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Indian summer monsoon rainfall predictionA comparison of ARIMA and ANN models
Dr. Abhishek Singh
Sunday, June 14, 2020
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 1 / 17
Introduction
Challenge: accurate forecasting of Indian summer monsoon rainfall(ISMR) from June through September.
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 2 / 17
Data
Data Soure: Indian Institute of Tropical Meteorology (IITM), Pune.
contains monthly rainfall data for 146 years (1871-2016).
The data were divided into:
training (1871-1960), andtesting (1961-2016) data sets
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 3 / 17
Data
Data Soure: Indian Institute of Tropical Meteorology (IITM), Pune.contains monthly rainfall data for 146 years (1871-2016).
The data were divided into:
training (1871-1960), andtesting (1961-2016) data sets
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 3 / 17
Data
Data Soure: Indian Institute of Tropical Meteorology (IITM), Pune.contains monthly rainfall data for 146 years (1871-2016).
The data were divided into:
training (1871-1960), andtesting (1961-2016) data sets
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 3 / 17
Data
Data Soure: Indian Institute of Tropical Meteorology (IITM), Pune.contains monthly rainfall data for 146 years (1871-2016).
The data were divided into:training (1871-1960), and
testing (1961-2016) data sets
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 3 / 17
Data
Data Soure: Indian Institute of Tropical Meteorology (IITM), Pune.contains monthly rainfall data for 146 years (1871-2016).
The data were divided into:training (1871-1960), andtesting (1961-2016) data sets
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 3 / 17
Methods
The following methods were used to forecast the values of ISMR:
Autoregressive Integrated Moving Average (ARIMA) Model
Non-linear Artificial Neural Network (NANN) Model
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 4 / 17
Methods
The following methods were used to forecast the values of ISMR:Autoregressive Integrated Moving Average (ARIMA) Model
Non-linear Artificial Neural Network (NANN) Model
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 4 / 17
Methods
The following methods were used to forecast the values of ISMR:Autoregressive Integrated Moving Average (ARIMA) Model
Non-linear Artificial Neural Network (NANN) Model
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 4 / 17
ISRM training data (1871-1960)
Time
Sea
sona
l Rai
nfal
l Mon
soon
(in
mm
)
1880 1900 1920 1940 1960
6000
7000
8000
9000
1000
0
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 5 / 17
Augmented Dickey-Fuller Test (1871-1960)
Augmented Dickey-Fuller Test
data: trainingdataDickey-Fuller = -4.1077, Lag order = 4, p-value = 0.01alternative hypothesis: stationary
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 6 / 17
Partial Autocorrelation Function (1871-1960)
5 10 15
−0.
2−
0.1
0.0
0.1
0.2
Lag
Par
tial A
CF
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 7 / 17
Autocorrelation Function (1871-1960)−
0.3
−0.
2−
0.1
0.0
0.1
0.2
0.3
Lag
AC
F
5 10 15
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 8 / 17
Parameter Estimation
Thus the proposed model is ARIMA(0, 0, 0).
Series: trainingdataARIMA(0,0,0) with non-zero mean
Coefficients:mean
8566.6444s.e. 85.1768
sigma^2 estimated as 660294: log likelihood=-730.22AIC=1464.44 AICc=1464.58 BIC=1469.44
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 9 / 17
Forecasts from ARIMA(0,0,0)
Years
Sea
sona
l Rai
nfal
l Mon
soon
(in
mm
)
1900 1950 2000
6000
7000
8000
9000
1000
0
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 10 / 17
Simple Neural Netwrok
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 11 / 17
Multilayer Feed-Forwad Neural Netwrok
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 12 / 17
Proposed NANN(p,k) Model
The proposed model is NANN(1, 1).
p = 1 is lagged inputk = 1 is number of node(s) in hidden layer
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 13 / 17
Proposed NANN(p,k) Model
The proposed model is NANN(1, 1).p = 1 is lagged input
k = 1 is number of node(s) in hidden layer
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 13 / 17
Proposed NANN(p,k) Model
The proposed model is NANN(1, 1).p = 1 is lagged inputk = 1 is number of node(s) in hidden layer
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 13 / 17
Forecasts from NANN(1,1)
Years
Sea
sona
l Rai
nfal
l Mon
soon
(in
mm
)
1900 1950 2000
6000
7000
8000
9000
1000
0
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 14 / 17
Conclusion
Both of the methods ARIMA(0, 0, 0) and NANN(1, 1) provide samelevel of prediction.
The behavior of their predication intervals differ significantly.
The possible reason may be that, neural networks are not based on awell-defined stochastic model.Thus, prediction intervals were calculated from the simulation models.
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 15 / 17
Conclusion
Both of the methods ARIMA(0, 0, 0) and NANN(1, 1) provide samelevel of prediction.
The behavior of their predication intervals differ significantly.
The possible reason may be that, neural networks are not based on awell-defined stochastic model.Thus, prediction intervals were calculated from the simulation models.
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 15 / 17
Conclusion
Both of the methods ARIMA(0, 0, 0) and NANN(1, 1) provide samelevel of prediction.
The behavior of their predication intervals differ significantly.The possible reason may be that, neural networks are not based on awell-defined stochastic model.
Thus, prediction intervals were calculated from the simulation models.
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 15 / 17
Conclusion
Both of the methods ARIMA(0, 0, 0) and NANN(1, 1) provide samelevel of prediction.
The behavior of their predication intervals differ significantly.The possible reason may be that, neural networks are not based on awell-defined stochastic model.Thus, prediction intervals were calculated from the simulation models.
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 15 / 17
Take Away
Making interpretations and further policy implications using ANN weshould be very cautious due to the limitations on prediction interval.
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 16 / 17
References
Box, George EP, Gwilym M Jenkins, Gregory C Reinsel, and Greta M Ljung.2015. Time Series Analysis: Forecasting and Control. John Wiley & Sons.
IITM. 2020. “Indian Institute of Tropical Meteorology.”https://www.tropmet.res.in.
Sivanandam, SN, and SN Deepa. 2007. Principles of Soft Computing (withCd). John Wiley & Sons.
Dr. Abhishek Singh Indian summer monsoon rainfall prediction Sunday, June 14, 2020 17 / 17
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