short run water level forecasting of indravati reservoir

8/7/2019 SHORT RUN WATER LEVEL FORECASTING OF INDRAVATI RESERVOIR

1/14

SHORT RUN WATER LEVEL FORECASTING OF

INDRAVATI RESERVOIR THROUGH ARIMA-

GARCH MODELING

Ankan Kumar Bandyopadhyaya

&

Mahuya Basu

Session IIIC


2/14

BACKGROUND

Emphasis on hydroelectricity power development as anational policy.

Increased concern on carbon emission.

Increase in private participation in power sector

Need for better risk management in electricity sector

Power as a product cannot be stored.

The demand for power is random.

The generation of hydroelectricity is weather dependant.


3/14

RESERVOIR LEVEL & ENERGY AVAILABILITY

Weather affect the reservoirlevel which act as energy

content forhydroelectricity & in turn

affect the generationcapacity of the plant.


4/14

OBJECTIVE

The aim of the study is to develop a model & predict the daily

water level from the information contained in its own pastvalues and current and past values of the error term

through ARIMA-GARCH


5/14

DATA & METHODOLOGY

In sample data: July 1st 2001 toJune 30th 2008

Out of sample data: July 1st 2008

to June 30

th

2009

No structural change in thereservoir during the period & nocapacity enhancement.

In the first seven years therewere 2557 data value for dailywater level (including 366 dailydata of two lip-years 2004 &2008)

Daily res ervoir level of Indravati

624.0

626.0

628.0

630.0

632.0

634.0

636.0

638.0

640.0

642.0

644.0

0 500 1000 1500 2000 2500 3000

days(1st July 2001 to 30th June 2008)

L

evel


6/14

SEASONAL CHARACTER OF DATA

The data depicts a strong seasonal

cycle reaching maximum level during

September- October & steadily

decline afterwards till May & again

starts rising from the second week of

June.

average daily level

626.00

628.00

630.00

632.00

634.00

636.00

638.00

640.00

642.00

9-Feb 20-May 28-Aug 6-Dec 15-Mar 23-Jun

date

reservoirlevel

SD of daily leve l

0.00

1.00

2.00

3.00

4.00

5.00

6.00

9- Feb 20- May 28- Aug 6- Dec 15- Mar 23- Jun

date

SD

the standard deviation of the value

changes over time period. The SD is

maximum during July-September &minimum during January-March. The

period of high SD is normally followed by

high SD & period of low SD is normally

followed by low SD


7/14

REMOVING SEASONALITY & TREND

An average year is considered by taking theeight years average for each day

This average year is used to smooth out the

seasonality by taking the difference of thedaily water level from long term average

Deseasonalised reservoir level data

-10.000

-5.000

0.000

5.000

10.000

15.000

0 500 1000 1500 2000 2500 3000

d a y s

d

eseaso

n

allevel

Dicky Fuller unit root test is used tocheck the stationary condition which

indicates that the series is not stationary

first difference is taken to remove thenon stationary character present

F irs t Differenc e of de-seas onal level

-8 .0 0 0

-6 .0 0 0

-4 .0 0 0

-2 .0 0 0

0 .0 0 0

2 .0 0 0

4 .0 0 0

6 .0 0 0

8 .0 0 0

0 5 00 1 0 0 0 1 5 0 0 2 0 0 0 25 0 0 3 0 0 0

d a y s

valu

es


8/14

ARIMA ORDER DETERMINATION

Both ACF & PACF is significant till three period lag with no

other significant spike

Akaikes information criteria is used as the main measure for

selecting the AR & MA order

all possible ARIMA combination is considered from ARIMA

(1,1,1) to ARIMA ( 4,1,4)

Considering the result an ARIMA (4, 1, 3) model is selected


9/14

TEST OF HETEROSCEDASTICITY

An ARCH-LM test is conducted & a significant presence ofheteroscedasticity is identified.

Including the ARCH effect, the study fits ARIMA( 4,1,3) GARCH(1,1) model

The coefficient of MA(2) , MA(3) & AR(3) & AR(4) becomestatistically insignificant

The study drops those terms from the equation & fit anARIMA ( 2,1,1 ) GARCH(1,1) model.


10/14

FORECASTING RESULT

For all forecasted result the ARIMA(2, 1, 1) with GARCH (1, 1) model

works better as compare to the

simple ARIMA model

the model work better in short runduration of one month as compare

to three months duration

the model work better during Jan-

March period when daily SD of thewater level is lower as compare to

July-September when daily SD of

the reservoir level is the maximum.

ARIMA( 4,1,3) Forecast Result

Jul-08

July-

Sept 08 Jan-09

Jan-

Mar09

MAE 0.117 0.175 0.022 0.057

Theil Inequality

Coeff 0.802 0.867 0.71 0.79

ARIMA(2,1,1) with GARCH(1,1) Forecast result

MAE 0.09 0.146 0.02 0.056

Theil Inequality

Co-eff 0.5 0.52 0.69 0.77


11/14

Forecasted v/s Actual level data using ARIMA & ARIMA-GAARCH

model during high variance Period

July Forecast ARIMA

624.0

625.0

626.0

627.0

628.0

629.0

630.0

631.0

1 4 7 10 1 3 16 19 2 2 25 2 8 31

day

Level

Actual

Fitted

ly-Sep

e

a

6 1 5 . 0

6 2 0 . 0

6 2 5 . 0

6 3 0 . 0

6 3 5 . 0

6 4 0 . 0

6 4 5 . 0

1 8 1 5 22 2 9 3 6 4 3 5 0 57 6 4 7 1 7 8 85 9 2

d a y

L

eve

l

A c tual

Fitted

ly e a

wi

h G

CH Effe

625.5

626.0

626.5

627.0

627.5

628.0

1 4 7 10 1 3 16 19 2 2 2 5 28 3 1

day

level

A c t u a l

Fitted

ly-Se p e a wi h G CH Effe

615.0

620.0

625.0

630.0

635.0

640.0

645.0

1 7 1 3 1 9 25 3 1 3 7 43 4 9 5 5 6 1 67 7 3 7 9 85 9 1

day

level Actual

Fitted


12/14

Forecasted v/s Actual level data using ARIMA & ARIMA-GARCH

model during low variance Period

Jan Forecast ARIMA

634.00

634.50

635.00

635.50

636.00

636.50

637.00

1 4 7 10 13 16 19 22 25 2 8 31

day

level

Actual

Fitted

a

-!

a" #

h$ % "

e#a

&

'

624.00

626.00

628.00

630.00

632.00

634.00

636.00

638.00

1 8 1 5 22 2 9 36 43 5 0 5 7 64 7 1 7 8 85

day(

level

Actual

Fitted

)

a0

1

2

3 e4

a 56

wi6

h G7

8 CHEffe4

6

634.00

634.50

635.00

635.50

636.00

636.50

637.00

1 4 7 10 1 3 1 6 19 2 2 25 28 31

day

level

Actual

Fitted

a - a e a wi h G CH Effe

624.00

626.00

628.00

630.00

632.00

634.00

636.00

638.00

1 8 1 5 2 2 2 9 36 4 3 5 0 5 7 6 4 71 7 8 85

day

level

Actual

Fitted


13/14

CONCLUSIONS

The model may act as a short run production planning tool for

hydro generation

The model may indicate the exposure of the firm to weather

risk &necessity of using proper risk management tool.

The model may work as a basis on which the firm can decide

its trading position in the spot & future energy and/or carbonmarket.


14/14

Thanks

short run water level forecasting of indravati reservoir

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