Presentation is loading. Please wait.

Presentation is loading. Please wait.

Copyright 2011 John Wiley & Sons, Inc. 1 Chapter 11 Time Series and Business Forecasting 11.1 Time Series Data 11.2 Simple Moving Average Model 11.3 Weighted.

Published byAnna Fitzgerald Modified over 7 years ago

Similar presentations

Presentation on theme: "Copyright 2011 John Wiley & Sons, Inc. 1 Chapter 11 Time Series and Business Forecasting 11.1 Time Series Data 11.2 Simple Moving Average Model 11.3 Weighted."— Presentation transcript:

1 Copyright 2011 John Wiley & Sons, Inc. 1 Chapter 11 Time Series and Business Forecasting 11.1 Time Series Data 11.2 Simple Moving Average Model 11.3 Weighted Moving Average 11.4 Exponential Smoothing

2 Copyright 2011 John Wiley & Sons, Inc. 2 Time-series data Data gathered on a given characteristic over a period of time at regular intervals Forecasting. To analyze time series in order to detect patterns that will enable us to forecast future values of the time series Time-series forecasting techniques Attempt to account for changes over time by examining patterns, cycles, trends, or using information about previous time periods Method in time series forecasting Averaging Smoothing 11.1 Time-Series Data

3 Copyright 2011 John Wiley & Sons, Inc. 3 Time Series Components Trend – long term general direction. Cycles (Cyclical effects) – patterns of highs and lows through which data move over time periods usually of more than a year. Seasonal effects – shorter cycles, which usually occur in time periods of less than one year. Irregular fluctuations – rapid changes or “bleeps” in the data, which occur in even shorter time frames than seasonal effects. Stationary time-series - data that contain no trend, cyclical, or seasonal effects.

4 Copyright 2011 John Wiley & Sons, Inc. 4 Time-Series Effects

5 Copyright 2011 John Wiley & Sons, Inc. 5 11.1 Time Series Data Trend A.k.a secular trend. Long term smooth pattern/direction exhibited by a series. Have a duration of more than one year. Not always linear

6 Copyright 2011 John Wiley & Sons, Inc. 6 11.1 Time Series Data Cyclical Wavelike pattern describing long term-trend. Have a duration over a number of years. Resulting in a cyclical effect. Hard to make prediction.

7 Copyright 2011 John Wiley & Sons, Inc. 7 11.1 Time Series Data Seasonal. Cycles that occur over short repetitive periods, which is less than one year. E.g: Systematic pattern that occur during a month.

8 Copyright 2011 John Wiley & Sons, Inc. 8 11.1 Time Series Data Irregular. Causes by unpredictable changes in a time series that are not cause by any other components. Exist in almost all time series. This component need to be reduce in order to describe and measure other components – to make accurate predictions.

9 Copyright 2011 John Wiley & Sons, Inc. 9 Error of individual forecast e t – the difference between the actual value x t and the forecast of that value F t. Measurement of Forecasting Error

10 Copyright 2011 John Wiley & Sons, Inc. 10 Mean Absolute Deviation (MAD) - is the mean, or average, of the absolute values of the errors. Mean Square Error (MSE) - circumvents the problem of the canceling effects of positive and negative forecast errors. Computed by squaring each error and averaging the squared errors.

11 Copyright 2011 John Wiley & Sons, Inc. 11 YearActualForecastError 11402 214581402.056.0 315531441.2111.8 416131519.593.5 516761584.991.1 617551648.7106.3 718071723.183.9 818241781.842.2 918261811.314.7 1017801821.6-41.6 1117591792.5-33.5 Nonfarm Partnership Tax Returns: Actual and Forecast

12 Copyright 2011 John Wiley & Sons, Inc. 12 YearActualForecastError|Error| 11402.0 21458.01402.056.0 31553.01441.2111.8 41613.01519.593.5 51676.01584.991.1 61755.01648.7106.3 71807.01723.183.9 81824.01781.842.2 91826.01811.314.7 101780.01821.6-41.641.6 111759.01792.5-33.533.5 674.5 Mean Absolute Deviation: Nonfarm Partnership Forecasted Data

