Datta Meghe Institute of Management Studies Quantitative Techniques Unit No.:04 Unit Name: Time Series Analysis and Forecasting 1

Datta Meghe Institute of Management Studies 2 Time Series Analysis and Forecasting - Components of Time Series, Trend - Moving averages, semi-averages and least-squares, seasonal variation, cyclic variation and irregular variation, Index numbers, calculation of seasonal indices, Additive and multiplicative models, Forecasting, Non linear trend – second degree parabolic trends SYLLABUS

Datta Meghe Institute of Management Studies Learning Objectives Describe what forecasting is Explain time series & its components Smooth a data series Moving average Exponential smoothing Forecast using trend models Measuring forecast error The multiplicative time series model Naïve extrapolation The mean forecast model Weighted moving average models Describe what forecasting is Explain time series & its components Smooth a data series Moving average Exponential smoothing Forecast using trend models Measuring forecast error The multiplicative time series model Naïve extrapolation The mean forecast model Weighted moving average models

What Is Forecasting? Process of predicting a future event Underlying basis of all business decisions – Production – Inventory – Personnel – Facilities Process of predicting a future event Underlying basis of all business decisions – Production – Inventory – Personnel – Facilities

Used when situation is vague & little data exist – New products – New technology Involve intuition, experience e.g., forecasting sales on Internet Used when situation is vague & little data exist – New products – New technology Involve intuition, experience e.g., forecasting sales on Internet Qualitative Methods Forecasting Approaches Quantitative Methods

Used when situation is ‘stable’ & historical data exist – Existing products – Current technology Involve mathematical techniques e.g., forecasting sales of color televisions Used when situation is ‘stable’ & historical data exist – Existing products – Current technology Involve mathematical techniques e.g., forecasting sales of color televisions Forecasting Approaches Used when situation is vague & little data exist –New products –New technology Involve intuition, experience e.g., forecasting sales on Internet Qualitative Methods Quantitative Methods

Datta Meghe Institute of Management Studies Quantitative Forecasting Quantitative Forecasting Select several forecasting methods ‘Forecast’ the past Evaluate forecasts Select best method Forecast the future Monitor continuously forecast accuracy Select several forecasting methods ‘Forecast’ the past Evaluate forecasts Select best method Forecast the future Monitor continuously forecast accuracy

Datta Meghe Institute of Management Studies Quantitative Forecasting Methods

Datta Meghe Institute of Management Studies Quantitative Forecasting Methods Quantitative Forecasting

Datta Meghe Institute of Management Studies Quantitative Forecasting Methods Quantitative Forecasting Time Series Models

Datta Meghe Institute of Management Studies Causal Models Quantitative Forecasting Methods Quantitative Forecasting Time Series Models

Datta Meghe Institute of Management Studies Causal Models Quantitative Forecasting Methods Quantitative Forecasting Time Series Models Exponential Smoothing Trend Models Moving Average

Datta Meghe Institute of Management Studies Causal Models Quantitative Forecasting Methods Quantitative Forecasting Time Series Models Regression Exponential Smoothing Trend Models Moving Average

Datta Meghe Institute of Management Studies Causal Models Quantitative Forecasting Methods Quantitative Forecasting Time Series Models Regression Exponential Smoothing Trend Models Moving Average Casual Models

Datta Meghe Institute of Management Studies What is a Time Series? Set of evenly spaced numerical data – Obtained by observing response variable at regular time periods Forecast based only on past values – Assumes that factors influencing past, present, & future will continue Example – Year: – Sales: Set of evenly spaced numerical data – Obtained by observing response variable at regular time periods Forecast based only on past values – Assumes that factors influencing past, present, & future will continue Example – Year: – Sales:

Datta Meghe Institute of Management Studies Time Series vs. Cross Sectional Data Time series data is a sequence of observations –collected from a process –with equally spaced periods of time. Time series data is a sequence of observations –collected from a process –with equally spaced periods of time.

Datta Meghe Institute of Management Studies Time Series vs. Cross Sectional Data Contrary to restrictions placed on cross-sectional data, the major purpose of forecasting with time series is to extrapolate beyond the range of the explanatory variables.

Time Series vs. Cross Sectional Data Time series is dynamic, it does change over time.

Datta Meghe Institute of Management Studies Time Series vs. Cross Sectional Data When working with time series data, it is paramount that the data is plotted so the researcher can view the data.

Datta Meghe Institute of Management Studies Time Series Components

Datta Meghe Institute of Management Studies Time Series Components Trend

Datta Meghe Institute of Management Studies Time Series Components TrendCyclical

Datta Meghe Institute of Management Studies Time Series Components Trend Seasonal Cyclical

Datta Meghe Institute of Management Studies Time Series Components Trend Seasonal Cyclical Irregular

Datta Meghe Institute of Management Studies Trend Component Persistent, overall upward or downward pattern Due to population, technology etc. Several years duration Persistent, overall upward or downward pattern Due to population, technology etc. Several years duration Mo., Qtr., Yr. Response © T/Maker Co.

