2024年2月29日发(作者：庄安露)
I.J. Modern Education and Computer Science, 2017, 4, 57-63
Published Online April 2017 in MECS (/)
DOI: 10.5815/ijmecs.2017.04.07
A Study of Time Series Models ARIMA and ETS
Er. Garima Jain
Galgotias College of Engineering and Technology/Computer Science, , 201310, India
Email: jaingarima2011@
Dr. Bhawna Mallick
Galgotias College of Engineering and Technology /HOD (Computer Science), , 201310, India
Email: k@
Abstract—The aim of the study is to introduce some of the sky to extremely advance computerized
appropriate approaches which might help in improving mathematical Models [6].
the efficiency of weather’s parameters. Weather is a
ive
natural phenomenon for which forecasting is a great
challenge today. Weather parameters such as Rainfall,
The main goal of the study is to research a technique
Relative Humidity , Wind Speed , Air Temperature are
that improves the forecasting estimate of various
highly non-linear and complex phenomena, which
parameters. We would like to match the forecasting of
include statistical simulation and modeling for its correct
automatic forecasting methods in predicting the weather
forecasting. Weather Forecasting is used to simplify the
parameters such as Rainfall, Relative Humidity, Air
purpose of knowledge and tools which are used for the
pressure and Wind Speed etc. However predicting the
state of atmosphere at a given place. The expectations are
weather considers many forms, which mainly depend
becoming more complicated due to changing weather
upon the required applications. The forecasting challenge
state. There are different software and their types are
of weather is equal to very first major difficulty depend
available for Time Series forecasting. Our aim is to
on non-linear equations which leads to numerical means
analyze the parameter and do the comparison of some
and mathematical physics. However meteoric knowledge
strategies in predicting these temperatures. Here we tend
is tentative (unsure) in nature where knowledge on
to analyze the data of given parameters and to notice their
weather is mostly outlined.
predictions for a particular period by using the strategy of
Weather knowledge has the noises and outliers this is
Autoregressive Integrated Moving Average (ARIMA)
why analyzed may not be correct. Noises are the random
and Exponential Smoothing (ETS) .The data from
error therefore we need prepossessing of a Weather
meteorological centers has been taken for the comparison
knowledge to improve the standard of knowledge for
of methods using packages such as ggplot2, forecast,
precise weather prediction, or to improve the value of
time Date in R and automatic prediction strategies which
exact data for weather estimation. This paper gives an
are available within the package applied for modeling
idea to compare the two automatic forecasting methods
with ARIMA and ETS methods. On the basis of accuracy
ETS (Exponential Smoothing) and ARIMA
we tend to attempt the simplest methodology and then we
(Autoregressive Integrate Moving Average) using the
will compare our model on the basis of MAE, MASE,
data of various weather parameters such as Rainfall,
MAPE and RMSE. An identification of model will be the
Relative Humidity, Air Temperature , Pressure , Wind
chromatic checkup of both the ACF and PACF to
speed etc. For convenience the paper provided with some
hypothesize many probable models which are going to be
basic definition and background that designates the
projected by selection AIC, AICc and BIC.
strategies followed by the analysis of weather data by
estimation and verification of varies forecasting methods.
Index Terms—ARIMA (Autoregressive Integrated
The accuracy of various strategies is compared by MAE
Moving Average), ETS (Exponential Smoothing), AIC
(Moving Absolute Error), MASE (Moving Absolute
(Akaike’s Information Criteria), and BIC (Bayesian
Scaled Error), MAPE (Moving Absolute Percentage
Information Criteria), AIC (Akaike’s Information
Error) and RMSE (Root Mean Square Error). We also
Criteria), RMSE (Root Mean Square Error).
include the criteria AIC (Akaike’s Information Criteria)
and BIC (Bayesian Information Criteria).The methods
which gives the best forecast will use for comparison and
I.