13 Copyright 2011 John Wiley & Sons, Inc. 13 Mean Square Error: Nonfarm Partnership Forecasted Data YearActualForecastErrorError 2 11402 214581402.056.0 315531441.2111.8 416131519.593.5 516761584.991.1 617551648.7106.3 718071723.183.9 818241781.842.2 918261811.314.7 1017801821.6-41.6 1117591792.5-33.5 55864.2 3136.0 12499.2 8749.7 8292.3 11303.6 7038.5 1778.2 214.6 1731.0 1121.0

14 Copyright 2011 John Wiley & Sons, Inc. 14 Smoothing Techniques Several techniques are available to forecast time- series data that are stationary or that include no significant trend, cyclical, or seasonal effects. This technique called smoothing technique. Smoothing techniques produce forecasts based on “smoothing out” the irregular fluctuation effects in the time-series data. Three general categories of smoothing technique 1.Naïve forecasting models 2.Averaging models 3.Exponential smoothing

15 Copyright 2011 John Wiley & Sons, Inc. 15 Naive Forecasting Models Simple models in which it is assumed that the more recent time periods of data represent the best predictions or forecasts for future outcomes. The assumption of this method is what happen yesterday will also happen today. where

16 Copyright 2011 John Wiley & Sons, Inc. 16 11.1 Time Series Data Example: An operator of five independent gas stations recorded the quarterly fuel sale (in thousand litre) for the past 4 years. Forecast the fuel sale for period 2 through period 16 using naïve method. Time period YearQuarterFuel sale (in thousand litre) 11139 2237 3361 4458 52118 6256 7382 8427 93141 10269 11349 12466 134154 14242 15390 16466

17 Copyright 2011 John Wiley & Sons, Inc. 17 11.1 Time Series Data Solution Time periodFuel sale (X)Naïve method (F) 139 - 23739 36137 45861 51858 65618 78256 82782 94127 106941 114969 126649 135466 144254 159042 166690

18 Copyright 2011 John Wiley & Sons, Inc. 18 MonthYear Cents per GallonMonthYear Cents per Gallon January261.3January358.2 February63.3February58.3 March62.1March57.7 April59.8April56.7 May58.4May56.8 June57.6June55.5 July55.7July53.8 August55.1August52.8 September55.7September October56.7October November57.2November December58.0December Simple Average Model The monthly average last 12 months was 56.45, so I predict 56.45 for September. The monthly average last 12 months was 56.45, so I predict 56.45 for September. The forecast for time period t is the average of the values for a given number of previous time periods. Cost of Residential Heating Oil

19 Copyright 2011 John Wiley & Sons, Inc. 19 11.2 Moving Average A moving average is an average that is updated or recomputed for every new time period being considered. The most recent information is utilized in each new moving average. Disadvantage: 1.It is difficult to choose optimal length of time for which to compute moving average 2.Moving average do not usually adjust for time series effects as trend, cycles or seasonality To determine the more optimal length, we need to forecast with several average length and compare error produce by them

20 Copyright 2011 John Wiley & Sons, Inc. 20 Shown in the following table here are shipments (in millions of dollars) for electric lighting and wiring equipment over a 12-month period. Use these data to compute a 4-month moving average for all available months. Demonstration Problem 15.1: Four-Month Simple Moving Average

21 Copyright 2011 John Wiley & Sons, Inc. 21 MonthsShipments 4-Mo Moving Average Forecast Error January1056 February1345 March1381 April1191 May12591243.2515.75 June13611294.0067.00 July11101298.00-188.00 August13341230.25103.75 September14161266.00150.00 October12821305.25-23.25 November13411285.5055.50 December13821343.2538.75 Demonstration Problem 15.1: Four-Month Simple Moving Average

22 Copyright 2011 John Wiley & Sons, Inc. 22 Demonstration Problem 15.1: Four-Month Moving Average

23 Copyright 2011 John Wiley & Sons, Inc. 23 11.2 Simple moving Average Example An operator of five independent gas stations recorded the quarterly fuel sale (in thousand litre) for the past 4 years. Calculate the three-moving averages and five-moving averages. Time period YearQuarterFuel sale (in thousand litre) 11139 2237 3361 4458 52118 6256 7382 8427 93141 10269 11349 12466 134154 14242 15390 16466