Datta Meghe Institute of Management Studies Trend Component Overall Upward or Downward Movement Data Taken Over a Period of Years Overall Upward or Downward Movement Data Taken Over a Period of Years Sales Time Upward trend

Datta Meghe Institute of Management Studies Cyclical Component Repeating up & down movements Due to interactions of factors influencing economy Usually 2-10 years duration Repeating up & down movements Due to interactions of factors influencing economy Usually 2-10 years duration Mo., Qtr., Yr. Response Cycle

Datta Meghe Institute of Management Studies Cyclical Component Upward or Downward Swings May Vary in Length Usually Lasts Years Upward or Downward Swings May Vary in Length Usually Lasts Years Sales Time Cycle

Datta Meghe Institute of Management Studies Regular pattern of up & down fluctuations Due to weather, customs etc. Occurs within one year Regular pattern of up & down fluctuations Due to weather, customs etc. Occurs within one year Seasonal Component Mo., Qtr. Response Summer © T/Maker Co.

Datta Meghe Institute of Management Studies Upward or Downward Swings Regular Patterns Observed Within One Year Upward or Downward Swings Regular Patterns Observed Within One Year Seasonal Component Sales Time (Monthly or Quarterly) Winter

Datta Meghe Institute of Management Studies Irregular Component Erratic, unsystematic, ‘residual’ fluctuations Due to random variation or unforeseen events – Union strike – War Short duration & nonrepeating Erratic, unsystematic, ‘residual’ fluctuations Due to random variation or unforeseen events – Union strike – War Short duration & nonrepeating © T/Maker Co.

Datta Meghe Institute of Management Studies Random or Irregular Component Erratic, Nonsystematic, Random, ‘Residual’ Fluctuations Due to Random Variations of – Nature – Accidents Short Duration and Non-repeating Erratic, Nonsystematic, Random, ‘Residual’ Fluctuations Due to Random Variations of – Nature – Accidents Short Duration and Non-repeating

Datta Meghe Institute of Management Studies Time Series Forecasting

Datta Meghe Institute of Management Studies Time Series Forecasting Time Series

Datta Meghe Institute of Management Studies Time Series Forecasting Time Series Trend?

Datta Meghe Institute of Management Studies Time Series Forecasting Time Series Trend? Smoothing Methods No

Datta Meghe Institute of Management Studies Time Series Forecasting Time Series Trend? Smoothing Methods Trend Models Yes No

Datta Meghe Institute of Management Studies Time Series Forecasting Time Series Trend? Smoothing Methods Trend Models Yes No Exponential Smoothing Moving Average

Datta Meghe Institute of Management Studies Time Series Forecasting

Datta Meghe Institute of Management Studies Time Series Analysis

Datta Meghe Institute of Management Studies Plotting Time Series Data

Datta Meghe Institute of Management Studies Moving Average Method

Datta Meghe Institute of Management Studies Time Series Forecasting

Datta Meghe Institute of Management Studies Moving Average Method Series of arithmetic means Used only for smoothing – Provides overall impression of data over time Series of arithmetic means Used only for smoothing – Provides overall impression of data over time

Datta Meghe Institute of Management Studies Moving Average Method Series of arithmetic means Used only for smoothing – Provides overall impression of data over time Used for elementary forecasting Series of arithmetic means Used only for smoothing – Provides overall impression of data over time Used for elementary forecasting

Datta Meghe Institute of Management Studies Moving Average Graph Year Sales Actual

Datta Meghe Institute of Management Studies Moving Average Moving Average [An Example] You work for Firestone Tire. You want to smooth random fluctuations using a 3-period moving average , , , , ,000

Datta Meghe Institute of Management Studies Moving Average [Solution] YearSalesMA(3) in 1, ,000NA ,000( )/3 = ,000( )/3 = ,000( )/3 = ,000NA YearSalesMA(3) in 1, ,000NA ,000( )/3 = ,000( )/3 = ,000( )/3 = ,000NA

Datta Meghe Institute of Management Studies Moving Average Year Response Moving Ave NA NA Sales

Datta Meghe Institute of Management Studies Exponential Smoothing Method

Datta Meghe Institute of Management Studies Time Series Forecasting

Datta Meghe Institute of Management Studies Exponential Smoothing Method Form of weighted moving average – Weights decline exponentially – Most recent data weighted most Requires smoothing constant (W) – Ranges from 0 to 1 – Subjectively chosen Involves little record keeping of past data Form of weighted moving average – Weights decline exponentially – Most recent data weighted most Requires smoothing constant (W) – Ranges from 0 to 1 – Subjectively chosen Involves little record keeping of past data

Datta Meghe Institute of Management Studies Exponential Smoothing Exponential Smoothing [An Example] You’re organizing a Kwanza meeting. You want to forecast attendance for 1998 using exponential smoothing (  =.20). Past attendance (00) is: © 1995 Corel Corp.

