Time-Series Forecasting

1
Time-Series Forecasting

• Overview
• Moving Averages
• Exponential Smoothing
• Seasonality

2
Time Series Forecasting
Moving Averages Exponential Smoothing Seasonal
Methods
Time series data is simply a set of values of
some variable measured at regular intervals over
time. One data set (variable) over time. Based
on historical data. The more data the
better. Assumption Past behavior helps us
predict future behavior. Time series data can
have one or more of the following components /
factors / variations. Trend Seasonal Cyclical
Random
3
Moving Averages
4
Moving Averages
5
Moving Averages
6
Moving Averages
7
Exponential Smoothing
8
Multiplicative Method
9
Multiplicative Method
Multiplicative seasonal method, whereby seasonal
factors are multiplied by an estimate of the
average demand to arrive at a seasonal forecast

1. For each year, calculate the average demand for
   each season by dividing annual demand by the
   number of seasons per year
2. For each year, divide the actual demand for each
   season by the average demand per season,
   resulting in a seasonal index for each season
3. Calculate the average seasonal index for each
   season using the results from Step 2
4. Calculate each seasons forecast for next year

10
Multiplicative Method
Year1 Year2 Year3 Year4 Yr5Forecast
Q1 45 70 100 100 132.82
Q2 335 370 585 725 843.62
Q3 520 590 830 1160 1300.03
Q4 100 170 285 215 323.52
           
Totals 1000 1200 1800 2200 2600
Average 250 300 450 550 650
           
           
  SFYr1 SFYr2 SFYr3 SFYr4 AvgSF
Q1 0.18 0.23 0.22 0.18 0.20
Q2 1.34 1.23 1.30 1.32 1.30
Q3 2.08 1.97 1.84 2.11 2.00
Q4 0.40 0.57 0.63 0.39 0.50
11
Homework (7)
Applying Time Series Techniques Moving
Averages Exponential smoothing alpha0.10 Exponent
ial smoothing alpha0.90
b. Use exponential smoothing with a smoothing
constant of 0.10 to forecast sales for the months
May through December. Start with a January
forecast of 20. c. Use exponential smoothing
with a smoothing constant of 0.90 to forecast
sales for the months May through December. Start
with a January forecast of 20. d. Compute the
errors for each forecasting period for each
method. Use absolute values so that all errors
are positive. Next average the errors (for the
periods May through December) for each of the
three forecasting methods. Which method gives
the smallest mean error, i.e. is best?
12
Homework (7)
Applying Time Series Techniques Multiplicative
Seasonal Method for handling data with seasonal
trends.