5 page paper
budsimpson
365_02_forecasting2.pptxCalifornia State University, East Bay College of Business and Economics MGMT 365 Enterprise Resource Planning and Control
Forecasting
Dr. Z. Radovilsky
Lecture Materials
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
1
1
Developed by Dr. Zinovy Radovilsky, Professor of Management and Finance
California State University, Hayward
All rights reserved
Lecture Overview
Science and art of forecasting
Forecasting categories
Forecasting principles and methods
Discussion of popular forecasting techniques:
Moving averages
Weighted moving averages
Exponential smoothing
Linear trend projection
Linear trend with seasonality (seasonal forecast)
Forecast accuracy and choosing the best forecast
Selecting forecasting techniques
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
2
2
Why Forecasting?
Nothing happens until somebody forecasts something
Forecasting is a necessary tool to reduce the uncertainty (risk) in decision making
Better decisions come from better forecasts
Forecasting serves as a starting point of major decisions in managing resources in finance, marketing, operations, purchasing, and other functions
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Forecasting in Enterprise Resource Management
| Supply Management | Identifying material stock level Predicting cost of materials Developing annual buying plan Projecting material requirements Identifying material delivery schedules Predicting storage capacity Predicting safety stock levels |
| Operations | Predicting demands of new and existing products Predicting results of new product research and development Projecting quality improvement Anticipating capacity needs Predicting new facility location Identifying labor requirements Developing production schedules Creating maintenance schedules |
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Forecasting Equals Science Plus Art
Successful Forecasting = Science + Art
"Science" implies that the body of the forecasting knowledge lies on the solid ground of quantitative forecasting methods and their correct utilization for various business situations
"Art" represents a combination of a decision maker's experience, logic, and intuition to supplement the forecasting quantitative analysis. Management abilities should be involved in forecasting process
Both the science and art of forecasting are essential in developing accurate forecasts
All managers are forecasters
Better forecasts are even more critical today
Cost will be $200 Million!
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Forecast Categories
Forecasting Time Horizon
Long-term
for duration of 3-5 years or more (on annual basis)
Medium-term
for duration of up to one year (on quarterly or monthly basis)
Short-term
for duration of up to month (on daily, weekly, or monthly basis)
Objectives of Forecast
Technological
technological development on a long- and medium-term basis
Economic
economic cycles or economic parameters using economic indicators
Demand
demand or sales for finished products and/or services
Resource
material/inventory, labor, and finance resources
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Forecast Categories (continued)
Forecasting Approaches
Qualitative
Executive opinion of managers
Consumer surveys
Sales force surveys
Quantitative
Times series methods
Causal methods
Inventory
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Quantitative Approaches (Methods) in Forecasting
Time series is an uninterrupted set of data observations that have been ordered in time in equally spaced intervals (units of time). Time series models predict on the assumption that the future is a function of the past
Time series methods
Moving average
Weighted moving average
Exponential smoothing
Exponential smoothing with trend
Linear trend
Linear trend with seasonality
Associative or causal forecasting is based on identification of variables (factors) that can predict values of the variable in question
Causal forecasting methods
Simple regression
Multiple regression
Nonlinear regression
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Time Series Forecasting: Monthly Forecast of Energy
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Associative Forecasting: Daily Energy Forecast
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Principles of Forecasting
Main assumption
Past pattern repeats itself into the future
Forecasts are rarely perfect
Don't expect forecasts to be exactly equal to the actual data.
The science and art of forecasting try to minimize, but not to eliminate, forecast errors
Forecast errors mean the difference between actual and forecasted values.