24 Copyright 2011 John Wiley & Sons, Inc. 24 11.2 Simple moving Average Solution Time periodFuel sale (D) Three-Moving averages (F) Five-Moving averages (F) 139 -- 237 - - 361 - - 458 45.7 - 518 52.0 - 656 45.7 42.6 782 44.0 46 827 52.0 55 941 55.0 48.2 1069 50.0 44.8 1149 45.7 55 1266 53.0 53.6 1354 61.3 50.4 1442 56.3 55.8 1590 54.0 56 1666 62.0 60.2 3-Moving Average 5-Moving Average

25 Copyright 2011 John Wiley & Sons, Inc. 25 A moving average in which some time periods are weighted differently than others. 11.3 Weighted Moving Average Forecasting Model Where last month’s value value for the previous month value for the month before the previous month The denominator = the total number of weights Example 3 month Weighted average

26 Copyright 2011 John Wiley & Sons, Inc. 26 Demonstration Problem 15.2: Compute a 4-month weighted moving average for the electric lighting and wiring data from Demonstration Problem 15.1, using weights of 4 for last month's value, 2 for the previous month's value, and 1 for each of the values from the 2 months prior to that

27 Copyright 2011 John Wiley & Sons, Inc. 27 MonthsShipments 4-Month Weighted Moving Average Forecast Error January1056 February1345 March1381 April1191 May12591240.8818.13 June13611268.0093.00 July11101316.75-206.75 August13341201.50132.50 September14161272.00144.00 October12821350.38-68.38 November13411300.5040.50 December13821334.7547.25 Demonstration Problem 15.2: Four-Month Weighted Moving Average

28 Copyright 2011 John Wiley & Sons, Inc. 28  is the exponential smoothing constant Used to weight data from previous time periods with exponentially decreasing importance in the forecast 11.4 Exponential Smoothing

29 Copyright 2011 John Wiley & Sons, Inc. 29 The U.S. Census Bureau reports the total units of new privately owned housing started over a 16-year recent period in the United States are given here. Use exponential smoothing to forecast the values for each ensuing time period. Work the problem using  =.2,.5, and.8. Demonstration Problem 15.3:  = 0.2

30 Copyright 2011 John Wiley & Sons, Inc. 30  = 0.2 Year Housing Units (1,000)Fe|e|e2e2 19901193-- 199110141193.0-179179 32041 199212001157.242.8 1832 199312881165.8122.2 14933 199414571190.2266.8 71182 199513541243.6110.4 12188 199614771265.7211.3 44648 199714741307.9166.1 27589 199816171341.1275.9 76121 199916411396.3244.7 59878 200015691445.2123.8 15326 200116031470.0133.0 17689 200217051496.6208.4 43431 200318481538.3309.7 95914 200419561600.2355.8 126594 200520681671.4396.6 157292 3146.5796657 MAD209.8 MSE53110 Demonstration Problem 15.3:  = 0.2

31 Copyright 2011 John Wiley & Sons, Inc. 31  = 0.8 Year Housing Units (1,000)Fe|e|e2e2 19901193-- 199110141193.0-17917964.0 199212001049.8150.2 3770.0 199312881170.0118.0 29832.2 199414571264.4192.6 27736.9 199513541418.5-64.564.521114.6 199614771366.9110.1 44970.2 199714741455.019.0 49023.4 199816171470.2146.8 20083.9 199916411587.653.4 13535.8 200015691630.3-61.361.336967.3 200116031581.321.7 4166.2 200217051598.7106.3 12120.0 200318481683.7164.3 361.7 200419561815.1140.9 21551.3 200520681927.8140.2 6140.4 1668.3228896 MAD111.2 MSE15245.9 Demonstration Problem 15.3:  = 0.8

32 Copyright 2011 John Wiley & Sons, Inc. 32 Exercise Use the following time-series data to answer the given questions A.Develop forecasts for periods 5 through 10 using 4-month moving averages. B.Develop forecasts for periods 5 through 10 using 4-month weighted moving averages. Weight the most recent month by a factor of 4, the previous month by 2, and the other months by 1. C.Compute the errors of the forecasts in parts (a) and (b) and observe the differences in the errors forecast by the two different techniques.

