PERAMALAN DATA TIME SERIES
PERAMALAN DATA TIME SERIES
DATA TIME SERIES
Time series merupakan data yang
diperoleh dan disusun berdasarkan
urutan waktu atau data yang
dikumpulkan dari waktu ke waktu.
Waktu yang digunakan dapat berupa
minggu, bulan, tahun dan sebagainya.
DATA TIME SERIES
• The rate variable is collected at equally spaced time periods, as
is typical in most time series and forecasting applications.
• Many business applications of forecasting utilize daily, weekly, monthly,
quarterly, or annual data.
• The data may be:
• Instantaneous, such as the viscosity of a chemical product at the point in time where it is
measured;
• It may be cumulative, such as the total sales of a product during the month; or
• It may be a statistic that in some way reflects the activity of the variable during the time
period, such as the daily closing price of a specific stock on the New York Stock Exchange.
CONTOH 1
Harga saham AAPL: 5 tahun, direkam dalam data per minggu
http://finance.yahoo.com/quote/AAPL?ltr=1
CONTOH 2
http://kursdollar.net/
FORECAST
KEGIATAN PERAMALAN (FORECASTING)
Merupakan bagian integral dari pengambilan keputusan.
Mengurangi ketergantungan pada hal-hal yang belum
pasti (intuitif).
Ada saling ketergantungan antar divisi.
Contoh , kesalahan proyeksi penjualan akan mempengaruhi
ramalan anggaran, pengeluaran operasi, arus kas, persediaan, dst.
Dua hal utama dalam proses peramalan yang akurat dan
bermanfaat:
Pengumpulan data yang relevan.
Pemilihan teknik peramalan yang tepat.
FIELD OF FORECASTING
The reason that forecasting is so important is that prediction of future events is a critical
input into many types of planning and decision-making processes, with application to areas
such as the following:
Operation Management: Business organizations
routinely use forecasts of product sales or demand
for services in order to schedule production, control
inventories, manage the supply chain, determine
staffing requirements, and plan capacity
Marketing: Forecasts of sales response to advertising
expenditures, new promotions, or changes in pricing
polices enable businesses to evaluate their
effectiveness, determine whether goals are being
met, and make adjustments.
Finance and Risk Management: Investors in financial
assets are interested in forecasting the returns from their
investments. Financial risk management requires forecasts
of the volatility of asset returns so that the risks
associated with investment portfolios can be evaluated
Economics: Governments, fnancial institutions, and policy
organizations require forecasts of major economic
variables, such as gross domestic product, population
growth, unemployment, interest rates, inflation, job
growth, production, and consumption
Industrial process control
Demography
METODE PERAMALAN
Terdapat dua pendekatan peramalan :
Kualitatif
Kuantitatif.
METODE PERAMALAN KUALITATIF
Metode ini digunakan ketika data historis langka atau bahkan tidak tersedia sama
sekali;
Metode ini (biasanya) menggunakan opini dari para ahli untuk memprediksi
kejadian secara subyektif;
Contoh: penjualan dari produk baru, lingkungan dan teknologi di masa mendatang.
Keuntungan: berguna ketika tidak ada data historis;
Kelemahan: subyektif
GLAD YOU DIDN’T SAY IT
METODE PERAMALAN KUANTITATIF
Metode ini digunakan ketika tersedia data historis;
Metode ini mengkonstruksi model peramalan dari data yang tersedia atau
teori peramalan;
Keuntungan: Obyektif
Metode kuantitatif dibagi menjadi 2 jenis: time series dan causal
Metode peramalan causal
Meliputi faktor-faktor yang berhubungan dengan variabel yang diprediksi seperti analisis regresi.
Mengasumsikan bahwa satu atau lebih faktor (variabel independen) memprediksi masa datang.
