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
Copyright 2011 John Wiley & Sons, Inc. 2 Time-series data: data gathered on a given characteristic over a period of time at regular intervals Time-series techniques Attempt to account for changes over time by examining patterns, cycles, trends, or using information about previous time periods Averaging Smoothing Time-Series Data
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.
Copyright 2011 John Wiley & Sons, Inc. 4 Time-Series Effects
Copyright 2011 John Wiley & Sons, Inc. 5 Stationary time-series - data that contain no trend, cyclical, or seasonal effects. Error of individual forecast e t – the difference between the actual value x t and the forecast of that value F t. Time Series Components
Copyright 2011 John Wiley & Sons, Inc. 6 Error of the Individual Forecast (e t = X t – F t ) the difference between the actual value x t and the forecast of that value F t. 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. Measurement of Forecasting Error
Copyright 2011 John Wiley & Sons, Inc. 7 YearActualForecastError Nonfarm Partnership Tax Returns: Actual and Forecast with =.7
Copyright 2011 John Wiley & Sons, Inc. 8 YearActualForecastError|Error| Mean Absolute Deviation: Nonfarm Partnership Forecasted Data
Copyright 2011 John Wiley & Sons, Inc. 9 Mean Square Error: Nonfarm Partnership Forecasted Data YearActualForecastErrorError
Copyright 2011 John Wiley & Sons, Inc. 10 Smoothing Techniques Smoothing techniques produce forecasts based on “smoothing out” the irregular fluctuation effects in the time-series data. 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.
Copyright 2011 John Wiley & Sons, Inc. 11 Smoothing techniques produce forecasts based on “smoothing out” the irregular fluctuation effects in the time-series data. Averaging Models - the forecast for time period t is the average of the values for a given number of previous time periods: Simple Averages Weighted Moving Averages Exponential Smoothing - is used to weight data from previous time periods with exponentially decreasing importance in the forecast. Smoothing Techniques
Copyright 2011 John Wiley & Sons, Inc. 12 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 for September. The monthly average last 12 months was 56.45, so I predict for September. The forecast for time period t is the average of the values for a given number of previous time periods.
Copyright 2011 John Wiley & Sons, Inc. 13 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
Copyright 2011 John Wiley & Sons, Inc. 14 MonthsShipments 4-Mo Moving Average Forecast Error January1056 February1345 March1381 April1191 May June July August September October November December Demonstration Problem 15.1: Four-Month Simple Moving Average
Copyright 2011 John Wiley & Sons, Inc. 15 Demonstration Problem 15.1: Four-Month Moving Average
Copyright 2011 John Wiley & Sons, Inc. 16 A moving average in which some time periods are weighted differently than others. 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
Copyright 2011 John Wiley & Sons, Inc. 17 MonthsShipments 4-Mo Weighted Moving Average Forecast Error January1056 February1345 March1381 April1191 May June July August September October November December Demonstration Problem 15.2: Four-Month Weighted Moving Average
Copyright 2011 John Wiley & Sons, Inc. 18 is the exponential smoothing constant Used to weight data from previous time periods with exponentially decreasing importance in the forecast Exponential Smoothing
Copyright 2011 John Wiley & Sons, Inc. 19 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
Copyright 2011 John Wiley & Sons, Inc. 20 = 0.2 Year Housing Units (1,000)Fe|e|e2e MAD209.8 MSE53110 Demonstration Problem 15.3: = 0.2
Copyright 2011 John Wiley & Sons, Inc. 21 = 0.8 Year Housing Units (1,000)Fe|e|e2e MAD111.2 MSE Demonstration Problem 15.3: = 0.8
Copyright 2011 John Wiley & Sons, Inc. 22 Trend – long run general direction of climate over an extended time Linear Trend Quadratic Trend Holt’s Two Parameter Exponential Smoothing - Holt’s technique uses weights (β) to smooth the trend in a manner similar to the smoothing used in single exponential smoothing (α) Trend Analysis
Copyright 2011 John Wiley & Sons, Inc. 23 Following table provides the data needed to compute a quadratic regression trend model on the manufacturing workweek data Average Hours Worked per Week by Canadian Manufacturing Workers
Copyright 2011 John Wiley & Sons, Inc. 24 PeriodHoursPeriodHoursPeriodHoursPeriodHours Average Hours Worked per Week by Canadian Manufacturing Workers
Copyright 2011 John Wiley & Sons, Inc. 25 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA SSMSFSignificance F Regression Residual Total CoefficientsStandard Errort StatP-value Intercept Period df Excel Regression Output using Linear Trend
Copyright 2011 John Wiley & Sons, Inc. 26 Regression Statistics Multiple R R Square0.761 Adjusted R Square0.747 Standard Error0.405 Observations35 ANOVA dfSSMSFSignificance F Regression E-10 Residual Total CoefficientsStandard Errort StatP-value Intercept E-49 Period E-07 Period E-05 Excel Regression Output using Quadratic Trend
Copyright 2011 John Wiley & Sons, Inc. 27 Excel Graph of Canadian Manufacturing Data with a Second-Degree Polynomial FIt