Visualization IN DATA ANALYTICS IN TIME SERIES

TIME SERIES FORECASTING
9-Jan-18 1
haritika74@gmail.com
BABIINTLMAY19001
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VISUALIZING TIME SERIES
COMPONENTS
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Steps in Forecasting
1. Problem definition:
2. Gathering information
3. Preliminary (exploratory) analysis.
4. Choosing and fitting models
5. Using and evaluating a forecasting model.
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Objective of this lesson is to explore several time series data
sets and apply visual methods using R to extract information
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Problem Definition
Time series forecasting involves
• Understanding historical pattern of data
• Using past knowledge forecasting for future
Before a forecasting problem is taken up, decision needs to be
made regarding the forecast horizon
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Forecast Range
Different industry needs different forecast range for different purpose
Example: Airlines industry: Interested in passenger volume forecast
Passenger volume is the driving force behind all its operation
• Long-term forecast: 5-10 years
̶ Required for strategic decision making
̶ Acknowledging limited reliability of these forecasts
• Mid-term forecast: 2-5 years
̶ Manpower hiring
̶ Decision on addition/alteration in new and existing routes
• Short-term forecast: 2 weeks – 6 months
̶ Manpower rostering
̶ Dynamic pricing
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Forecast Range
• Supply Chain: Responds to customer demand
̶ Very long range forecast will not serve the purpose well
̶ In addition to taking into account the past demand, lead time
and planned advertising and other marketing activity must be
incorporated into forecast horizon
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• Contract Research Organization doing clinical trials
̶ 2000 trials running simultaneously across the world
̶ Need to forecast monthly for each of some 5000 items required
for trials for next 6 months
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Gathering Information
Historical data required for future prediction
If volume of data is limited, forecasts will not
be reliable enough
If data is available for very long past, data may
not be useful at all
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Example: Clay Brick Production
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Example: Clay Brick Production
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Series not stable
Use stable part for forecast
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Example: Crest Toothpaste
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0
0.1
0.2
0.3
0.4
0.5
0.6
Week
0001
W07
0001
W14
0001
W21
0001
W28
0001
W35
0001
W42
0001
W49
0002
W04
0002
W11
0002
W18
0002
W25
0002
W32
0002
W39
0002
W46
0003
W01
0003
W08
0003
W15
0003
W22
0003
W29
0003
W36
0003
W43
0003
W50
0004
W05
0004
W12
0004
W19
0004
W26
0004
W33
0004
W40
0004
W47
0005
W02
0005
W09
0005
W16
0005
W23
0005
W30
0005
W37
0005
W44
0005
W51
0006
W06
0006
W13
Weekly Market Share
Use later part only for forecast
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Exploratory analysis
Plotting of both series highlighted the changed pattern in the
series
First step: Plot the time series.
Graphs enable many features of the data to be visualized,
including patterns, unusual observations, changes over time,
and relationships between variables.
Appropriate graph captures the inherent features of time
series
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Time Series in R
 A time series is saved as a ts object in R with special properties
appropriate to the series
USGDP <- ts(US_GDP[,2], start=c(1929,1), end=c(1991,1),
frequency=1)
plot(USGDP)
Shoe <- ts(Shoe_Sales[,3], start=c(2011,1), frequency=12)
plot(Shoe)
Income <- ts(Quarterly_Income[,3], start=c(2000,4), frequency=4)
plot(Income)
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What do graphs reveal?
GDP shows a continuous upward movemet
Shoe sales show two features:
There is a typical movement within a year
This type of shoe sales went up from 2011 – 2014 and past that
it shows decline
Quarterly income started low, went up to some extent but
movement of this series is spikey – some quarters show sudden
jump
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What do graphs reveal?
These observations give clue to inherent features of the time
series, known as components of time series
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Components of Time Series
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Time Series Components
 Trend
 Seasonal component
 Cyclic component
 Irregular component (Error or Random Component)
Graphs highlight variety of patterns inherent to TS
A TS can be split into several components, each representing one of the
underlying categories of patterns,
Systematic
Component
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Trend
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• Long term movement of a series: either increasing or
decreasing
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Example: Demand of Bricks
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75
95
115
135
155
175
195
215
1988-01
1988-02
1988-03
1988-04
1988-05
1988-06
1988-07
1988-08
1988-09
1988-10
1988-11
1988-12
1989-01
1989-02
1989-03
1989-04
1989-05
1989-06
1989-07
1989-08
1989-09
1989-10
1989-11
1989-12
1990-01
1990-02
1990-03
1990-04
1990-05
1990-06
1990-07
1990-08
1990-09
1990-10
1990-11
1990-12
1991-01
1991-02
1991-03
1991-04
1991-05
1991-06
1991-07
1991-08
1991-09
1991-10
1991-11
1991-12
Bricks
High Demand (May)
Low Demand (Jan)
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Example: Demand of Bricks
Across each year demand for bricks follow a
repetitive pattern
In a particular month (Jan) demand is the