INTRODUCTION prediction. As of India Meteorological Department
information can even be composed that is over all India
Weather Prediction System is having most complex
climate stations head place of work. In information set
Systems Equation that can only solve by Computer.
we are having the parameters that are: Air Temperature,
Weather Forecasting is an inspiration about future
Rainfall, Relative Humidity and Wind Speed among
weather. There are various techniques concern with
which we consider one. In this paper ARIMA
weather forecasting from comparatively easy observation
(Autoregressive Integrated Moving Average) and ETS
Copyright © 2017 MECS I.J. Modern Education and Computer Science, 2017, 4, 57-63
58 A Study of Time Series Models ARIMA and ETS
(Exponential Smoothing) is use for analysis and
predicting weather information that are mentioned above.
A Comparative study brings between the ETS and
ARIMA Model through SSE, MAE, RMSE, MASE and
MAPE also include the criteria AIC and BIC result from
the given parameters. Automatic forecasting by ARIMA
and ETS is performed by using the forecast, time Date,
ggplot2, and Zoo packages in R for Time Series analysis,
and also various attributes are predicted by considering
Correlations. Efforts are being intense to use statistic
Autoregressive Moving Average (ARMA) model to
forecast or to predict hydrological information. The
ARMA Model is use even as a result of its theoretical
base in hydrological Studies.
e
The paper is organized as follows. Section II gives you
study on topic as Literature review on related work.
Section III presents some theory and concepts of time
series ARIMA modeling and forecasting, used to
analyses the algorithm on which our future
implementation will based on. Section IV gives some
overview about Time Series Concept. Section V provides
the detailed analysis of ETS Model and the comparison
of proposed models. Section VI gives some suggestions
for further research and areas of interests.
II.
RELATED
WORKS
A.
Defination
Around the world weather predicting is one of the
most challenging difficulties, due to its practical value in
popular scope for scientific study and meteorology. The
different , Statistical Decomposition
Models, Exponential Smoothing Model (ETS) and
Autoregressive Integrated Moving Average (ARIMA)
Model variable Time series and following informative
variables etc., is used for forecasting purposes. Several
Trainings have taken place among the analysis of pattern
and circulation in various parameters in different regions
of the World. Regression Analysis could be applied for
statistical technique and it should be widely used in
several sciences and many other relevant Areas.
B. Background
Agrawal et al. (1980) explained the phenomena for
time series regression models for forecasting the yield of
rice in Raipur district on weekly data using weather
parameters [1].Box and Jenkins (1994), in early 1970's,
pioneered in developing methodologies for statistic
representing within the univariate case often referred to
as Univariate Box-Jenkins (UBJ) ARIMA modeling in
this approach of the author [2]. Akaike, H. (1976) an
information criterion (AIC) which is used as a parameter
estimation to check the performance of Model which
gives history for the development of statistical theory
testing in time series analysis was studied concisely and
it was pointed out that the theory testing procedure is not
effectively defined as the technique for statistical model
identification. The most likelihood estimation process
was reviewed and a new estimate least information
theoretical criterion (AIC) estimate was introduced [4].
Hyndman, R.J.,& Kandahar, Y(2007). Automatic time
series for forecasting: the forecast package for R .Monash
University, Department of Econometrics and Business
Statistics [5]. Weather forecasts provide critical
information about future weather. There are various
techniques involved in weather forecasting, from
relatively simple observation of the sky to highly
complex computerized scientific models (M. Tektas,
2010) [6].An Integrated Approach for Weather
Forecasting based on Data Mining and Forecasting
Analysis by Krishna where in this paper the
weather data was considered with attributes, such as wind
pressure, humidity, Temperature, Forecast and Type, of
Visakhapatnam city for a period of 97days. The
forecasting experiment was carried out for test, the
weather condition for the following 15 days by enabling
the ARIMA model to predict the forecasts [7]. An
Introductory Study on Time Series Modeling and
Forecasting by Ratnadip Adhikari and R. K. Agrawal has
given an idea about Time series forecasting as a fast
growing area of research which provides many scope for
predicting future works. One of them is the Combining
Approach, i.e. to combine a number of approaches to
improve forecast accuracy. Combining with other
analysis in time series prediction, we have thought to
estimate an efficient combining model, in future with the
aim of further studies in time series modeling and
forecasting [8].Prediction Of Rainfall Using Data
Minning Technique Over by Pinky Saikia Dutta which
describe the model by considering temperature, wind
speed, Mean sea level as Predictors. They found 63%
accuracy in variation of rainfall for our proposed model.