Datta Meghe Institute of Management Studies Exponential Smoothing E i = W·Y i + (1 - W)·E i-1 ^

Datta Meghe Institute of Management Studies Exponential Smoothing [Graph] Year Attendance Actual

Datta Meghe Institute of Management Studies Forecast Effect of Smoothing Coefficient (W) Y i+1 = W·Y i + W·(1-W)·Y i-1 + W·(1-W) 2 ·Y i ^

Datta Meghe Institute of Management Studies Linear Time-Series Forecasting Model

Datta Meghe Institute of Management Studies Time Series Forecasting

Datta Meghe Institute of Management Studies Linear Time-Series Forecasting Model Used for forecasting trend Relationship between response variable Y & time X is a linear function Coded X values used often – Year X: – Coded year:01234 – Sales Y: Used for forecasting trend Relationship between response variable Y & time X is a linear function Coded X values used often – Year X: – Coded year:01234 – Sales Y:

Datta Meghe Institute of Management Studies Linear Time-Series Model b 1 > 0 b 1 < 0

Datta Meghe Institute of Management Studies Linear Time-Series Model [An Example] You’re a marketing analyst for Hasbro Toys. Using coded years, you find Y i =.6 +.7X i Forecast 2000 sales. You’re a marketing analyst for Hasbro Toys. Using coded years, you find Y i =.6 +.7X i Forecast 2000 sales. ^

Datta Meghe Institute of Management Studies Linear Time-Series [Example] YearCoded YearSales (Units) ? 2000 forecast sales: Y i =.6 +.7·(5) = 4.1 The equation would be different if ‘Year’ used. YearCoded YearSales (Units) ? 2000 forecast sales: Y i =.6 +.7·(5) = 4.1 The equation would be different if ‘Year’ used. ^

Datta Meghe Institute of Management Studies The Linear Trend Model Year Coded Sales Projected to year 2000 Excel Output

Datta Meghe Institute of Management Studies Time Series Plot

Datta Meghe Institute of Management Studies Time Series Plot [Revised]

Datta Meghe Institute of Management Studies Seasonality Plot

Datta Meghe Institute of Management Studies Trend Analysis

Datta Meghe Institute of Management Studies Quadratic Time-Series Forecasting Model

Datta Meghe Institute of Management Studies Time Series Forecasting

Datta Meghe Institute of Management Studies Quadratic Time-Series Forecasting Model Used for forecasting trend Relationship between response variable Y & time X is a quadratic function Coded years used Used for forecasting trend Relationship between response variable Y & time X is a quadratic function Coded years used

Datta Meghe Institute of Management Studies Quadratic Time-Series Forecasting Model Used for forecasting trend Relationship between response variable Y & time X is a quadratic function Coded years used Quadratic model Used for forecasting trend Relationship between response variable Y & time X is a quadratic function Coded years used Quadratic model

Datta Meghe Institute of Management Studies Quadratic Time-Series Model Relationships b 11 > 0 b 11 < 0

Datta Meghe Institute of Management Studies Quadratic Trend Model Excel Output Year Coded Sales

Datta Meghe Institute of Management Studies Exponential Time-Series Model

Datta Meghe Institute of Management Studies Time Series Forecasting

Datta Meghe Institute of Management Studies Exponential Time-Series Forecasting Model Used for forecasting trend Relationship is an exponential function Series increases (decreases) at increasing (decreasing) rate Used for forecasting trend Relationship is an exponential function Series increases (decreases) at increasing (decreasing) rate

Datta Meghe Institute of Management Studies Exponential Time-Series Forecasting Model Used for forecasting trend Relationship is an exponential function Series increases (decreases) at increasing (decreasing) rate Used for forecasting trend Relationship is an exponential function Series increases (decreases) at increasing (decreasing) rate

Datta Meghe Institute of Management Studies Exponential Time-Series Model Relationships b 1 > 1 0 < b 1 < 1

Datta Meghe Institute of Management Studies Exponential Weight [Example Graph] Sales Year Data Smoothed

Datta Meghe Institute of Management Studies Exponential Trend Model or Excel Output of Values in logs Year Coded Sales

Datta Meghe Institute of Management Studies Described what forecasting is Explained time series & its components Smoothed a data series –Moving average –Exponential smoothing Forecasted using trend models Described what forecasting is Explained time series & its components Smoothed a data series –Moving average –Exponential smoothing Forecasted using trend models 81 SUMMARY

Datta Meghe Institute of Management Studies 82 LONG & SHORT QUESTION

Datta Meghe Institute of Management Studies Statistics : Theory and Practice - R.S.N. Pillai & Bhagwati Fundamentals of Statistics - S.C. Gupta Statistics : Theory and Practice - R.S.N. Pillai & Bhagwati Fundamentals of Statistics - S.C. Gupta 83 BOOKS REFERRED