Forecasts for a shorter period tend to be more accurate
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Historical Data and Chart
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Historical Data Patterns
Trend patterns represent a general increase or decrease in a time series over several consecutive periods (some sources present six-seven or more periods)
Examples of forecasting methods: linear trend, exponential smoothing with trend
Stationary patterns are the result of many influences that act independently so as to yield nonsystematic and nonrepeating patterns about some average value
Examples of forecasting methods: moving averages, weighted moving average, exponential smoothing
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Historical Data Patterns
Seasonal Patterns represent patterns that are periodic and recurrent (usually on a quarterly, monthly, or annual basis)
Forecasting methods: linear trend with seasonality, exponential smoothing with trend and seasonality
Cyclical patterns are the result of economic and business expansions (increasing demand) and contractions (recessions and depressions) and usually repeat every two-five years
Forecasting methods: simple and multiple linear regressions
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Moving Averages Forecast
One of the most common techniques used in time series forecasting
The term "moving averages" represents the fact that as each new actual data point becomes available, a revised moving average is computed for the next data period requiring forecasting
Each forecasted value is based on the following formula:
where
Ft = forecast in the next period t
n=number of periods in the moving average
At-1, At-2,.., At-n = actual values in period t-1, t-2, …, t-n
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Example of Moving Averages Forecast
MA, n=2, Forecast for period 25: F25 = (A24 + A23)/2 = (147.31+146.62)/2 = 146.96
MA, n=4, Forecast for period 25: F23 = (A24 + A23 + A22 + A21)/4 = (147.31+146.62+139.87+144.95)/4 = 144.68
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Characteristics of Moving Averages
Simple method
Takes into consideration several most recent periods with the same weight of 1
The number of historical observations must exceed the number of periods in the moving average
The bigger the number of items in a moving average, the smoother the forecast
To identify the best number of periods (n), use measures of forecast accuracy
Does not work well if the data have a trend or seasonal pattern
Can be used for a short-term forecasting of stationary data
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Forecast Accuracy
To be an effective forecaster, it is very important to understand the way forecasting techniques are judged and selected based on forecast accuracy.
Forecast accuracy refers to how close forecasts come to actual data.
Accuracy is usually measured in forecasting by the value of its adverse characteristic--forecast error.
Forecast error or residual is the difference between actual and forecasted values in the same period.
et = At - Ft
where:
et= forecast error,
At= actual value in period t,
Ft=forecasted value in period t.
The smaller the forecast error, the closer the forecasted value to the actual value and the more accurate the forecast.
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Measuring Forecast Accuracy
Mean Absolute Deviation (MAD)
measures the average absolute error of a forecast. A sign of an error, which represents over- or underestimation, is really not important in most cases; we are rather concerned with the value of deviation.
where:
At = actual value in period t,
Ft = forecasted value in period t,
et = forecast error in period t,
n = number of errors.
Mean Absolute Percentage Error (MAPE)
is conceptually similar to MAD except that it is expressed in percentage terms. It is especially productive when the actual values are relatively large.
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Measuring Forecast Accuracy: MAD and MAPE for Moving Averages
MAD for MA, n=2: MAD = ()/22= 4.19
MAPE for MA, n=2: MAPE = ()/22= 0.0293 = 2.93%
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Weighted Moving Averages
Weighted moving average allows any weight to be placed on each element of the moving average forecast, providing that the total of weights is equal to 1:
where:
Ft = forecast in the next period t
n=number of periods in the moving average
At-1, At-2,.., At-n = actual values in period t-1, t-2, …, t-n
w1 = Weight to be given to the actual data for the period t-1
w2 = Weight to be given to the actual data for the period t-2
wn = Weight to be given to the actual data for the period t-n
How to choose weights
Trial and error
Experience (the most recent past should get higher weight)
Seasonal weights
Weight optimization using appropriate software and tools (Excel Solver, for example)
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Example of Weighted Moving Average
WMA, n=4, Forecast for period 25: F25 = w1 A24 + w2 A23 + w3 A22 + w4 A21 = 0.40*147.31 + 0.30*146.62 + 0.20*139.87+0.10*144.95 = 145.38
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Exponential Smoothing
A very popular forecasting technique
In exponential smoothing, only three pieces of data are needed to forecast the future: the most recent forecast, the actual data that occurred for that forecast period, and a smoothing constant alpha ():
or
where
Ft = new forecast for period t
Ft-1 = forecast for previous period (t-1)
At-1 = actual demand for previous period (t-1)
= smoothing constant
0 ≤ ≤ 1
Can be used for a short-term forecasting of stationary data.
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Exponential Smoothing Forecast
ES, 0.1, Forecast for period 25: F25 = α* A24 + (1-α)*F24 = 0.1*147.31 + 0.9*143.01 = 143.44
ES, 0.5, Forecast for period 25: F25 = α* A24 + (1-α)*F24 = 0.5*147.31 + 0.5*144.43 = 145.87
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Forecasting at Hard Rock Café: Original Data and Chart
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Forecasting with Linear Trend
Uses time as an independent variable to forecast a dependent variable (the variable to be predicted):
Y = bo + b1 X
where:
Y = dependent variable
x = independent variable (time)
bo = y-axis intercept
b1 = slope of the regression line
To identify the coefficients a and b, the least squares method is used. This method is based on minimizing the total square of the forecast errors.