33 Copyright 2011 John Wiley & Sons, Inc. 33 Solution a.) 4-mo. mov. avg. error 44.75 14.25 52.75 13.25 61.50 9.50 64.75 21.25 70.50 30.50 81.00 16.00 b.) 4-mo. wt. mov. avg. error 53.25 5.75 56.375 9.625 62.875 8.125 67.25 18.75 76.375 24.625 89.125 7.875 c.) difference in errors 14.25 - 5.75 = 8.5 3.626 1.375 2.5 5.875 8.125 In each time period, the four-month moving average produces greater errors of forecast than the four- month weighted moving average.

Download ppt "Copyright 2011 John Wiley & Sons, Inc. 1 Chapter 11 Time Series and Business Forecasting 11.1 Time Series Data 11.2 Simple Moving Average Model 11.3 Weighted."

Similar presentations

Forecasting OPS 370.

Forecasting OPS 370.
Operations Management Forecasting Chapter 4

Operations Management Forecasting Chapter 4
Exponential Smoothing Methods

Exponential Smoothing Methods
T18-03 - 1 T18-03 Exponential Smoothing Forecast Purpose Allows the analyst to create and analyze the Exponential Smoothing Average forecast. The MAD.

T T18-03 Exponential Smoothing Forecast Purpose Allows the analyst to create and analyze the "Exponential Smoothing Average" forecast. The MAD.
Analyzing and Forecasting Time Series Data

Analyzing and Forecasting Time Series Data
Chapter 12 - Forecasting Forecasting is important in the business decision-making process in which a current choice or decision has future implications:

Chapter 12 - Forecasting Forecasting is important in the business decision-making process in which a current choice or decision has future implications:
Copyright 2006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Forecasting Operations Management - 5 th Edition Chapter 11.

Copyright 2006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Forecasting Operations Management - 5 th Edition Chapter 11.
Lecture 3 Forecasting CT – Chapter 3.

Lecture 3 Forecasting CT – Chapter 3.
Chapter 3 Forecasting McGraw-Hill/Irwin

Chapter 3 Forecasting McGraw-Hill/Irwin
To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 5-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 PERTEMUAN 14.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 5-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ PERTEMUAN 14.
Chapter 13 Forecasting.

Chapter 13 Forecasting.
Forecasting & Time Series Minggu 6. Learning Objectives Understand the three categories of forecasting techniques available. Become aware of the four.

Forecasting & Time Series Minggu 6. Learning Objectives Understand the three categories of forecasting techniques available. Become aware of the four.
Operations Management R. Dan Reid & Nada R. Sanders

Operations Management R. Dan Reid & Nada R. Sanders
Operations Management Forecasting Chapter 4

Operations Management Forecasting Chapter 4
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-1 Operations Management Forecasting Chapter 4.

© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J Operations Management Forecasting Chapter 4.
Part II – TIME SERIES ANALYSIS C2 Simple Time Series Methods & Moving Averages © Angel A. Juan & Carles Serrat - UPC 2007/2008.

Part II – TIME SERIES ANALYSIS C2 Simple Time Series Methods & Moving Averages © Angel A. Juan & Carles Serrat - UPC 2007/2008.
Copyright 2006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Forecasting Operations Chapter 12 Roberta Russell & Bernard.

Copyright 2006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Forecasting Operations Chapter 12 Roberta Russell & Bernard.
Forecasting McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 11 Solved Problems 1. Exhibit 11.2 Example Linear and Nonlinear Trend Patterns 2.

Chapter 11 Solved Problems 1. Exhibit 11.2 Example Linear and Nonlinear Trend Patterns 2.
Slides 13b: Time-Series Models; Measuring Forecast Error

Slides 13b: Time-Series Models; Measuring Forecast Error

Similar presentations

Ads by Google