Lecture 14: Chapter 8: Time series analysis and forecasting | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

8.1. TIME SERIES PATTERNS A time series is a sequence of observations on a variable measured at successive points in time or over successive periods of time.The pattern of the data is an important factor in understanding how the time series has behaved in the past. Tài liệu giúp bạn tham khảo, ôn tập và đạt kết quả tốt. Mời bạn đọc đón xem!

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Môn: Applied statistics (ENEE1006IU)

Trường: Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

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lOMoARcPSD| 45903860
APPLIED STATISTICS
COURSE CODE: ENEE1006IU
Lecture 14:
Chapter 8: Time series analysis and
forecasng
(3 credits: 2 is for lecture, 1 is for lab-work)
1
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CHAPTER 8: TIME SERIES ANALYSIS AND FORECASTING
•8.1. Time series paerns
•8.2. Forecast accuracy
•8.3. Trend projecon
•8.4. Time series decomposion
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8.1. TIME SERIES PATTERNS
•A me series is a sequence of observaons on a variable measured at successive
points in me or over successive periods of me.
•The paern of the data is an important factor in
understanding how the me series has behaved in
the past.
•To idenfy the underlying paern in the data, a
useful rst step is to construct a me series plot.
•A me series plot is a graphical presentaon of the
relaonship between me and the me series
variable; me is on the horizontal axis and the me
series values are shown on the vercal axis.
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8.1. TIME SERIES PATTERNS
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•Horizontal Paern: a horizontal paern exists when the data uctuate around
a constant mean
•Trend Paern: a trend is usually the result of long-term factors; gradual
shis or movements to relavely higher or lower values over a longer period
of me
•Seasonal Paern: Seasonal paerns are recognized by seeing the same
repeang paerns over successive periods of me
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8.1. TIME SERIES PATTERNS
•Trend and Seasonal Paern: in such
cases we need to use a forecasng
method that has the capability to deal
with both trend and seasonality
•Cyclical Paern: a cyclical paern exists
if the me series plot shows an
alternang sequence of points below
and above the trend line lasng more
than one year. cyclical eects are oen
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combined with long-term trend eects and referred to as trend-cycle eects
8.2. FORECAST ACCURACY
•Principles of Forecasng:
Many types of forecasng models that dier in complexity and amount of data &
way they generate forecasts:
1. Forecasts are rarely perfect
2. Forecasts are more accurate for grouped data than for individual items
3. Forecast are more accurate for shorter than longer me periods
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TYPES OF FORECASTING METHODS
•Decide what needs to be forecast
Level of detail, units of analysis & me horizon required
•Evaluate and analyze appropriate data
Idenfy needed data & whether it’s available
•Select and test the forecasng model
Cost, ease of use & accuracy
•Generate the forecast
•Monitor forecast accuracy over me
TYPES OF FORECASTING METHODS
•Forecasng methods are classied into two groups:
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•Qualitave methods – judgmental
methods
Forecasts generated
subjecvely by the
forecaster
Educated guesses
•Quantave methods –
based on mathemacal
modeling
Forecasts generated
through mathemacal
modeling
QUANTITATIVE METHODS
•Time Series Models:
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Assumes informaon needed to generate a forecast is contained in a me series of data
Assumes the future will follow same paerns as the past
•Causal Models or Associave Models:
Explores cause-and-eect relaonships
Uses leading indicators to predict the future
Housing starts and appliance sales
TIME SERIES MODELS
•Forecaster looks for data paerns as
Data = historic paern + random variaon
•Historic paern to be forecasted:
Level (long-term average) – data uctuates around a constant mean
Trend – data exhibits an increasing or decreasing paern
