Statistics for Management Chapter 8 – Time Series and Forecasting Prepared and Delivered by, Sithari Herath Statistics for Management_Time Series and Forecasting 1
Scope • Variations in Time Series • Cyclical Variation • Forecasting Statistics for Management_Time Series and Forecasting 2
Variations in in Tim ime Series Term “Time Series” is used to refer any group of statistical information accumulated at regular intervals. Four kinds of change, variation involved in time series: • Secular trend – Value of the variable tend to increase or decrease • Cyclical fluctuation – Business cycle • Seasonal variation – Trend gets repeated from year to year • Irregular variation – Unpredictable variation Statistics for Management_Time Series and Forecasting 3
Cyclic lical l Varia iatio ion Cyclical variation is the component of a time series that tends to oscillate above and below the secular trend line for periods longer than 1 year. Example: Below table elaborates grain received by farmers, cooperative over 8 years. Year (x) Actual bushels Estimated bushels 9.2 (‘ 000) (y) (‘ 000) (y) 9 8.8 Cyclical fluctuations 2012 7.5 7.6 above the trend line 8.6 Graph of Bushels ('000 ) 2013 7.8 7.8 8.4 actual points 2014 8.2 8.0 Cyclical fluctuations 8.2 below the trend line 8 2015 8.2 8.2 7.8 Trend line graph (y) 2016 8.4 8.4 7.6 2017 8.5 8.6 7.4 2012 2013 2014 2015 2016 2017 2018 2019 2018 8.7 8.8 Year 2019 9.1 9.0 Actual bushels (‘0000) (y) Estimated bushels (‘0000) Statistics for Management_Time Series and Forecasting 4
Measures of f cycli lical variation 𝑧 −𝑧 𝑧 𝑧 ∗ 100 ∗ 100 Percent of trend = Relative cyclical residual= 𝑧 Example 1: (a) Graph percent of trend. (b) Interpret percent of trend and relative cyclical residual for year 2019. Example 2: A computer firm specializing in software engineering, has complied the following revenue records for the years 2013 to 2019. Year 2013 2014 2015 2016 2017 2018 2019 Revenue (lacks) 1.1 1.5 1.9 2.1 2.4 2.9 3.5 (a) Apply measures of cyclical variation for above data. (b) Plot the percent of trend line. (c) In which year does the largest fluctuation of trend occur, and is it the same for both methods? Statistics for Management_Time Series and Forecasting 5
Seasonal variation Besides secular trend and cyclical variation, a time series also includes seasonal variation. Seasonal variation is defined as repetitive and predictable movement around the trend line in one year or less. In order to detect seasonal variation time intervals must be measured in small units, such as days, weeks, months, or quarters. Why seasonal variation? • Establish the pattern of past changes. • Project past patterns into the future. • Eliminates seasonal patterns effects from the time series. Statistics for Management_Time Series and Forecasting 6
Sim imple moving average Example: ABC company has identified following sales values for past few months of the business. Month Sales revenue ($) January 209 February 240 March 220 April 201 May 210 June 211 July 215 August 220 Calculate forecasted sales revenue for September applying 3-months moving average. Statistics for Management_Time Series and Forecasting 7
Weighted moving average Month Sales revenue ($) January 209 February 240 March 220 April 201 May 210 June 211 July 215 August 220 Calculate forecasted sales revenue for September applying 3-months weighted moving average. (Use the weights 0.5, 0.3 and 0.2) Statistics for Management_Time Series and Forecasting 8
Exponential Smoothing Month Sales revenue ($) January 209 February 240 March 220 April 201 May 210 June 211 July 215 August 220 Calculate forecasted sales revenue for September applying 3-months weighted moving average. (Use alpha 0.3) Statistics for Management_Time Series and Forecasting 9
Example Following data represents number of repeated customers that were visiting a particular shop for 8 quarters. a) Forecast the number of repetitive customers Year Quarter Number of repetitive for 2020 first quarter applying simple 2 quarter customers moving average. 2018 Q1 35 b) Forecast the number of repetitive customers Q2 32 for 2020 first quarter applying weighted 2 quarter moving average. (Use 0.6 to the latest Q3 27 quarter) Q4 30 c) Forecast the number of repetitive customers 2019 Q1 24 for 2020 first quarter applying exponential smoothing. (alpha =0.2) Q2 28 d) If the actual number of repetitive customers Q3 29 was 34 for first quarter in 2020, conclude the Q4 33 most accurate method for above mentioned forecasting. Statistics for Management Time Series and Forecasting 10
ThankYou! Statistics for Management_Time Series and Forecasting 11
Questions create Knowledge Statistics for Management_Time Series and Forecasting 12
Recommend
More recommend
