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Register a new userA Study of Prediction Methods by Using Seasonal Time Series
دراسة طرائق التنبؤ باستخدام المتسلسلات الزمنية الموسمية
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Added by
University of Aleppo رسالة ماجستير
Publication date
2017
fields
Mathematical Statistics
and research's language is
العربية
Created by
Omar Bitar
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استعرضنا في هذا العمل بعض أهم أساليب التنبؤ بالمتسلسلات الزمنية وهي تحليل المتسلسلات الزمنية إلى مركباتها الأساسية (اتجاه عام، موسمية، دورية، عشوائية)، طرائق التمهيد الأسي، نماذج الانحدار الذاتي والمتوسطات المتحركة التكاملية، ثم استعرضنا عدة طرائق هجينة للتنبؤ، ثم قدمنا طريقة جديدة مقترحة للتنبؤ تعتمد على دمج طريقتي التمهيد الأسي و بوكس-جنكينز وذلك وفق المتوسط الموزون بقيم معايير متوسط الأخطاء المطلق النسبي MAPE لكلا الطريقتين، وطبقنا الطرائق السابقة على ثلاث متسلسلات زمنية موسمية، الأولى متسلسلة درجات الحرارة الجافة ساعياُ في مدينة حلب وذلك في شهر آب للعام 2011 أي طول الدورة الموسمية s=24، والثانية متسلسلة كمية إنتاج الحليب شهرياً في استراليا مقاسة بالرطل لكل بقرة وذلك من شهر كانون الثاني عام 1962 ولغاية شهر كانون الأول عام 1975 أي طول الدورة الموسمية s=12، أما الثالثة متسلسلة كمية الكهرباء المنتجة في استراليا فصلياً وذلك في الفترة الممتدة من آذار 1956 ولغاية أيلول للعام 1994 أي طول الدورة الموسمية s=4، وقارننا النتائج التي توصلنا إليها فكانت أفضل طريقة للتنبؤ هي الطريقة المقترحة.
We discussed in this work some predictive methods for time series and it is decomposing time series to its component (trend, Seasonality, cycle, random), Exponential smoothing, ARIMA, then we discussed some combining methods, then we formed a new combine for predict time series which depends on combining exponential smoothing and ARIMA using weighted average with MAPE weights, and applied all methods above on three seasonal time series , first hourly temperature in Aleppo in august 2011 ,second monthly milk production peer cow in Australia from Jan 1962 to Dec 1975,third quartly electricity production in Australia from Mar 1956 to Sep 1994, and compared the results which approved that the suggested method is the best.
References used
Hyndman R.; Kandhakar Y., 2008- Automatic Time Series Forecasting: the Forecast Package for R. Journal of Statistical Software, 26(3), 1-22.
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حظيت نمذجة وتوقع السلاسل الزمنية بأهمية كبيرة في العديد من المجالات التطبيقية كالتنبؤ بالطقس وأسعار العملات ومعدلات استهلاك الوقود والكهرباء، إن توقع السلاسل الزمنية من شأنه أن يزود المنظمات والشركات بالمعلومات الضرورية لاتخاذ القرارات الهامة، وبسبب
أهمية هذا المجال من الناحية التطبيقية فإن الكثير من الأعمال البحثية التي جرت ضمنه خلال السنوات الماضية، إضافةً إلى العدد الكبير من النماذج والخوارزميات التي تم اقتراحها في أدب البحث العلمي والتي كان هدفها تحسين كل من الدقة والكفاءة في نمذجة وتوقع السلاسل الزمنية.
The study aims at comparing ARIMA models and the exponential
smoothing method in forecasting. This study also highlights the special
and basic concepts of ARIMA model and the exponential smoothing
method.
The comparison focuses on the ability
of both methods to forecast
the time series with a narrow range of one point to another and the time
series with a long range of one point to another, and also on the different
lengths of the forecasting periods. Currency exchange rates of Shekel to
American dollar were used to make this comparison in the period
between 25/1/2010 to 22/10/2016. In addition, weekly gold prices were
considered in the period between 10/1/2010 to 23/10/2016. RMSE
standard was used in order to compare between both methods. In this
study, the researcher came up with the conclusion that ARIMA models
give a better forecasting for the time series with a long range of one point
to another and for long term forecasting, but cannot produce a better
forecasting for time series with a narrow range of one point to another as
in currency exchange prices.
On the contrary, exponential smoothing method can give better
forecasting for Exchange Rates that has a narrow range of one point to
another for its time series, while it cannot give better forecasting for long
term forecasting periods
The study and design of water dams depend essential on prediction of water volumes
or future predicted in rivers, by using the time series analysis of the historical
measurements.
The research aims to make statistical study of monthly water volume
s incoming in
AL-Aroos River in Syrian coastal and future prediction of these volumes. And the
Box-Jenkins models is adopt to analysis the time series data, because of its high accuracy.
We attend the monthly water volumes for 15 years. And after doing the wanted tests on
model residuals we found that the best model to represent the data is SARIMA(0,1,2)
(1,2,1)12 , and after dividing the data to 14 years to build the model and one year to test it ,
and depending on the smallest of weighted mean of criteria RMSE, MAP, MAE,. The best
predicted model is SARIMA (1,1,0) (0,1,1)12 and the model give the nearest predicted of
measured data actually.
The study and design of water-intakes on springs is based on the analysis of time series of
historical measurements to achieve prediction of incoming water volumes or future
expected.
The research aims to model the monthly water flows of AL-SIN Sp
ring in Syrian Coast
and future expectations of these flows, by adopting the Box-Jenkins models to analyze the
time series data, due to its reliable accuracy. Monthly water flows, thus, monthly volumes,
for 101 month (from June 2008 to October 2016) were processed. Performing the stability
of the time series on variance and median and non-seasonality and making the wanted tests
on model residuals, we found that the best model to represent the data is SARIMA(2,0,1)
(2,1,0)12 , and after dividing the data into 81 month to build the model and 20 month to test
it. Depending on the smallest of weighted mean of criteria RMSE, MAP, MAE,. The best
predicted model was SARIMA (3,1,0) (1,1,0)12 and the model gave the nearest predicted
values to actually measured data in spring.
The four components of temperature (max., min.) phenomena, seasonal(S), Trend(T),
cyclical(C), and random (I) for Tartous city have been studied. Four different methods
(Average percentages method, Percentage of the general trend method, The ratio
of the
moving average method, Link Relative method) are used to deduct the (S) components
and seasonal index for each method is determined.
The statistical inferences pointed that the Average percentages method can be used in
the prediction of temperature. for the year 2003 depending on a historical record (1957-
2002). The result of this deduction showed that the temperature is a cyclical phenomena.
The known statistical test like mean, Standard deviation and cumulative probability have
been done which showed a good correlation between the predicted and historical data.
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