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Seasonality – any paern that regularly repeats itself and is of a constant length
Cycle – paerns created by economic uctuaons
•Random Variaon cannot be predicted
TIME SERIES MODELS
•Naive: Ft 1 At
The forecast is equal to the actual value observed during the last period – good
for level paerns
•Simple Mean: Ft 1 At /n
The average of all available data - good for level paerns
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•Moving Average: Ft 1 At /n
The average value over a set me period
(e.g.: the last four weeks)
Each new forecast drops the oldest data point & adds a new observaon
More responsive to a trend but sll lags behind actual data
TIME SERIES MODELS
•Weighted Moving Average: F
t 1
C
t
A
t
•All weights must add to 100% or 1.00
e.g. C
t
=0.5, C
t-1
=0.3, C
t-2
=0.2 (weights add to 1.0)
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•Allows emphasizing one period over others; above indicates more weight on
recent data (C
t
=0.5)
•Diers from the simple moving average that weighs all periods equally more
responsive to trends
TIME SERIES MODELS
•Exponenal Smoothing: F
t 1
αA
t
1 α F
t
Most frequently used me series method because of ease of use and minimal
amount of data needed
•Need just three pieces of data to start:
Last period’s forecast (F
t
)
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Last periods actual value (A
t
)
Select value of smoothing coecient, α,between 0 and 1.0
•If no last period forecast is available, average the last few periods or use naive
method
•Higher α values (e.g. 0.7 or 0.8) may place too much weight on last period’s
random variaon
MEASURING FORECAST ERROR
•Forecasts are never perfect
•Need to know how much we should rely on our chosen forecasng method
•Measuring forecast error:
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Et At Ft
•Note that over-forecasts = negave errors and under-forecasts = posive
errors
MEASURING FORECASTING ACCURACY
•Mean Absolute Deviaon (MAD)
measures the total error in a forecast
without regard to sign
•Cumulave Forecast Error (CFE)
Measures any bias in the forecast
•Mean Square Error (MSE)
Penalizes larger errors
•Tracking Signal
Measures if your model
is working
MAD actual forecast n
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CFE actual forecast
actual - forecast
2
MSE
n
TS CFE MAD
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HOMEWORKS (1)
Note: Each table
for each method
Compute the forecasts and measures of forecast accuracy, using:
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lOMoAR cPSD| 45903860 APPLIED STATISTICS COURSE CODE: ENEE1006IU Lecture 14:
Chapter 8: Time series analysis and forecasting
(3 credits: 2 is for lecture, 1 is for lab-work) 1 lOMoAR cPSD| 45903860
CHAPTER 8: TIME SERIES ANALYSIS AND FORECASTING •8.1. Time series patterns •8.2. Forecast accuracy •8.3. Trend projection
•8.4. Time series decomposition 2 lOMoAR cPSD| 45903860 8.1. TIME SERIES PATTERNS
•A time series is a sequence of observations on a variable measured at successive
points in time or over successive periods of time.
•The pattern of the data is an important factor in
understanding how the time series has behaved in the past.
•To identify the underlying pattern in the data, a
useful first step is to construct a time series plot.
•A time series plot is a graphical presentation of the
relationship between time and the time series
variable; time is on the horizontal axis and the time
series values are shown on the vertical axis. 3 lOMoAR cPSD| 45903860 8.1. TIME SERIES PATTERNS 4 lOMoAR cPSD| 45903860
•Horizontal Pattern: a horizontal pattern exists when the data fluctuate around a constant mean
•Trend Pattern: a trend is usually the result of long-term factors; gradual
shifts or movements to relatively higher or lower values over a longer period of time
•Seasonal Pattern: Seasonal patterns are recognized by seeing the same
repeating patterns over successive periods of time 5 lOMoAR cPSD| 45903860 8.1. TIME SERIES PATTERNS
•Trend and Seasonal Pattern: in such
cases we need to use a forecasting
method that has the capability to deal
with both trend and seasonality
•Cyclical Pattern: a cyclical pattern exists
if the time series plot shows an
