Time series: Syed S. Hossain Lesson 21 Time series Analysis 21.1 Introduction Forecasting or predicting is an essential tool in any decision making process. Its uses vary from determining inventory requirements for a local shoe store to estimating the annual sales of high-tech computers. The quality of the forecasts management can make is strongly related to the information that can be extracted and used from past data. Time series analysisis one quantitative method we can use to determine patterns in data collected over time. Table 21.1 presents an example of time series data. Time series data:A time is a set of observation taken at specific times, usually at equal intervals. Mathematically, a time series is defined by the values ,...,21YYof a variable Yat times ,...,21tt. Example 21.1Consider the data in Table 21.1 where the quarterly S&P 500 indices from 1900 to 1995 are presented in order of time. This is a proper example of a time series data. The change and variation pattern of the data over the period and making future forecast from the observed pattern are of simultaneous interest and studying these characteristics of the data is termed as time series
Time series: Syed S. Hossain analysis. The example considers a data for a substantially long period and this is often a requirement for valid future prediction. For simplicity of the analysis, the quarter January 1900 can be coded as quarter 1 (or 1t) and the corresponding index value is read as 1Y, the quarter April 1900 can be coded as quarter 2 (or 2t) and the corresponding index value is read as 2Y, … and so on up to the index 380Ycorresponding to the quarter October 1995. The data is given in Table A21.1. A line diagram of the data in Table 21.1 is presented in Figure 21.1, where the fluctuation of the S&P 500 index over the study period 1900-1995 is pronounced. Figure 21.1:The line diagram of quarterly S&P 500 index from 1900-1995 21.1.1 The uses and utilities of Time series analysisThe analysis of time series can be helpful in economist, business people, the scientist, social researchers and many other groups of people. The following utilities are rendered very important: It helps understand the past behaviour of any physical phenomenon . It helps in planning the future and policy making It helps evaluating current achievement or accomplishment It helps researchers to compare change behaviour in different data. 21.2 Variations in time series
Time series: Syed S. Hossain We use the term time series to refer to any group of statistical information accumulated at regular intervals. There are four kinds of change or variation involved in time series analysis, or in other words we can say there are four components of time series data: Secular trend: The smooth gradual direction of increase or decrease behavior over long time.