The model can forecast monthly rainfall. Some predictor
like wind direction is not included due to constraints on
data collection which could give more accurate result.
The work can be extended for multiple stations in future.
The resulted rainfall amounts was intended to help
farmers in making decision about their
crop[9].Mahmudur Rahman, A.H.M. Saiful Islam , Sahah
Yaser Maqnoon Nadvi , Rashedur M Rahman (2013)
consider Arima and Anfis Model and explained how
ARIMA Model can more efficiently capture the dynamic
behavior of the weather property say, Minimum
Temperature , Maximum Temperature, Humidity and Air
pressure which must be compared by different
performance metrics, such as, with Root Mean Square
Error (RMSE), R-Square Error and The Sum of the
Square Error(SSE) and author can prove that ARIMA
would give the more efficient result than other modeling
techniques like ANFIS[10]. Prediction of rainfall using
an autoregressive integrated moving average model: Case
of Kinshasa city (Democratic Republic of the Congo),
from the period of 1970 to 2009 by Dedetemo Kimilita
Patrick1, Phuku Phuati Edmond2, Tshitenge Mbwebwe
Jean-Marie2, Efoto Eale Louis2, Koto-te-Nyiwa
Ngbolua3, There aim is to present study of the test a
Copyright © 2017 MECS I.J. Modern Education and Computer Science, 2017, 4, 57-63
A Study of Time Series Models ARIMA and ETS 59
model of simulation on the monthly series of
precipitations data from the Binza meteorological station
of Kinshasa/Democratic Republic of the Congo. After
their stationnarization of the Time series, we applied an
Auto-Regressive Integrated Moving Average (ARIMA)
model into the starting series. There model also makes it
possible to predict implication of rainfall on the lifestyle
of the Kinshasa inhabitants [11].
III.
AUTO
REGRESSIVE
INTEGRATED
MOVING
AVERAGE
ARIMA Stand for Auto Regressive Integrated Moving
Average. ARIMA model was popularized by Box and
Jenkins (1976).It is combination of three statistical
models. It uses Autoregressive, Integrated and Moving
Average (ARIMA) model for statistical information. The
ARIMA Model analyze and Forecasts uniformly spaced
univariate statistic information, transmission of function
data, and intercession information that is done by using
Auto Regressive Integrated Moving Average (ARIMA)
and Auto Regressive Moving Average (ARMA).An
ARIMA Model forecasts a value in a response of time
series which is linear combination of its own related past
values, past Errors and current past values of alternative
Time Series. ARIMA Model aims to explain the Auto
Correlation within the information and may applied to
stationary and non-stationary statistic. The Model written
as ARIMA (p, d, q) where p, d, q≥ ARIMA Model
corresponds to ARMA after finitely many times
differences the data .The elements p and q are the order
for Auto Regressive and Moving average Components,
because the degree of differencing is written as d.
Differencing is usually accustomed eliminated the Trend
which may Linear and Exponential in a Time Series.
The differencing order d relates that how many times
the method yt must be differenced to become stationary.
The prediction method was applied by summing last
period’s value with some constant, this indirectly help to
estimate the prediction changes on a mean at specific
interval of time. Various Transformation Techniques may
be used for variance stabilization, e.g.., Box-cox
Transformation, Log Transformations. We can also make
use of Auto Correlation Function (ACF) to visualize if
the statistic is stationary or not. Auto Regressive
indicated the Regression of a variable itself. In ARE
Models the forecasting variables is a linear combination
of its own earlier observations.