lowest
In some other months, demand fluctutaes
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Seasonality
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• Representing intra-year stable fluctuations repeatable year
after year with respect to timing, direction and magnitude
• Normal variations that recur every year to the
same extent
• A Yearly series does not have seasonality
.
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Seasonality
• Demand for winter clothes
• Airlines and train ticket demands
• Incidence of influenza or other vector-borne
diseases
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Stock prices typically will not show any
seasonal pattern
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Example: Sale of Shoes
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2011-13 demand increasing
2013-15 stable demand
2015 onwards demand declining
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Cyclical Component
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• In addition to within year stable fluctuation,
demand for this particular style of shoes show
increase over years for a period and then decrease
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Systematic Components
• Trend, Seasonality, Cyclicality are part of
systematic component
• These patterns are interpretable
• These can be estimated
• Forecast of time series involves estimation
and extrapolation of these components
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We focus on Trend and Seasonality only
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Irregular Component
The error or variability associated with the series is the Irregular
component
This component is a random component
The part of the series that cannot be explained through Systematic
component forms the Irregular Component
Other names of this component is Error or White Noise
This component is assumed to have a normal distribution with 0 mean and
constant variance σ2
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Graphically identify Important
Characteristics
• Time Series plots are the first step in understanding the
pattern of the data
• Not only it identifies whether there are trend, seasonality or
cyclicality, it also identifies
̶ Which historical horizon to include for forecasting
̶ Is there any abrupt change in the level of the series?
̶ Whether there are any unusual observations in the series
̶ sudden spikes or sudden drops!
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Time Series: Important Characteristics
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 Is there a Trend?
 Is there a Seasonality?
 Are there Outliers? [How to handle?]
 Is there a Long-run cycle?
 Is there any Abrupt change in the level?
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Example 1: Reserve Bank of Australia
Govt Bond 2-Year Security
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Example 1: Important Characteristics
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 Is there a Trend? No perceptible trend overall; might
depend on which portion you are considering
 Is there a Seasonality? No seasonality
 Are there Outliers? Does not look like
 Is there a Long-run cycle? Difficult to say
 Is there any Abrupt change in the level? Yes
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Example 2: Champagne Sales
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 Is there a Trend? No
 Is there a Seasonality? Definite seasonality
 Is there a Long-run cycle? No
 Is there any Abrupt change in the level? No
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Example 3: International Air Passengers
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 Is there a Trend? Yes, increasing trend
 Is there a Seasonality? Definite seasonality
 Is there a Long-run cycle? No
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Example 4: Brick Production
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 Is there a Trend? Increasing to start but after a while
became constant
 Is there a Seasonality? Yes
 Are there Outliers? Yes, possibly
 Is there a Long-run cycle? Most likely, yes
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Visualization for Seasonality:
Seasonal Subseries for Champagne
Sales
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Visualization for Seasonality:
Seasonal Subseries
• Emphasizes the seasonality pattern where the data for each
season are collected together in separate mini time plots.
• The horizontal lines indicate the means for each season.
• The underlying seasonal pattern are clearly seen
• Changes in seasonality over time is clear
̶ Higher fluctuations in the later months
̶ Maximum fluctuation in Nov & Dec
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Seasonal Subplot: Airlines
Passengers
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Every month of
every year
passenger volume
increases
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Seasonal Subplot: Quarterly
Income
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Initially revenue
was low in every
quarter
Q3 shows one
high spike –
unusual
observation?
Q4 movements
almost
metronomic!
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Seasonal Subplot: Quarterly
Income
A thought:
Since all quarters of initial
years’ revenue seems
significantly lower compared
to the later years, would it
make more sense to discard
those initial years data for
forecasting?
9-Jan-18 39
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Next Step
In the next lesson we extract the components
of time series, namely trend and seasonality, to
improve understanding of time series and use
the information for forecasting
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9-Jan-18
Thank You
BABIINTLMAY19001

Visualization IN DATA ANALYTICS IN TIME SERIES

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