Linear trend can be effectively used to forecasting historical data with trend and seasonal patterns.
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Forecasting with Linear Trend
Forecast for period 21: F21 = 81.593 + 0.826*X = 81.593 + 0.826*21 = 98.9
Forecast for period 22: F22 = 81.593 + 0.826*X = 81.593 + 0.826*22 = 99.8
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Linear Trend and Seasonality
A forecasting method that is commonly used in short- to long-term forecasting for the historical data with trend and seasonality:
F = T*S multiplicative seasonal model
where:
F = actual value of time series
T = linear trend projections (unadjusted forecast)
S = seasonal component (seasonal index)
In the multiplicative model, the trend component is measured in the same units as the original historical time series
The seasonal components are represented by respective seasonal indexes describing variations of data in different seasons (periods) of the year
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Linear Trend and Seasonal Forecast
Forecast for period 21: F21 = T21 * S21 = 98.4 * 1.0485 = 103.1
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
Conclusion: How to Choose Forecast
Get historical data
Plot the data and identify historical patterns
Select several alternative techniques
Develop forecast for each technique and identify its accuracy
Compare techniques and identify the best forecast
Reevaluate your forecast as new historical data become available
MGMT 365 Enterprise Resource Planning
Dr. Z. Radovilsky
‹#›
MGMT 6130 Enterprise Planning
Dr. Z. Radovilsky
‹#›
500,000550,000600,000650,000700,000750,000800,000850,000900,000950,000JanFebMarAprMayJunJulAugSepOctNovDecJanFebMarAprMayJunJulAugSepOctNovDecJanFebMarAprMayJunJulAugSepOctNovDecJanFebMarAprMayJunJulAugSepOctNovDecJanFebMarAprMayJunJulAugSepOctNovDec20062007200820092010
Actual kWhForecasted kWh
0.05,000.010,000.015,000.020,000.025,000.030,000.035,000.040,000.045,000.050,000.01112131415161718191101111121131141151161171181191201211221231241251261271281291301311321331341351361371Total Daily kW (kWh)Forecast
YearMonthPeriod
Sales (in
$Mln)
2012Jan1140.11
Feb2142.04
Mar3142.43
Apr4138.88
May5145.40
Jun6148.93
Jul7140.44
Aug8146.71
Sep9148.37
Oct10143.89
Nov11149.01
Dec12147.40
2013Jan13141.02
Feb14138.17
Mar15142.12
Apr16143.36
May17137.90
Jun18137.36
Jul19144.76
Aug20146.76
Sep21144.95
Oct22139.87
Nov23146.62
Dec24147.31
2014Jan25
Feb26
Mar27
135.00140.00145.00150.00JanFebMarAprMayJunJulAugSepOctNovDecJanFebMarAprMayJunJulAugSepOctNovDec20122013
Sales (in $Mln)
Sales (in $Mln)
n
A
+
...
+
A
+
A
+
A
=
F
n
-
t
3
-
t
2
-
t
1
-
t
t
YearMonthPeriod
Sales (in
$Mln)
2-Period
MA, n=2
4-Period
MA, n=4
6-Period
MA, n=6
2012Jan1140.11#N/A#N/A#N/A
Feb2142.04#N/A#N/A#N/A
Mar3142.43141.08#N/A#N/A
Apr4138.88142.24#N/A#N/A
May5145.40140.65140.87#N/A
Jun6148.93142.14142.19#N/A
Jul7140.44147.16143.91142.96
Aug8146.71144.69143.41143.02
Sep9148.37143.58145.37143.80
