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New Criteria to Compare Interval Estimat
Fuzzy Time Series Methods
Erol Eǧrioǧlu, V. Rezan Uslu and Senem Koc
M Advanced Network System Lab, Chonnam National University
Rischan Mafrur
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Introduction
What is the problem?What is the approach of this paper / contrib
What is the result of this paper?
What is the conclusion?
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Problem
When we want to analyze the time seri
data, in this case is for the forecasting, hdetermine the interval estimates ?
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Approach
1. Fuzzy ARIMA & Fuzzy SARIMA are aimed tointerval estimates.
2. Using both methods then make comparison
the best interval estimates)
3. Use the air pollution time series data of Anbetween March 94 and April 02.
4. Conclude which methods that has the best r
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Requirements
For understanding this paper we shouldunderstand:
1. The concept of Fuzzy ARIMA
2. The concept of Fuzzy SARIMA
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Fuzzy (S)ARIMA
What is this?Fuzzy + AR + I + MA
S : Seasonal
AR : AutoRegressiveI : Integrated
MA : Moving Average
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Why we need AR & MA?
because any autocorrelation between varia
AR : model in which the value of variable in one period is
its values in previous periods.
MA : model account for the possibility of relationship betwvariable and the residuals from previous periods.
Brief Concept
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Before processing the data we need to c
the data stationarity.
If the data is stationer oke, we can conti
but if the data is not stationer we should
the data to stationer. (differencing)
In this paper author combine three methfuzzy regression + AR + I + MA + S
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Lists of Equation
(1) Fuzzy
(2) Simple
(3) Memb
triangular fuz
(4) Memb
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Lists of Equation
(5) Memb
value of Zi shthan predete
(6) Total u
FARIMA
(7) Fuzzy
parameters.
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Lists of Equation(8) Estim
parameters
Model.
(9) Tens
number
(10,1SARIMA m
(8)
(9)
(10)
(11)
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Experiment & ResultNew criteria for comparison of interval estimates : [Use Median Range & Ratio]
Range i = [Lower Limit i - Upper Limit i ], i=1,2MR = Median(Range)
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Ratio
Ratio = k/nk = number of intervals which contain tru
value.
n = number of intervals
the best model = least MR & greatest
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Seasonal Data Plot (Air pollution of An
SARIMA(1,1,result : All
are found statistic
AR(1) : 0.316
MA(1) : 0.970SMA(1) : 0.714
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Getting interval estimates
The Final Result is MR & Ratio.
only SARIMA MR : 63 and Ratio 0.9459
Fuzzy SARIMA MR : 20.1021 and Ratio : 1
because the best model = least greatest Ratio
Fuzzy SARIMA has better result.
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Conclusion
When the normality assumption is alreadsatisfied ARIMA & SARIMA also provid
interval estimates. According to this res
result Fuzzy SARIMA improve the inter
estimates.
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Thank you..