100 (Appendix 9). The actual value shows that in 2012 the UK's death rate decreased compared to 2007 (Appendix 10).

Forecasts

Forecasting is the technique that shows the relationships and trends and that value projected into the future. There are three commonly used quantitative methods, moving averages, exponential smoothing and linear regression (Carlberg,2016). The method of smoothing the trend in data moving average is used. The exponential smoothing is like moving average, and it is based on the past smoothing trend data. The forecast value shows the confidence interval range and 95% is the confidence interval's default level (Weigend, 2018). The seasonality can be detected using a forecast chart. The forecasted graph have the actual, predicted and lower and upper confidence interval. The linear forecast is the prediction of future value with a linear trend.

Time series is the method of analyzing and exploring the data to extract meaningful information from a period. In the Burglaries data, the Exponential forecast value for 2012 is 193.98. The upper and lower confidence bound is 212.64 and 175.33. The forecasted value for 2013 is 175.98, with lower and upper confidence bound are 156.74 and 195.22. To linear forecasting in 2012 shows that there is a difference in actual and predicted value from 2012 first quarter to 2012 third quarter. The exponential forecast value for gas and electricity sales are 143.44 with lower and upper interval 136.63 and 150.26. The linear predicted value for fuel is different from the actual value. In the first quarter, the actual value is 202.46, and the predicted value is 156.68. In the second quarter, the actual value is 116.96, and the predicted value is 132.24, so there is a difference between the actual and predicted value. The birth rate in 2012 is 167.225, and the upper and lower confidence bounds are 167.23, the predicted value for 2013 is 162.33, and the lower and upper confidence interval are 159.73 and 164.93. The rate of marriage forecasted value for 2013 is 68.47, and it gradually decreases compared to 2012. The death rate decreased in 2013 as compared to 2007. The chart shows that the UK's birth rate increases where the death rate also decreases and the marriage rate also slightly decreases. There is a difference in actual and predicted figure in Burglaries data. In Fuel data, there is a difference in actual and predicted data in the 2012 year. The Birth, Marriage and Death figure show the difference in actual value and the forecast value. The time series is the numerical data in successive order. The time series forecasting uses historical values. The forecast used to predict numerical values. It forecasts the future value using linear regression. It inputs the historical data and predicts the future trend.

Critical explanation of using clustering as part of time series analysis

The partition of the time series data into different groups based on distance and their similarity. So in the same cluster, time series are similar. Time-series clustering is the cluster of individual time series based on their similarity (Maharaj, Teles & Brito, 2019). The clustering is the conventional applying clustering in the discrete object, and the discrete objects are the time series. Clustering is the classifying the enormous data where there is no early knowledge about the classes. To do the time series analysis need the historical dataset. The next to measure the similarity of the data. The distance measures using the Euclidean distance, Pearson correlation distance and others. To measure the simplicity of Pearson correlation distance. After calculating the distance next step is to sort the data by distance from the lowest to highest and check the sample overlapping. The clustering in time series is the unsupervised classification. The set of time series that are not labelled combined into groups and clusters and all the same cluster sequences should be homogeneous and coherent.

The time series analysis's major issue is noise, temporal order, and high dimensionality in time series clustering. The clustering in the time series is the temporal proximity-based clustering If it works directly on raw data, either time domain or frequency. Two key aspects for efficiency and effectiveness. Time-series clustering divided into three major categories depending upon work directly on raw data and extracted features from raw data. The main components of time series forecasting are seasonality and trend. It is the process of clustering research on similarity searches among the time series. When the time series is the high dimension, there is become intractable in some clustering algorithms. By applying dimension reduction, the long length time series can cluster in very high efficiency when the clustering algorithm based on Euclidean distance on a distance metrics, time series with missing data cannot handle. The two categories in clustering time series are whole clustering and subsequence clustering. The clustering of individual time series into the group and similar groups into the cluster. Subsequence clustering is the single time series extraction to find dissimilarity and similarity among different time. Based on similarity distance, the time series data partition into two groups. So in the same cluster, the time series are similar. Between two-time series, dynamic time warping is the first optional alignment. The dynamic time warping is used as a distance metrics. Each time series are identical due to Euclidean distance. The time series is the temporal data's simplest form.

Conclusion

Time series is the forecasting of future events using existing data. It allows studying the indicators in time. It is the statistical indicator, and it is arranged in chronological order. Taking the model fit on historical data and uses that data to predict the future observation is called forecasting.

Reference

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