Oct10143.89147.54146.11144.79
Nov11149.01146.13144.85145.62
Dec12147.40146.45147.00146.23
2013Jan13141.02148.20147.17145.97
Feb14138.17144.21145.33146.07
Mar15142.12139.59143.90144.64
Apr16143.36140.14142.18143.60
May17137.90142.74141.17143.51
Jun18137.36140.63140.39141.66
Jul19144.76137.63140.18139.99
Aug20146.76141.06140.84140.61
Sep21144.95145.76141.69142.04
Oct22139.87145.86143.46142.51
Nov23146.62142.41144.09141.93
Dec24147.31143.24144.55143.39
2014Jan25146.96144.68145.04
n
|
e
|
=
n
|
F
-
A
|
=
MAD
t
n
1
=
t
t
t
n
1
=
t
å
å
n
A
F
-
A
|
=
MAPE
t
t
t
n
1
=
t
|
å
YearMonthPeriod
Sales (in
$Mln)
2-Period MA,
n=2Error|Error|
%
|Error|
4-Period MA,
n=4Error|Error|
%
|Error|
2012Jan1140.11#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A
Feb2142.04#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A
Mar3142.43141.081.361.360.010#N/A#N/A#N/A#N/A
Apr4138.88142.24-3.363.360.024#N/A#N/A#N/A#N/A
May5145.40140.654.754.750.033140.874.534.530.031
Jun6148.93142.146.796.790.046142.196.746.740.045
Jul7140.44147.16-6.726.720.048143.91-3.473.470.025
Aug8146.71144.692.032.030.014143.413.303.300.022
Sep9148.37143.584.794.790.032145.373.003.000.020
Oct10143.89147.54-3.653.650.025146.11-2.232.230.015
Nov11149.01146.132.882.880.019144.854.154.150.028
Dec12147.40146.450.950.950.006147.000.400.400.003
2013Jan13141.02148.20-7.187.180.051147.17-6.156.150.044
Feb14138.17144.21-6.046.040.044145.33-7.167.160.052
Mar15142.12139.592.532.530.018143.90-1.781.780.013
Apr16143.36140.143.213.210.022142.181.181.180.008
May17137.90142.74-4.854.850.035141.17-3.273.270.024
Jun18137.36140.63-3.273.270.024140.39-3.023.020.022
Jul19144.76137.637.137.130.049140.184.574.570.032
Aug20146.76141.065.705.700.039140.845.925.920.040
Sep21144.95145.76-0.810.810.006141.693.263.260.022
Oct22139.87145.86-5.995.990.043143.46-3.593.590.026
Nov23146.62142.414.214.210.029144.092.532.530.017
Dec24147.31143.244.074.070.028144.552.762.760.019
2014Jan25146.96144.68
MAD4.193.65
MAPE2.93%2.54%
å
=
-
-
-
=
+
+
+
=
n
i
i
n
t
n
t
t
w
A
w
A
w
A
w
1
2
2
1
1
t
1
...
F
YearMonthPeriod
Sales (in
$Mln)
4-Period
WMA
2012Jan1140.11#N/A
Feb2142.04#N/A
Mar3142.43#N/A
Apr4138.88#N/A
May5145.40140.70
Jun6148.93142.51
Jul7140.44145.21
Aug8146.71143.82
Sep9148.37145.14
Oct10143.89146.34
Nov11149.01145.45
Dec12147.40147.12
2013Jan13141.02147.28
Feb14138.17144.82
Mar15142.12141.95
Apr16143.36141.24
May17137.90141.72
Jun18137.36140.41
Jul19144.76139.20
Aug20146.76141.03
Sep21144.95143.40
Oct22139.87144.70
Nov23146.62143.26
Dec24147.31144.27
2014Jan25145.38
MAD3.72
MAPE2.59%
4-Period WMA
Weights w1w2w3w4
0.400.300.200.10
Total w1.00
)
(
1
1
1
-
-
-
-
+
=
t
t
t
t
F
A
F
F
a
1
1
)
1
(
-
-
-
+
=
t
t
t
F
A
F
a
a
YearMonthPeriod
Sales (in
$Mln)ES, 0.1ES, 0.5
2012Jan1140.11#N/A#N/A
Feb2142.04140.11140.11
Mar3142.43140.30141.08
Apr4138.88140.52141.76
May5145.40140.35140.32
Jun6148.93140.86142.86
Jul7140.44141.66145.89
Aug8146.71141.54143.17
Sep9148.37142.06144.94
Oct10143.89142.69146.66
Nov11149.01142.81145.27