An AR (p) Model is often delineated as:
2024年2月29日发(作者：庄安露)
I.J. Modern Education and Computer Science, 2017, 4, 57-63
Published Online April 2017 in MECS (/)
DOI: 10.5815/ijmecs.2017.04.07
A Study of Time Series Models ARIMA and ETS
Er. Garima Jain
Galgotias College of Engineering and Technology/Computer Science, , 201310, India
Email: jaingarima2011@
Dr. Bhawna Mallick
Galgotias College of Engineering and Technology /HOD (Computer Science), , 201310, India
Email: k@
Abstract—The aim of the study is to introduce some of the sky to extremely advance computerized
appropriate approaches which might help in improving mathematical Models [6].
the efficiency of weather’s parameters. Weather is a
ive
natural phenomenon for which forecasting is a great
challenge today. Weather parameters such as Rainfall,
The main goal of the study is to research a technique
Relative Humidity , Wind Speed , Air Temperature are
that improves the forecasting estimate of various
highly non-linear and complex phenomena, which
parameters. We would like to match the forecasting of
include statistical simulation and modeling for its correct
automatic forecasting methods in predicting the weather
forecasting. Weather Forecasting is used to simplify the
parameters such as Rainfall, Relative Humidity, Air
purpose of knowledge and tools which are used for the
pressure and Wind Speed etc. However predicting the
state of atmosphere at a given place. The expectations are
weather considers many forms, which mainly depend
becoming more complicated due to changing weather
upon the required applications. The forecasting challenge
state. There are different software and their types are
of weather is equal to very first major difficulty depend
available for Time Series forecasting. Our aim is to
on non-linear equations which leads to numerical means
analyze the parameter and do the comparison of some
and mathematical physics. However meteoric knowledge
strategies in predicting these temperatures. Here we tend
is tentative (unsure) in nature where knowledge on
to analyze the data of given parameters and to notice their
weather is mostly outlined.
predictions for a particular period by using the strategy of
Weather knowledge has the noises and outliers this is
Autoregressive Integrated Moving Average (ARIMA)
why analyzed may not be correct. Noises are the random
and Exponential Smoothing (ETS) .The data from
error therefore we need prepossessing of a Weather
meteorological centers has been taken for the comparison
knowledge to improve the standard of knowledge for
of methods using packages such as ggplot2, forecast,
precise weather prediction, or to improve the value of
time Date in R and automatic prediction strategies which
exact data for weather estimation. This paper gives an
are available within the package applied for modeling
idea to compare the two automatic forecasting methods
with ARIMA and ETS methods. On the basis of accuracy
ETS (Exponential Smoothing) and ARIMA
we tend to attempt the simplest methodology and then we
(Autoregressive Integrate Moving Average) using the
will compare our model on the basis of MAE, MASE,
data of various weather parameters such as Rainfall,
MAPE and RMSE. An identification of model will be the
Relative Humidity, Air Temperature , Pressure , Wind
chromatic checkup of both the ACF and PACF to
speed etc. For convenience the paper provided with some
hypothesize many probable models which are going to be
basic definition and background that designates the
projected by selection AIC, AICc and BIC.
strategies followed by the analysis of weather data by
estimation and verification of varies forecasting methods.
Index Terms—ARIMA (Autoregressive Integrated
The accuracy of various strategies is compared by MAE
Moving Average), ETS (Exponential Smoothing), AIC
(Moving Absolute Error), MASE (Moving Absolute
(Akaike’s Information Criteria), and BIC (Bayesian
Scaled Error), MAPE (Moving Absolute Percentage
Information Criteria), AIC (Akaike’s Information
Error) and RMSE (Root Mean Square Error). We also
Criteria), RMSE (Root Mean Square Error).
include the criteria AIC (Akaike’s Information Criteria)
and BIC (Bayesian Information Criteria).The methods
which gives the best forecast will use for comparison and
I.