Input: variabel
dependent
dan
independent
Proses:
hubungan
sebab-akibat
Output: model
untuk
meramalkan
var dependen
Metode Peramalan time series
merupakan metode kuantitatif untuk menganalisis data masa lampau yang telah dikumpulkan
secara teratur dengan menggunakan teknik yang tepat.
Data historis digunakan untuk memprediksi masa datang
Input: data
historis
Proses:
pembangki
tan proses
Output: model
untuk meramalkan
data masa datang
Hasilnya dapat dijadikan acuan untuk peramalan nilai di masa yang akan datang (Makridakis. S., 1999).
SYARAT-SYARAT PERAMALAN KUANTITATIF
1.
Tersedia info pada waktu lalu
2.
Info tersebut dapat dikuantitatifkan
3.
Diasumsikan pola pada waktu-waktu lalu akan berlanjut di masa yang akan
datang (assumption of constancy)
TIPE-TIPE METODE KUANTITATIF
1. Naif/intuitif
yt 1
yt yt 1
yt
yt
Data mendatang = data sekarang + proporsi
peningkatan
2. Formal
• Berdasarkan prinsip-prinsip statistik
KOMPONEN TIME SERIES
Trend
Cyclical
Seasonal
Random/
horisontal
KOMPONEN/POLA DATA
Terdapat empat pola data yang lazim dalam peramalan:
1. Pola horisontal
2. Pola musiman
3. Pola siklis
4. Pola tren
HORISONTAL
Pola horisontal: Terjadi bila mana data berfluktuasi di sekitar rata-ratanya.
MUSIMAN
Pola musiman: Terjadi bila mana nilai data dipengaruhi oleh faktor musiman
(misalnya kuartal tahun tertentu, bulanan atau mingguan).
Menunjukkan puncak-puncak (peaks) dan lembah-lembah (valleys) yang berulang
dalam interval yang konsisten.
SIKLIS
Pola siklis. Terjadi bila mana datanya dipengaruhi oleh fluktuasi ekonomi jangka
panjang seperti yang berhubungan dengan siklus bisnis.
Pergerakan seperti gelombang yang lebih panjang daripada satu tahun. Belum tentu
berulang pada interval waktu sama.
TREND
Pola trend. Terjadi bila mana ada kecenderungan kenaikan atau penurunan dalam
data.
SIMPLE AVERAGE
•We will first investigate some averaging methods, such as the "simple"
average of all past data.
•Example. Seorang manager toko computer mempunyai data
penjualan notebook perbulan. Dia mempunyai data 12 bulan penjualan
sebagai berikut :
DATA
Bulan
1
2
3
4
5
6
Amount
9
8
9
12
9
12
Bulan
7
8
9
10
11
12
Amount
11
7
13
9
11
10
The computed mean or average of the data = 10.
The manager decides to use this as the estimate for
next demand. Is this a good or bad estimate?
MSE
•We shall compute the "mean squared error":
• The "error" = true amount spent minus the estimated amount.
• The "error squared" is the error above, squared.
•The "SSE" is the sum of the squared errors.
• The "MSE" is the mean of the squared errors.
•The SSE = 36 and the MSE = 36/12 = 3.
KOMPUTASI
Bulan
1
2
3
4
5
6
7
8
9
10
11
12
$
9
8
9
12
9
12
11
7
13
9
11
10
Error
-1
-2
-1
2
-1
2
1
-3
3
-1
1
0
Error Squared
1
4
1
4
1
4
1
9
9
1
1
0
MSE TERBAIK
So how good was the estimator for the next demand ? Let us compare the estimate
(10) with the following estimates: 7, 9, and 12.
Performing the same calculations we arrive at:
Estimator
7
9
10
12
SSE
144
48
36
84
MSE
12
4
3
7
BUKTI ANALISIS
Dapat dibuktikan secara matematis bahwa estimator yang
meminimalkan MSE pada himpunan data random adalah mean.
d n
2
Minimum MSE Yi a 0
da i 1
DATA WITH TREND
Selanjutnya kita lihat data timeseries yang mengandung trend.