Dec12147.40143.43147.14
2013Jan13141.02143.83147.27
Feb14138.17143.55144.14
Mar15142.12143.01141.16
Apr16143.36142.92141.64
May17137.90142.96142.50
Jun18137.36142.46140.20
Jul19144.76141.95138.78
Aug20146.76142.23141.77
Sep21144.95142.68144.27
Oct22139.87142.91144.61
Nov23146.62142.60142.24
Dec24147.31143.01144.43
2014Jan25143.44145.87
Feb26
Mar27
MAD3.633.59
MAPE2.52%2.50%
YearQuarterPeriod
Guests (in
thousand)
2009Q1188.2
Q2271.3
Q3388.9
Q4492.6
2010Q1590.4
Q2673.3
Q3786.9
Q4893.7
2011Q1992.3
Q21080.4
Q31189.8
Q41290.9
2012Q113100.4
Q21482.4
Q31598.1
Q41699.5
2013Q117101.9
Q21884.3
Q31998.0
Q420102.0
2014Q121
Q222
Q323
Q424
70.075.080.085.090.095.0100.0105.0Q1Q2Q3Q4Q1Q2Q3Q4Q1Q2Q3Q4Q1Q2Q3Q4Q1Q2Q3Q420092010201120122013
Guest Data (in Thousand)
Guests (in thousand)
(
)
2
2
1
1
1
x
n
x
y
x
n
y
x
b
i
n
i
i
i
n
i
-
å
-
å
=
=
=
x
b
y
b
o
1
-
=
YearQuarterPeriod
Guests (in
thousand)
Linear
Trend
ForecastInterceptSlope
2009Q1188.282.481.5930.826
Q2271.383.2
Q3388.984.1
Q4492.684.9
2010Q1590.485.7
Q2673.386.5
Q3786.987.4
Q4893.788.2
2011Q1992.389.0
Q21080.489.9
Q31189.890.7
Q41290.991.5
2012Q113100.492.3
Q21482.493.2
Q31598.194.0
Q41699.594.8
2013Q117101.995.6
Q21884.396.5
Q31998.097.3
Q420102.098.1
2014Q12198.9
Q22299.8
Q323100.6
Q424101.4
MAD6.0
MAPE6.9%
70.075.080.085.090.095.0100.0105.0110.0
Q1Q2Q3Q4Q1Q2Q3Q4Q1Q2Q3Q4Q1Q2Q3Q4Q1Q2Q3Q4Q1Q2Q3Q4200920102011201220132014
Linear Trend Forecast
Guests (in thousand)Linear Trend Forecast
YearQuarterPeriod
Guests
(in
thousand)
Trend
Forecast
Seasonal
Index
Seasonal
ForecastYearQuarterPeriod
Guests (in
thousand)AverageRatio
Seasonal
Index
Smoothed
Data
2009Q1188.282.91.048587.02009Q1188.290.270.97711.048584.1
Q2271.383.70.867972.7Q2271.390.270.78990.867982.2
Q3388.984.51.023086.4Q3388.990.270.98491.023086.9
Q4492.685.31.060790.4Q4492.690.271.02591.060787.3
2010Q1590.486.01.048590.22010Q1590.490.271.00151.048586.2
Q2673.386.80.867975.3Q2673.390.270.81210.867984.5
Q3786.987.61.023089.6Q3786.990.270.96271.023084.9
Q4893.788.31.060793.7Q4893.790.271.03811.060788.3
2011Q1992.389.11.048593.42011Q1992.390.271.02251.048588.0
Q21080.489.90.867978.0Q21080.490.270.89070.867992.6
Q31189.890.71.023092.7Q31189.890.270.99481.023087.8
Q41290.991.41.060797.0Q41290.990.271.00701.060785.7
2012Q113100.492.21.048596.72012Q113100.490.271.11231.048595.8
Q21482.493.00.867980.7Q21482.490.270.91290.867994.9
Q31598.193.71.023095.9Q31598.190.271.08681.023095.9
Q41699.594.51.0607100.2Q41699.590.271.10231.060793.8
2013Q117101.995.31.048599.92013Q117101.990.271.12891.048597.2
Q21884.396.00.867983.4Q21884.390.270.93390.867997.1
Q31998.096.81.023099.0Q31998.090.271.08571.023095.8
Q420102.097.61.0607103.5Q420102.090.271.13001.060796.2
2014Q12198.41.0485103.1
Q22299.10.867986.0
Q32399.91.0230102.2
Q424100.71.0607106.8
MAD1.9
MAPE2.2%
70.075.080.085.090.095.0100.0105.0110.0Q1Q2Q3Q4Q1Q2Q3Q4Q1Q2Q3Q4Q1Q2Q3Q4Q1Q2Q3Q4Q1Q2Q3Q4200920102011201220132014
Linear Trend and Seasonal Forecast
Guests (in thousand)Trend ForecastSeasonal Forecast