INTRODUCTION prediction. As of India Meteorological Department
information can even be composed that is over all India
Weather Prediction System is having most complex
climate stations head place of work. In information set
Systems Equation that can only solve by Computer.
we are having the parameters that are: Air Temperature,
Weather Forecasting is an inspiration about future
Rainfall, Relative Humidity and Wind Speed among
weather. There are various techniques concern with
which we consider one. In this paper ARIMA
weather forecasting from comparatively easy observation
(Autoregressive Integrated Moving Average) and ETS
Copyright © 2017 MECS I.J. Modern Education and Computer Science, 2017, 4, 57-63
58 A Study of Time Series Models ARIMA and ETS
(Exponential Smoothing) is use for analysis and
predicting weather information that are mentioned above.
A Comparative study brings between the ETS and
ARIMA Model through SSE, MAE, RMSE, MASE and
MAPE also include the criteria AIC and BIC result from
the given parameters. Automatic forecasting by ARIMA
and ETS is performed by using the forecast, time Date,
ggplot2, and Zoo packages in R for Time Series analysis,
and also various attributes are predicted by considering
Correlations. Efforts are being intense to use statistic
Autoregressive Moving Average (ARMA) model to
forecast or to predict hydrological information. The
ARMA Model is use even as a result of its theoretical
base in hydrological Studies.
e
The paper is organized as follows. Section II gives you
study on topic as Literature review on related work.
Section III presents some theory and concepts of time
series ARIMA modeling and forecasting, used to
analyses the algorithm on which our future
implementation will based on. Section IV gives some
overview about Time Series Concept. Section V provides
the detailed analysis of ETS Model and the comparison
of proposed models. Section VI gives some suggestions
for further research and areas of interests.
II.
RELATED
WORKS
A.
Defination
Around the world weather predicting is one of the
most challenging difficulties, due to its practical value in
popular scope for scientific study and meteorology. The
different , Statistical Decomposition
Models, Exponential Smoothing Model (ETS) and
Autoregressive Integrated Moving Average (ARIMA)
Model variable Time series and following informative
variables etc., is used for forecasting purposes. Several
Trainings have taken place among the analysis of pattern
and circulation in various parameters in different regions
of the World. Regression Analysis could be applied for
statistical technique and it should be widely used in
several sciences and many other relevant Areas.
B. Background
Agrawal et al. (1980) explained the phenomena for
time series regression models for forecasting the yield of
rice in Raipur district on weekly data using weather
parameters [1].Box and Jenkins (1994), in early 1970's,
pioneered in developing methodologies for statistic
representing within the univariate case often referred to
as Univariate Box-Jenkins (UBJ) ARIMA modeling in
this approach of the author [2]. Akaike, H. (1976) an
information criterion (AIC) which is used as a parameter
estimation to check the performance of Model which
gives history for the development of statistical theory
testing in time series analysis was studied concisely and
it was pointed out that the theory testing procedure is not
effectively defined as the technique for statistical model
identification. The most likelihood estimation process
was reviewed and a new estimate least information
theoretical criterion (AIC) estimate was introduced [4].
Hyndman, R.J.,& Kandahar, Y(2007). Automatic time
series for forecasting: the forecast package for R .Monash
University, Department of Econometrics and Business
Statistics [5]. Weather forecasts provide critical
information about future weather. There are various
techniques involved in weather forecasting, from
relatively simple observation of the sky to highly
complex computerized scientific models (M. Tektas,
2010) [6].An Integrated Approach for Weather
Forecasting based on Data Mining and Forecasting
Analysis by Krishna where in this paper the
weather data was considered with attributes, such as wind
pressure, humidity, Temperature, Forecast and Type, of
Visakhapatnam city for a period of 97days. The
forecasting experiment was carried out for test, the
weather condition for the following 15 days by enabling
the ARIMA model to predict the forecasts [7]. An
Introductory Study on Time Series Modeling and
Forecasting by Ratnadip Adhikari and R. K. Agrawal has
given an idea about Time series forecasting as a fast
growing area of research which provides many scope for
predicting future works. One of them is the Combining
Approach, i.e. to combine a number of approaches to
improve forecast accuracy. Combining with other
analysis in time series prediction, we have thought to
estimate an efficient combining model, in future with the
aim of further studies in time series modeling and
forecasting [8].Prediction Of Rainfall Using Data
Minning Technique Over by Pinky Saikia Dutta which
describe the model by considering temperature, wind
speed, Mean sea level as Predictors. They found 63%
accuracy in variation of rainfall for our proposed model.