Next we will examine the mean to see how well it predicts net income over time for
data having a trend. The next table gives the income before taxes of a PC
manufacturer between 1985 and 1994.
KOMPUTASI DATA
Year $ (millions)
1985
46.163
1986
46.998
1987
47.816
1988
48.311
1989
48.758
1990
49.164
1991
49.548
1992
48.915
1993
50.315
1994
50.768
Mean
48.776
48.776
48.776
48.776
48.776
48.776
48.776
48.776
48.776
48.776
Error Squared Error
-2.613
6.828
-1.778
3.161
-0.960
0.922
-0.465
0.216
-0.018
0.000
0.388
0.151
0.772
0.596
1.139
1.297
1.539
2.369
1.992
3.968
BUKTI EMPIRIS
The question arises: can we use the mean to forecast income if we suspect a trend ?
A look at the graph below shows clearly that we should not do this.
Kasus di atas dapat diselesaikan antara lain dengan menggunakan
regresi trend atau metode perataan yang lain seperti MA ganda,
Metode Eksponensial Smoothing Linear Holt atau Brown.
FORECASTING PROCESS
DIAGRAM FORECASTING PROCESS
Problem definition:
Data collection:
• Understanding of how forecast will be used
by customer
• The desired form of the forecast (e.g., are
monthly forecasts required)
• Obtaining the relevant history for the
variable(s) that are to be forecast,
including historical information
• The key here is “relevant”; not all
historical data are useful for the
current problem
Data analysis:
Model selection and fitting:
• Selection of the
forecasting model to be used
• Time series plots of the data should be
constructed and visually inspected for
recognizable patterns, such as trends
and seasonal or other cyclical
components
• Consists of choosing one or more
forecasting models and fitting the
model to the data
• By fitting, we mean estimating
the unknown model parameters (OLS,
optimization method)
Model validation:
Forecasting model deployment:
• An evaluation of the forecasting model
to determine how it is likely to perform in
the intended application
• A widely used method for
validating: data splitting, where the data
are divided into two segments—a fitting
segment and a forecasting segment
• Involves getting the model and the
resulting forecasts in use by the customer
Monitoring forecasting model
performance:
• Should be an ongoing
activity after the model has been
deployed to ensure that it is still
performing satisfactorily
DATA FOR FORECASTING
http://www.icidigital.com/blog/digital-marketing/migration-nothing-etl-extract-transform-load
EXTRACT
Data extraction refers to obtaining data
from internal sources and from external
sources
Such as third party vendors or government
entities and financial service organizations
TRANSFORMATION
transformation stage involves
applying rules to prevent
duplication of records and dealing
with problems such as missing
information.
Sometimes we refer to the
transformation activities as data
cleaning
Data cleaning is the process of examining data to
detect potential errors, missing data, outliers or
unusual values, or other inconsistencies and then
correcting the errors or problems that are found.
LOAD
Finally, the data are loaded into the data
warehouse where
they are available for modeling and
analysis.
IMPUTATION
Data imputation is the process of correcting
missing data or replacing outliers with an
estimation process.
If the data does not have
any specific trend or
seasonal pattern
Imputation replaces missing or erroneous
values with a “likely” value based on other
available information
Mean value imputation consists of
replacing a missing value with
the sample average calculated from
the non-missing observations.
However, one must be careful if there are
trends or seasonal patterns
IMPUTATION
Stochastic mean value imputation:
Consider the time series 𝑦1 , 𝑦2 , … , 𝑦𝑇 and suppose that one observation
𝑦𝑗 is missing. We can impute the missing value as
where k would be based on the seasonal variability in the data. It is usually chosen as some
multiple of the smallest seasonal cycle in the data, example: 12 for monthly data.
IMPUTATION
Regression imputation
Is a variation of mean value imputation where the imputed value
is computed from a model used to predict the missing value. The
prediction model does not have to be a linear regression model.
REFERENCE
https://onlinecourses.science.psu.edu/stat510/node/47
DATA TIME SERIES
Time series merupakan data yang
diperoleh dan disusun berdasarkan
urutan waktu atau data yang
dikumpulkan dari waktu ke waktu.
Waktu yang digunakan dapat berupa
minggu, bulan, tahun dan sebagainya.
DATA TIME SERIES
• The rate variable is collected at equally spaced time periods, as
is typical in most time series and forecasting applications.
• Many business applications of forecasting utilize daily, weekly, monthly,
quarterly, or annual data.
• The data may be:
• Instantaneous, such as the viscosity of a chemical product at the point in time where it is
measured;
• It may be cumulative, such as the total sales of a product during the month; or
• It may be a statistic that in some way reflects the activity of the variable during the time
period, such as the daily closing price of a specific stock on the New York Stock Exchange.
CONTOH 1
Harga saham AAPL: 5 tahun, direkam dalam data per minggu
http://finance.yahoo.com/quote/AAPL?ltr=1
CONTOH 2
http://kursdollar.net/
FORECAST
KEGIATAN PERAMALAN (FORECASTING)
Merupakan bagian integral dari pengambilan keputusan.
Mengurangi ketergantungan pada hal-hal yang belum
pasti (intuitif).
Ada saling ketergantungan antar divisi.
Contoh , kesalahan proyeksi penjualan akan mempengaruhi
ramalan anggaran, pengeluaran operasi, arus kas, persediaan, dst.
Dua hal utama dalam proses peramalan yang akurat dan
bermanfaat:
Pengumpulan data yang relevan.
Pemilihan teknik peramalan yang tepat.
FIELD OF FORECASTING
The reason that forecasting is so important is that prediction of future events is a critical
input into many types of planning and decision-making processes, with application to areas
such as the following:
Operation Management: Business organizations
routinely use forecasts of product sales or demand
for services in order to schedule production, control
inventories, manage the supply chain, determine
staffing requirements, and plan capacity
Marketing: Forecasts of sales response to advertising
expenditures, new promotions, or changes in pricing
polices enable businesses to evaluate their
effectiveness, determine whether goals are being
met, and make adjustments.
Finance and Risk Management: Investors in financial
assets are interested in forecasting the returns from their
investments. Financial risk management requires forecasts
of the volatility of asset returns so that the risks
associated with investment portfolios can be evaluated
Economics: Governments, fnancial institutions, and policy
organizations require forecasts of major economic
variables, such as gross domestic product, population
growth, unemployment, interest rates, inflation, job
growth, production, and consumption
Industrial process control
Demography
METODE PERAMALAN
Terdapat dua pendekatan peramalan :
Kualitatif
Kuantitatif.
METODE PERAMALAN KUALITATIF
Metode ini digunakan ketika data historis langka atau bahkan tidak tersedia sama
sekali;
Metode ini (biasanya) menggunakan opini dari para ahli untuk memprediksi
kejadian secara subyektif;
Contoh: penjualan dari produk baru, lingkungan dan teknologi di masa mendatang.
Keuntungan: berguna ketika tidak ada data historis;
Kelemahan: subyektif
GLAD YOU DIDN’T SAY IT
METODE PERAMALAN KUANTITATIF
Metode ini digunakan ketika tersedia data historis;
Metode ini mengkonstruksi model peramalan dari data yang tersedia atau
teori peramalan;
Keuntungan: Obyektif
Metode kuantitatif dibagi menjadi 2 jenis: time series dan causal
Metode peramalan causal
Meliputi faktor-faktor yang berhubungan dengan variabel yang diprediksi seperti analisis regresi.
Mengasumsikan bahwa satu atau lebih faktor (variabel independen) memprediksi masa datang.
Input: variabel
dependent
dan
independent
Proses:
hubungan
sebab-akibat
Output: model
untuk
meramalkan
var dependen
Metode Peramalan time series
merupakan metode kuantitatif untuk menganalisis data masa lampau yang telah dikumpulkan
secara teratur dengan menggunakan teknik yang tepat.
