Description
The PPT explains on time series forecasting methods in detail. It covers Box Jenkins model in high detail along with ARIMA.
OPERATIONS MANAGEMENT
Time-Series Forecasting Methods
Time-Series Techniques
?
?
? ? ? ? ? ? ?
Rolling Forecast Moving Average Exponential Smoothing Extrapolation Linear Prediction Trend Estimation Growth Curve Box Jenkins Z-Chart
Box Jenkins Methodology
? ?
George Box and Gwilyn Jenkins (1976) Applies Autoregressive Integrated Moving Average (ARIMA) model to make forecasts
?
Its a 3 step process
? Model
Selection ? Parameter Estimation ? Model checking
Box Jenkins Pre-requisites
?
Data needs to be Stationary
? Stationary
means probability distribution does not change when shifted in time or space. ? As a result parameters like mean, autocorrelation and variance also do not change over time.
?
Any seasonality present, needs to be modeled.
ARIMA (p, d, q)
Generally written as ARIMA( p, d, q) where p = order of autoregressive model d = order of integration q = order of moving average model For e.g.:- ARIMA( 1,1,1) Equation :Xt = Yt – Yt-1 Xt = A + B1 Xt-1+ ut + C1ut-1
?
Forecasting of NO2 Concentrations
?
The presence of any pollutant today is related to its presence in the past – high correlation Prediction of NO2 air pollutant using Time series forecasting model has been done based on NAMP Data. Box-Jenkins approach is the most suitable one.
?
?
Case Study-NO2 forecast model
?
Three years data series for the period 2000-02 for NO2 at ITO, New Delhi was considered for fitting the Time Series Models.
?
The scatter plot was studied and the plot showed periodicity as well as seasonality .
Statistics for the Comparative Models
Description ARIMA(1,1,0) ARIMA(0,1,1) ARIMA(1,1,1) 2000-2002 No. of Observations Observed Mean 1096 67.02 2000-2002 1096 67.02 2000-2002 1096 67.02
Predicted Mean
Observed Standard Deviation
67.14
18.127
67.17
18.127 16.40 11.26 8391.069 126.80
67.18
18.134 15.93 11.11 8364.76 124.93
Predicted Standard Deviation 19.20 Standard Error 14.28 8879.11 203.99
Akaike Information Criterian(AIC)
Residual Variance
No2 Observed vs. Forecast series for the Year 2003, At ITO, New Delhi
250 No2 Observed 200
NO2 Concentrations
NO2 Predicted
150
100
50
0 1 Days
20 39 58 77 96 115 134 153 172 191 210 229 248 267 286 305 324 343 362
Conclusion of Study
?
The model based on Box-Jenkins approach has proved to be satisfactory seeing that Approx. 87% of the forecasts could be predicted correctly. The models are not responsive to the sudden change in the atmospheric conditions, emissions and other activities which result in sudden rise in the pollution levels.
?
Z Chart
?
Short term forecasting method Companies predict total sales at the end of year by observing 9 months data. 2 basic assumptions:same trends are being experienced. ? all the trading and working conditions remain same.
?
?
?
Example – Monthly Sales
Year
Month January February March April May June July August September October November December Total Sales 2003 940 580 690 680 710 660 630 470 480 590 450 430 7310 2004 520 380 480 490 370 390 350 440 360
Month January February March April May June July August September
2004 520 380 480 490 370 390 350 440 360
Cumulative Total 520 900
12 Months Moving Total 6890 6690 6480 6290 5950 5680 5400 5370 5250
1380 1870 2240 2630 2980 3420 3780
Thank You
doc_978029264.ppt
The PPT explains on time series forecasting methods in detail. It covers Box Jenkins model in high detail along with ARIMA.
OPERATIONS MANAGEMENT
Time-Series Forecasting Methods
Time-Series Techniques
?
?
? ? ? ? ? ? ?
Rolling Forecast Moving Average Exponential Smoothing Extrapolation Linear Prediction Trend Estimation Growth Curve Box Jenkins Z-Chart
Box Jenkins Methodology
? ?
George Box and Gwilyn Jenkins (1976) Applies Autoregressive Integrated Moving Average (ARIMA) model to make forecasts
?
Its a 3 step process
? Model
Selection ? Parameter Estimation ? Model checking
Box Jenkins Pre-requisites
?
Data needs to be Stationary
? Stationary
means probability distribution does not change when shifted in time or space. ? As a result parameters like mean, autocorrelation and variance also do not change over time.
?
Any seasonality present, needs to be modeled.
ARIMA (p, d, q)
Generally written as ARIMA( p, d, q) where p = order of autoregressive model d = order of integration q = order of moving average model For e.g.:- ARIMA( 1,1,1) Equation :Xt = Yt – Yt-1 Xt = A + B1 Xt-1+ ut + C1ut-1
?
Forecasting of NO2 Concentrations
?
The presence of any pollutant today is related to its presence in the past – high correlation Prediction of NO2 air pollutant using Time series forecasting model has been done based on NAMP Data. Box-Jenkins approach is the most suitable one.
?
?
Case Study-NO2 forecast model
?
Three years data series for the period 2000-02 for NO2 at ITO, New Delhi was considered for fitting the Time Series Models.
?
The scatter plot was studied and the plot showed periodicity as well as seasonality .
Statistics for the Comparative Models
Description ARIMA(1,1,0) ARIMA(0,1,1) ARIMA(1,1,1) 2000-2002 No. of Observations Observed Mean 1096 67.02 2000-2002 1096 67.02 2000-2002 1096 67.02
Predicted Mean
Observed Standard Deviation
67.14
18.127
67.17
18.127 16.40 11.26 8391.069 126.80
67.18
18.134 15.93 11.11 8364.76 124.93
Predicted Standard Deviation 19.20 Standard Error 14.28 8879.11 203.99
Akaike Information Criterian(AIC)
Residual Variance
No2 Observed vs. Forecast series for the Year 2003, At ITO, New Delhi
250 No2 Observed 200
NO2 Concentrations
NO2 Predicted
150
100
50
0 1 Days
20 39 58 77 96 115 134 153 172 191 210 229 248 267 286 305 324 343 362
Conclusion of Study
?
The model based on Box-Jenkins approach has proved to be satisfactory seeing that Approx. 87% of the forecasts could be predicted correctly. The models are not responsive to the sudden change in the atmospheric conditions, emissions and other activities which result in sudden rise in the pollution levels.
?
Z Chart
?
Short term forecasting method Companies predict total sales at the end of year by observing 9 months data. 2 basic assumptions:same trends are being experienced. ? all the trading and working conditions remain same.
?
?
?
Example – Monthly Sales
Year
Month January February March April May June July August September October November December Total Sales 2003 940 580 690 680 710 660 630 470 480 590 450 430 7310 2004 520 380 480 490 370 390 350 440 360
Month January February March April May June July August September
2004 520 380 480 490 370 390 350 440 360
Cumulative Total 520 900
12 Months Moving Total 6890 6690 6480 6290 5950 5680 5400 5370 5250
1380 1870 2240 2630 2980 3420 3780
Thank You
doc_978029264.ppt