The model can forecast monthly rainfall. Some predictor
like wind direction is not included due to constraints on
data collection which could give more accurate result.
The work can be extended for multiple stations in future.
The resulted rainfall amounts was intended to help
farmers in making decision about their
crop[9].Mahmudur Rahman, A.H.M. Saiful Islam , Sahah
Yaser Maqnoon Nadvi , Rashedur M Rahman (2013)
consider Arima and Anfis Model and explained how
ARIMA Model can more efficiently capture the dynamic
behavior of the weather property say, Minimum
Temperature , Maximum Temperature, Humidity and Air
pressure which must be compared by different
performance metrics, such as, with Root Mean Square
Error (RMSE), R-Square Error and The Sum of the
Square Error(SSE) and author can prove that ARIMA
would give the more efficient result than other modeling
techniques like ANFIS[10]. Prediction of rainfall using
an autoregressive integrated moving average model: Case
of Kinshasa city (Democratic Republic of the Congo),
from the period of 1970 to 2009 by Dedetemo Kimilita
Patrick1, Phuku Phuati Edmond2, Tshitenge Mbwebwe
Jean-Marie2, Efoto Eale Louis2, Koto-te-Nyiwa
Ngbolua3, There aim is to present study of the test a
Copyright © 2017 MECS I.J. Modern Education and Computer Science, 2017, 4, 57-63
A Study of Time Series Models ARIMA and ETS 59
model of simulation on the monthly series of
precipitations data from the Binza meteorological station
of Kinshasa/Democratic Republic of the Congo. After
their stationnarization of the Time series, we applied an
Auto-Regressive Integrated Moving Average (ARIMA)
model into the starting series. There model also makes it
possible to predict implication of rainfall on the lifestyle
of the Kinshasa inhabitants [11].
III.
AUTO
REGRESSIVE
INTEGRATED
MOVING
AVERAGE
ARIMA Stand for Auto Regressive Integrated Moving
Average. ARIMA model was popularized by Box and
Jenkins (1976).It is combination of three statistical
models. It uses Autoregressive, Integrated and Moving
Average (ARIMA) model for statistical information. The
ARIMA Model analyze and Forecasts uniformly spaced
univariate statistic information, transmission of function
data, and intercession information that is done by using
Auto Regressive Integrated Moving Average (ARIMA)
and Auto Regressive Moving Average (ARMA).An
ARIMA Model forecasts a value in a response of time
series which is linear combination of its own related past
values, past Errors and current past values of alternative
Time Series. ARIMA Model aims to explain the Auto
Correlation within the information and may applied to
stationary and non-stationary statistic. The Model written
as ARIMA (p, d, q) where p, d, q≥ ARIMA Model
corresponds to ARMA after finitely many times
differences the data .The elements p and q are the order
for Auto Regressive and Moving average Components,
because the degree of differencing is written as d.
Differencing is usually accustomed eliminated the Trend
which may Linear and Exponential in a Time Series.
The differencing order d relates that how many times
the method yt must be differenced to become stationary.
The prediction method was applied by summing last
period’s value with some constant, this indirectly help to
estimate the prediction changes on a mean at specific
interval of time. Various Transformation Techniques may
be used for variance stabilization, e.g.., Box-cox
Transformation, Log Transformations. We can also make
use of Auto Correlation Function (ACF) to visualize if
the statistic is stationary or not. Auto Regressive
indicated the Regression of a variable itself. In ARE
Models the forecasting variables is a linear combination
of its own earlier observations.
An AR (p) Model is often delineated as: