Time Series Analysis Chapter 7 PDF

# Chapter 7-Time Series Analysis ## University of Technology and Applied Sciences - Course: Managerial Statistics - Course Code: BSMS2209 - Specialization: COLLEGE REQUIREMENT - College: College of Economics and Business Administration ## Course Objective This course emphasizes the development o...

# Chapter 7-Time Series Analysis ## University of Technology and Applied Sciences - Course: Managerial Statistics - Course Code: BSMS2209 - Specialization: COLLEGE REQUIREMENT - College: College of Economics and Business Administration ## Course Objective This course emphasizes the development of practical computing skills and problem-solving skills in the field of business, using appropriate statistical tools and graphs, as well as the use of spreadsheets for data management and analysis. ## Learning Outcomes - **Learning Outcome 7:** Demonstrate the knowledge of time series concepts by applying them to real-world data and interpreting the results of the analysis. - **Learning Outcome 8:** Practice the fundamentals of descriptive and inferential data analysis using an Excel spreadsheet and SPSS. ## Chapter Outline - Time Series - Introduction - Importance of Time Series Analysis in Business - Components of Time Series - Measurement of Trend - Time Series Analysis Using - Excel Spread Sheet - Time Series Analysis Using - SPSS ## Introduction - A time series is a collection of values of a variable taken at different time periods. - The values of the concerned variable is not expected to be the same for every time period. - For example, if we consider the price of 1 kg tea of a particular brand, for over twenty years, we will note that the price is not the same for every year. - What has caused the price to vary? ## Time Series Data Time series data is a sequence of observations collected from a process with equally spaced periods of time. ## Definition of Time Series According to Merriam Webster Dictionary, time series is a set of data collected sequentially and usually at fixed intervals of time. ## Examples of Time Series - The number of packets of milk sold in a small shop. - Oil production in Oman in barrels/day. - Population in Oman in millions. ## Importance of Time Series Analysis in Business - Profit Planning - Sales Forecasting - Stock Market Analysis - Process and Quality Control - Economic Forecasting - Risk Analysis & Evaluation of changes ## Components of Time Series Any time series can contain some or all of the following components: - Secular trend or Long-term Variation - Seasonal variation - Cyclical variation - Irregular variation ## Secular Trend - The increase or decrease in the movements of a time series is called Secular trend. - Secular trend is a long term movement in a time series. - A time series data may show upward trend or downward trend for a period of years and this may be due to factors like - Increase in population - Change in technological progress - Large scale shift in consumers' demands ## Seasonal Variation - Seasonal variation are short-term fluctuation in a time series which occur periodically in a year. - In a time series, seasonal variations occur quite regularly. - The major factors that are weather conditions and customs of people. ### Examples of Seasonal Variation: - More woolen clothes are sold in winter than the season of summer. - Each year more ice creams are sold in summer and very little in winter season. - The sales in the departmental stores are more during festive seasons than in the normal days. - Even Banks have not escaped from seasonal variations. Banks observe heavy withdrawals in the first week of every month. ## Cyclical Variation - Cyclical variations are recurrent upward or downward movements in a time series but the period of cycle is greater than a year. - Cyclical variations are seldom periodic and they may or may not follow same pattern after equal interval of time. - Also, these variations are not regular as Seasonal variation. - In business and economic time series, business cycles are example of cyclical variations. ### Phases of a Business Cycle - Depression - Boom - Recovery - Decline ## Irregular Variation - Irregular variation are fluctuations in time series that are short in duration, erratic in nature and follow no regularity in the occurrence pattern. - Irregular fluctuations results due to the occurrence of unforeseen factors. - This component is unpredictable. ### Examples of Irregular Variations - Floods - Earthquakes - Wars - Famines ## Measurement of Trend - Free hand Graphic method - Semi average method - Moving average method - Least Square method ## Free Hand Graphic Method - In this method the data is denoted on graph paper. - Show "Time" on "X" axis and "Data" on the "Y" axis. - On graph there will be a point for every point of time. - Draw a smooth hand curve with the help of this plotted points. ## Semi Average Method - In this method the given data are divided into two parts, preferably with the equal number of years. - If the number of items is odd, then we make two equal parts by leaving the middle most value. - An average is obtained for each part. - Each such average is shown against the mid-point of the half period. - Obtain two points on a graph paper based on the averages of each part. - By joining these points, a straight line trend is obtained. ## Moving Average Method - This method is based on a series of arithmetic means as shown in the below example. ## Least Square Method (Linear Trend) - This is a mathematical method. - By using this method, we can find linear trend as well as non-linear trend of the corresponding data. - The equation of the required trend line can be expressed as: $Y = a + bX$ ...(1) - Where Y is the actual value, X is time, a, b are constants - The constants 'a' and 'b' are estimated by solving the following two normal equations $ΣΥ = n a + b ΣΧ$ ...(2) $ΣΧΥ = a ∑X + b ΣΧ2$ ...(3) - Where 'n' = number of years given in the data. - By taking the mid-point of the time as the origin, we get ∑X = 0 - When EX = 0, the two normal equations reduces to: $ΣΥ = n a + b (0) ; a=\frac { ΣY }{ n }$ =Y $ΣXY = a(0) + b 2X2 ; b=\frac { ΣXY }{ ΣΧ² } = \frac { ΣXY }{ ΣΧ² }$ - The constant 'a' gives the mean of Yand 'b' gives the rate of change (slope). - By substituting the values of 'a' and 'b' in the trend equation (1), we get the Line of Best Fit. ## References - Divyansh Choudhary. (2021). Business Statistics: Vol. First edition. Laxmi Publications Pvt Ltd. PP. 82-101. Retrieved from: https://search-ebscohost-com.masader.idm.oclc.org/login.aspx?direct=true&db=nlebk&AN=3103348&site=ehost-live. ## Contact Information - Dr. S. Porkodi - Office: BS032, Business Department - Email: [email protected] ## Version History | Version No | Date Approved | Changes incorporated | |---|---|---| | New Outcome Version: 01 | Sem. (1) 2022/2023 | |