1. FORECASTING THE SEISMICITY OF KOYNA – WARNA
REGION, INDIA USING THE ERROR CORRECTION
MODEL
D.V.Ramana *,J.Pavan Kumar ,R.N.Singh and R.K.Chadha
dvr@ngri.res.in
CSIR-National Geophysical Research Institute
Uppal Road, Hyderabad – 500007 .
2. OBJECTIVES
› Developed the error correction model to forecast the
seismicity by using co-integration analysis.
3. Methods
› cross-correlation is a measure of
similarity of two waveforms as a function
of a time-lag applied to one of them.
› A neural network is a parallel system,
capable of resolving paradigms that
linear computing cannot .
› Wavelets are mathematical functions
that cut up data into different frequency
components, and then study each
component with a resolution matched to
its scale.
› If two or more series are individually
integrated but some linear combination
of them has a lower order of integration,
then the series are said to be Co-
integrated.
4. Introduction
› The importance of stationary variables when running OLS
regressions.
› Explain the concept of Co integration.
› Importance of error correction models and their relationship
to co integration.
6. Stationary and Trend Stationary
› A stationary process is a stochastic process whose joint
probability distribution does not change when shifted in time
or space.
› The mean and variance are also do not change over time or
position.
tttt
ttt
uyyy
uyy
=∆=−
+=
−
−
1
1
To produce a stationary time series, the random walk needs to be first-differenced
trendt
uty tt
−
++= 10 ββA series is said to be trend stationary when it is stationary around a trend:
7. Augmented Dickey-Fuller Test
› The number of lagged dependent variables is determined by
an information criteria:
t
N
i
ittt uyyy +∆+=∆ ∑
=
−−
0
1β
8. Steps in Testing for Cointegration
1) Test all the variables to determine if they are I(0), I(1) or I(2)
using the ADF test.
2) If both variables are I(1), then carry out the test for
cointegration
3) If there is evidence of cointegration, use the residual to
form the error correction term in the corresponding ECM
4) Add in a number of lags of both explanatory and dependent
variables to the ECM
5) Omit those lags that are insignificant to form a
parsimonious model
6) Use the ECM for dynamic forecasting of the dependent
variable and assess the accuracy of the forecasts.
11. › The cointegrating relationship between Warna and Koyna
reservoir water levels was run,
W = 0.127*K + 531.494
W-Warna water level K – Koyna Water level
Based upon AIC( Akaike information criterion ) :optimal lag is 2.
(critical value=15.27168).
The Error correction model (ECM) result:
W = 1.034 * K - 0.832 * K(-1) + 0.828 * W(-1) - 25.49
K(-1) – 1st
order difference of Koyna water level.
W(-1) – 1st
order difference of Warna water level.
12.
13. The cointegrating relationship between Seismicity in the
Koyna-Warna region and reservoir water levels was run,
SC = -0.215*WL + 140.433
WL-Reservoir water level SC– Seismicity Count
Based upon AIC( Akaike information criterion ) :optimal lag is
2. (critical value=13.07).
The Error correction model (ECM) result:
SC=143.765-(0.333*WL)+(0.137*WL-1)+(0.342*SC-1)
WL(-1) – 1st
order difference of Reservoir water level.
SC(-1) – 1st
order difference of Seismicity Count.
16. Conclusions
› The regression analysis is still effective if two non stationary time
series of the model are cointegrated.
› Koyna and Warna reservoir water levels are cointegrated with lag 2.
› The Error correction model (ECM) is more adequate in forecasting
the reservoir water levels.
› The ECM is developed based on the cointegration technique
between the seismicity and the reservoir water levels .