alternating sequence of points below
and above the trend line lasting more
than one year. cyclical effects are often 6 lOMoAR cPSD| 45903860
combined with long-term trend effects and referred to as trend-cycle effects 8.2. FORECAST ACCURACY •Principles of Forecasting:
Many types of forecasting models that differ in complexity and amount of data & way they generate forecasts:
1. Forecasts are rarely perfect
2. Forecasts are more accurate for grouped data than for individual items
3. Forecast are more accurate for shorter than longer time periods 7 lOMoAR cPSD| 45903860 TYPES OF FORECASTING METHODS
•Decide what needs to be forecast
Level of detail, units of analysis & time horizon required
•Evaluate and analyze appropriate data
Identify needed data & whether it’s available
•Select and test the forecasting model
Cost, ease of use & accuracy •Generate the forecast
•Monitor forecast accuracy over time TYPES OF FORECASTING METHODS
•Forecasting methods are classified into two groups: 8 lOMoAR cPSD| 45903860
•Qualitative methods – judgmental methods Forecasts generated subjectively by the forecaster Educated guesses •Quantitative methods – based on mathematical modeling Forecasts generated through mathematical modeling QUANTITATIVE METHODS •Time Series Models: 9 lOMoAR cPSD| 45903860
Assumes information needed to generate a forecast is contained in a time series of data
Assumes the future will follow same patterns as the past
•Causal Models or Associative Models:
Explores cause-and-effect relationships
Uses leading indicators to predict the future
Housing starts and appliance sales TIME SERIES MODELS
•Forecaster looks for data patterns as
Data = historic pattern + random variation
•Historic pattern to be forecasted:
Level (long-term average) – data fluctuates around a constant mean
Trend – data exhibits an increasing or decreasing pattern 10 lOMoAR cPSD| 45903860
Seasonality – any pattern that regularly repeats itself and is of a constant length
Cycle – patterns created by economic fluctuations
•Random Variation cannot be predicted TIME SERIES MODELS •Naive: Ft 1 At
The forecast is equal to the actual value observed during the last period – good for level patterns •Simple Mean: Ft 1 At /n
The average of all available data - good for level patterns 11 lOMoAR cPSD| 45903860 •Moving Average: Ft 1 At /n
The average value over a set time period (e.g.: the last four weeks)
Each new forecast drops the oldest data point & adds a new observation
More responsive to a trend but still lags behind actual data TIME SERIES MODELS
•Weighted Moving Average: Ft 1 CtAt
•All weights must add to 100% or 1.00
e.g. Ct =0.5, Ct-1 =0.3, Ct-2 =0.2 (weights add to 1.0) 12 lOMoAR cPSD| 45903860
•Allows emphasizing one period over others; above indicates more weight on recent data (Ct=0.5)
•Differs from the simple moving average that weighs all periods equally more responsive to trends TIME SERIES MODELS •Exponential Smoothing: Ft 1 αAt 1 α Ft
Most frequently used time series method because of ease of use and minimal amount of data needed
•Need just three pieces of data to start:
Last period’s forecast (Ft) 13 lOMoAR cPSD| 45903860
Last periods actual value (At)
Select value of smoothing coefficient, α,between 0 and 1.0
•If no last period forecast is available, average the last few periods or use naive method
•Higher α values (e.g. 0.7 or 0.8) may place too much weight on last period’s random variation MEASURING FORECAST ERROR
•Forecasts are never perfect
•Need to know how much we should rely on our chosen forecasting method •Measuring forecast error: 14 lOMoAR cPSD| 45903860 Et At Ft
•Note that over-forecasts = negative errors and under-forecasts = positive errors
MEASURING FORECASTING ACCURACY
•Mean Absolute Deviation (MAD) •Mean Square Error (MSE)
measures the total error in a forecast Penalizes larger errors without regard to sign •Tracking Signal
•Cumulative Forecast Error (CFE) Measures if your model
Measures any bias in the forecast is working MAD actual forecast n 15 lOMoAR cPSD| 45903860 CFE actual forecast MSE n actual - forecast 2 TS CFE MAD 16 lOMoAR cPSD| 45903860 17 lOMoAR cPSD| 45903860 18 lOMoAR cPSD| 45903860 19 lOMoAR cPSD| 45903860 HOMEWORKS (1) Note: Each table for each method
Compute the forecasts and measures of forecast accuracy, using: 20