Data historis digunakan untuk memprediksi masa datang
Input: data
historis
Proses:
pembangki
tan proses
Output: model
untuk meramalkan
data masa datang
Hasilnya dapat dijadikan acuan untuk peramalan nilai di masa yang akan datang (Makridakis. S., 1999).
SYARAT-SYARAT PERAMALAN KUANTITATIF
1.
Tersedia info pada waktu lalu
2.
Info tersebut dapat dikuantitatifkan
3.
Diasumsikan pola pada waktu-waktu lalu akan berlanjut di masa yang akan
datang (assumption of constancy)
TIPE-TIPE METODE KUANTITATIF
1. Naif/intuitif
yt 1
yt yt 1
yt
yt
Data mendatang = data sekarang + proporsi
peningkatan
2. Formal
• Berdasarkan prinsip-prinsip statistik
KOMPONEN TIME SERIES
Trend
Cyclical
Seasonal
Random/
horisontal
KOMPONEN/POLA DATA
Terdapat empat pola data yang lazim dalam peramalan:
1. Pola horisontal
2. Pola musiman
3. Pola siklis
4. Pola tren
HORISONTAL
Pola horisontal: Terjadi bila mana data berfluktuasi di sekitar rata-ratanya.
MUSIMAN
Pola musiman: Terjadi bila mana nilai data dipengaruhi oleh faktor musiman
(misalnya kuartal tahun tertentu, bulanan atau mingguan).
Menunjukkan puncak-puncak (peaks) dan lembah-lembah (valleys) yang berulang
dalam interval yang konsisten.
SIKLIS
Pola siklis. Terjadi bila mana datanya dipengaruhi oleh fluktuasi ekonomi jangka
panjang seperti yang berhubungan dengan siklus bisnis.
Pergerakan seperti gelombang yang lebih panjang daripada satu tahun. Belum tentu
berulang pada interval waktu sama.
TREND
Pola trend. Terjadi bila mana ada kecenderungan kenaikan atau penurunan dalam
data.
SIMPLE AVERAGE
•We will first investigate some averaging methods, such as the "simple"
average of all past data.
•Example. Seorang manager toko computer mempunyai data
penjualan notebook perbulan. Dia mempunyai data 12 bulan penjualan
sebagai berikut :
DATA
Bulan
1
2
3
4
5
6
Amount
9
8
9
12
9
12
Bulan
7
8
9
10
11
12
Amount
11
7
13
9
11
10
The computed mean or average of the data = 10.
The manager decides to use this as the estimate for
next demand. Is this a good or bad estimate?
MSE
•We shall compute the "mean squared error":
• The "error" = true amount spent minus the estimated amount.
• The "error squared" is the error above, squared.
•The "SSE" is the sum of the squared errors.
• The "MSE" is the mean of the squared errors.
•The SSE = 36 and the MSE = 36/12 = 3.
KOMPUTASI
Bulan
1
2
3
4
5
6
7
8
9
10
11
12
$
9
8
9
12
9
12
11
7
13
9
11
10
Error
-1
-2
-1
2
-1
2
1
-3
3
-1
1
0
Error Squared
1
4
1
4
1
4
1
9
9
1
1
0
MSE TERBAIK
So how good was the estimator for the next demand ? Let us compare the estimate
(10) with the following estimates: 7, 9, and 12.
Performing the same calculations we arrive at:
Estimator
7
9
10
12
SSE
144
48
36
84
MSE
12
4
3
7
BUKTI ANALISIS
Dapat dibuktikan secara matematis bahwa estimator yang
meminimalkan MSE pada himpunan data random adalah mean.
d n
2
Minimum MSE Yi a 0
da i 1
DATA WITH TREND
Selanjutnya kita lihat data timeseries yang mengandung trend.
