introduction to global and local models forecasting
TRANSCRIPT
Introduction to
Global and Local Models
FORECASTING
This presentation uses materials jointly developed by the Integrative Studies 1 teaching team
WHY IS FORECASTING USEFUL?
Businesses need to plan for the future.
This is true for all types of business.
Requires some idea about what the future will be.
How do you do it?
Method 1: ROULETTE
Assume that the future will be the outcome of a pure chance process, and so is inherently unpredictable.
So don’t forecast just guess and hope.
Method 2: OSTRICH
Assume that the future will beidentical to the present (nothing changes).
Method 3: TRENDY
The past contains patterns (trends) that will continue into the future.
Future values are formed by identifying trends and projecting them forwards.
Method 4: MAD SCIENTIST
Find a theoretical cause and effect model: use knowable changes in causes to predict changes in effects.
Method 5: KALEIDOSCOPE
Develop a set of scenarios that are plausible stories about the future, knowing all that you do right now.
Keep all of these in mind. Evaluate your possible options against each of these.
Forecasting involves combining Statistics and our personal knowledge of the background of the data/problem
Global Models use all the data
Local Models use only a part of the data, often most recent
UK SALES of RECORDED MUSIC (MILLIONS)
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LPsCasssettesCDsSi ngl es
UK SALES of SINGLES (MILLIONS)
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1970 1975 1980 1985 1990 1995 2000
UK SALES of SINGLES (MILLIONS)
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1970 1975 1980 1985 1990 1995 2000
Best Fitting LINEAR Trend
UK SALES of SINGLES (MILLIONS)
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1970 1975 1980 1985 1990 1995 2000
Polynomial of Degree 2Best Fitting
UK SALES of SINGLES (MILLIONS)
y = 0.032x3 - 188.541x2 + 374302.894x - 247694272.834
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Polynomial of Degree 3Best Fitting
UK SALES of SINGLES (MILLIONS)
y = 0.03x3 - 1.45x2 + 19.21x + 1.03
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YEAR = 1970 +
Best Polynomial of Degree 3
UK SALES of SINGLES (MILLIONS)
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1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
Forecasts to Year 2010 usingBest Polynomial of Degree 3
Good Fit to Past Data But Unbelievable Forecasts
• SALES are between 50 and 90 Millions for the Past 30 Years
• Five Year Forecast is about 150 Millions, and
• Ten Year Forecast exceeds 300 Millions
A polynomial of high degree will usually fit past data welland forecast future very badly
In practice, NEVER forecast using Polynomial Trends of Degree higher than 1.
Degree 1 is LINEAR TREND
UK SALES of SINGLES (MILLIONS)
y = 0.0095x + 49.427
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Best Global LINEAR Trend
Y = 0.0095 * X + 49.4 (Millions)
Increasing X by 1 increases Y by 0.0095
X is YEAR, Y is SALES in Millions, and so
Each Year, SALES increase by 0.0095 Millions, i.e. 9,500
UK SALES of RECORDED MUSIC (MILLIONS)
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Consider last Six Years only (Local Model)
UK SALES of SINGLES 1992-1997 (MILLIONS)
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YEAR = 1990 +
UK SALES of SINGLES 1992-1997 (MILLIONS)
y = 7.0x + 36.6
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YEAR = 1990 +
Best Local LINEAR TREND
UK SALES of SINGLES 1992-1997 (MILLIONS)
y = 7.0x + 36.6
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YEAR = 1990 +
Over last 5 Years SALES GREW by 7.0 Million per Year
Global Linear Trend implies increases of 9,500 per year
Local Linear Trend implies increases of 7 Million per year
Statistics OK in Both Cases So, WHICH do we BELIEVE?
Y = 7.0 * X + 36.6 (Millions)
1998: X = 8 and
Forecast = 7*8 + 36.6 = 92.6
Forecast = 7*18 + 36.6 = 162.6
2008: X = 18 and
UK SALES of SINGLES 1992-1997 (MILLIONS)
y = 42.2e0.1x
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YEAR = 1990 +
Best Local Exponential Trend
Y = 42.2 e0.1 X
Interpretation?
Increasing X by 1 increases Y by approx 0.1 of itself i.e. approx 10% of itself
Implies Sales are increasing by 10% per Year (over last 5)
UK SALES of SINGLES 1992-1997 (MILLIONS)
y = 42.2e0.1x
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YEAR = 1990 +
SALES growing by 10% per year over last 5 years
Y = 42.2 e (Millions)
1998: X = 8 and
Forecast = 42.2 e = 93.9
Forecast = 42.2 e = 255.4
2008: X = 18 and
0.1 X
0.1*8
0.1*18
LINEAR and EXPONENTIAL TREND FORECASTS to 2010
UK SALES of SINGLES 1992-1997 (MILLIONS)
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YEAR = 1990 +
Both LINEAR and EXPONENTIAL Trends seem OK for short-term Forecasts here but Poor for long-term.
No surprise: both LOCAL i.e. chosen to fit most recent bit of past data
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LPsCasssettesCDsSi ngl es
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CDs SOLD IN LAST YEAR (Millions)
SIN
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(Mill
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y = 0.34x + 31.51
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CDs SOLD IN LAST YEAR (Millions)
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Y = 0.34 * X + 31.5
Single Sales Next Year =0.34 * CD Sales this Year + 31.5
1997: 158.8 Million CDs sold
1998 Forecast of Single SALES
0.34*158.8 + 31.5 = 85.5 Millions
NOTE: Cannot forecast Single Sales further ahead without forecasting CD Sales
Can we forecast next year’s Single Sales from last year’s?
Scatter Plot of Singles sold each year and previous year
y = 0.8x + 15.6
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SINGLES SOLD LAST YEAR (Millions)
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Singles: Sales Next Year =0.8 * Sales this Year + 15.6
1997: Sales = 87 Million
Forecast for 1998 is 0.8*87+15.6 = 85.2 Million
OK for short-term - What about long-term forecasts?
Sales Next Year =0.8 * Sales this Year + 15.6
Using this equation we can generate forecasts iteratively for any horizon, e.g.
Forecast for 1999 =0.8* Forecast for 1998 + 15.60.8*85.2 + 15.6 = 83.8
Proceeding in this way: Forecast for 2008 = 78.8 Million
Which is much more credible than any of our Trend Forecasts
Perhaps it is Pessimistic?
SALES NEXT YEAR = 0.8 * SALES THIS YEAR + 15.6 (Millions)
UK SINGLES SOLD and PREDICTED ONE YEAR AHEAD
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SINGLES SOLD
PREDICTED SALES
Compare the Forecasts made
1998 1999 2008
LINEAR TREND (GLOBAL) 68.4 68.4 68.5
LINEAR TREND (LOCAL) 92.6 99.6 162.6EXPONENTIAL TREND (LOCAL) 93.9 103.0 255.4
LAST YEAR'S CDs (LOCAL) 85.5
LAST YEAR'S SINGLES (GLOBAL) 85.2 83.8 78.8
ACTUAL VALUE 79.4 80.1
SALES of SINGLES (Millions)
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Use of a Forecasting method reflects our belief that the future behaviour of the data will be like it was in the past, and will not change over the forecast horizon.
This is NOT a Statistical criterion and so cannot be objectively tested.
Hence, choice of method requires much care & lots of reasoning as suggested, but also an Act of Faith.