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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..