Next we will examine the mean to see how well it predicts net income over time for
data having a trend. The next table gives the income before taxes of a PC
manufacturer between 1985 and 1994.
KOMPUTASI DATA
Year $ (millions)
1985
46.163
1986
46.998
1987
47.816
1988
48.311
1989
48.758
1990
49.164
1991
49.548
1992
48.915
1993
50.315
1994
50.768
Mean
48.776
48.776
48.776
48.776
48.776
48.776
48.776
48.776
48.776
48.776
Error Squared Error
-2.613
6.828
-1.778
3.161
-0.960
0.922
-0.465
0.216
-0.018
0.000
0.388
0.151
0.772
0.596
1.139
1.297
1.539
2.369
1.992
3.968
BUKTI EMPIRIS
The question arises: can we use the mean to forecast income if we suspect a trend ?
A look at the graph below shows clearly that we should not do this.
Kasus di atas dapat diselesaikan antara lain dengan menggunakan
regresi trend atau metode perataan yang lain seperti MA ganda,
Metode Eksponensial Smoothing Linear Holt atau Brown.
FORECASTING PROCESS
DIAGRAM FORECASTING PROCESS
Problem definition:
Data collection:
• Understanding of how forecast will be used
by customer
• The desired form of the forecast (e.g., are
monthly forecasts required)
• Obtaining the relevant history for the
variable(s) that are to be forecast,
including historical information
• The key here is “relevant”; not all
historical data are useful for the
current problem
Data analysis:
Model selection and fitting:
• Selection of the
forecasting model to be used
• Time series plots of the data should be
constructed and visually inspected for
recognizable patterns, such as trends
and seasonal or other cyclical
components
• Consists of choosing one or more
forecasting models and fitting the
model to the data
• By fitting, we mean estimating
the unknown model parameters (OLS,
optimization method)
Model validation:
Forecasting model deployment:
• An evaluation of the forecasting model
to determine how it is likely to perform in
the intended application
• A widely used method for
validating: data splitting, where the data
are divided into two segments—a fitting
segment and a forecasting segment
• Involves getting the model and the
resulting forecasts in use by the customer
Monitoring forecasting model
performance:
• Should be an ongoing
activity after the model has been
deployed to ensure that it is still
performing satisfactorily
DATA FOR FORECASTING
http://www.icidigital.com/blog/digital-marketing/migration-nothing-etl-extract-transform-load
EXTRACT
Data extraction refers to obtaining data
from internal sources and from external
sources
Such as third party vendors or government
entities and financial service organizations
TRANSFORMATION
transformation stage involves
applying rules to prevent
duplication of records and dealing
with problems such as missing
information.
Sometimes we refer to the
transformation activities as data
cleaning
Data cleaning is the process of examining data to
detect potential errors, missing data, outliers or
unusual values, or other inconsistencies and then
correcting the errors or problems that are found.
LOAD
Finally, the data are loaded into the data
warehouse where
they are available for modeling and
analysis.
IMPUTATION
Data imputation is the process of correcting
missing data or replacing outliers with an
estimation process.
If the data does not have
any specific trend or
seasonal pattern
Imputation replaces missing or erroneous
values with a “likely” value based on other
available information
Mean value imputation consists of
replacing a missing value with
the sample average calculated from
the non-missing observations.
However, one must be careful if there are
trends or seasonal patterns
IMPUTATION
Stochastic mean value imputation:
Consider the time series 𝑦1 , 𝑦2 , … , 𝑦𝑇 and suppose that one observation
𝑦𝑗 is missing. We can impute the missing value as
where k would be based on the seasonal variability in the data. It is usually chosen as some
multiple of the smallest seasonal cycle in the data, example: 12 for monthly data.
IMPUTATION
Regression imputation
Is a variation of mean value imputation where the imputed value
is computed from a model used to predict the missing value. The
prediction model does not have to be a linear regression model.
REFERENCE
https://onlinecourses.science.psu.edu/stat510/node/47