ayushiasthana.files.wordpress.com · web viewfigure 5.6 checking the stationarity using rolling...

IMPLEMENTATION

Figure 5.1 Holt Linear Method

Figure 5.2 Holt Winter Method

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Figure 5.3

Figure 5.4 Time Series of Land Average Temperature

Figure 5.5 Time Series Ocean Average temperature

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Figure 5.6 Checking the stationarity using Rolling mean and Standard Deviation

Figure 5.7 Applying Log Transformation

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Figure 5.8 Average Removal

Figure 5.9 Exponentially Weighted Average

Figure 5.10 Decomposition

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Figure 5.11 Trend

Figure 5.12 Seasonality

Figure 5.13 Residual

Figure 5.14 Differencing

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Figure 5.15 Checking for stationarity

Moving Average Model

Figure 5.16 Autocorrelation Function

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Figure 5.17 Visualizations of results of MA model vs Predicted

Figure 5.18 Training series combined with forecasted series.

Autoregressive Model

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Figure 5.19 Partial Autocorrelation Function

Figure 5.20 Visualization of AR model – Original vs Predicted

Figure 5.21 Training series combined with forecasted series for AR model

Figure 5.22 Training series combined with forecasted series for ARIMA mode

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Figure 5.23 LSTM model Forecasting vs Original

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1. TESTING REPORTS

Iteration NO. - 1Forecasted = 0.795276 Expected = 0.685637 Error = 15.990916 %Iteration NO. - 2Forecasted = 0.680479 Expected = 0.638481 Error = 6.577787 %Iteration NO. - 3Forecasted = 0.636038 Expected = 0.628786 Error = 1.153256 %Iteration NO. - 4Forecasted = 0.627831 Expected = 1.257384 Error = 50.068498 %Iteration NO. - 5Forecasted = 1.295931 Expected = 1.931208 Error = 32.895295 %Iteration NO. - 6Forecasted = 1.965912 Expected = 1.345931 Error = 46.063348 %Iteration NO. - 7Forecasted = 1.322335 Expected = 1.296826 Error = 1.966984 %Iteration NO. - 8Forecasted = 1.294874 Expected = 1.173469 Error = 10.345742 %Iteration NO. - 9Forecasted = 1.167471 Expected = 1.072747 Error = 8.830041 %Iteration NO. - 10Iteration NO. - 90Forecasted = 1.456534 Expected = 1.381751 Error = 5.412183 %Iteration NO. - 91Forecasted = 1.377239 Expected = 1.322023 Error = 4.176629 %Iteration NO. - 92Forecasted = 1.318472 Expected = 1.178119 Error = 11.913305 %Iteration NO. - 93Forecasted = 1.170582 Expected = 1.037642 Error = 12.811719 %Iteration NO. - 94Forecasted = 1.030508 Expected = 0.980334 Error = 5.118133 %Iteration NO. - 95Forecasted = 0.977098 Expected = 0.880989 Error = 10.909163 %Iteration NO. - 96Forecasted = 0.875620 Expected = 0.830910 Error = 5.380812 %Iteration NO. - 97Forecasted = 0.827991 Expected = 0.688177 Error = 20.316611 %Iteration NO. - 98Forecasted = 0.681037 Expected = 0.742365 Error = 8.261229 %

RESULTS OF MA MODEL

Means in Temperature 14.900387 %RMSE in Temperature 3.860102 %

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AUTO REGRESSIVE MODEL

Iteration NO. - 1Forecasted = 0.795032 Expected = 0.685637 Error = 15.955257 %Iteration NO. - 2Forecasted = 0.680225 Expected = 0.638481 Error = 6.538060 %Iteration NO. - 3Forecasted = 0.635792 Expected = 0.628786 Error = 1.114136 %Iteration NO. - 4Forecasted = 0.627739 Expected = 1.257384 Error = 50.075803 %Iteration NO. - 5Forecasted = 1.297061 Expected = 1.931208 Error = 32.836829 %Iteration NO. - 6Forecasted = 1.969929 Expected = 1.345931 Error = 46.361776 %Iteration NO. - 7Forecasted = 1.322836 Expected = 1.296826 Error = 2.005647 %Iteration NO. - 8Forecasted = 1.293816 Expected = 1.173469 Error = 10.255629 %Iteration NO. - 9Forecasted = 1.167282 Expected = 1.072747 Error = 8.812464 %Iteration NO. - 10Forecasted = 1.067544 Expected = 0.947476 Error = 12.672390 %Iteration NO. - 90Forecasted = 1.458513 Expected = 1.381751 Error = 5.555450 %Iteration NO. - 91Forecasted = 1.377730 Expected = 1.322023 Error = 4.213793 %Iteration NO. - 92Forecasted = 1.318193 Expected = 1.178119 Error = 11.889669 %Iteration NO. - 93Forecasted = 1.170235 Expected = 1.037642 Error = 12.778289 %Iteration NO. - 94Forecasted = 1.029988 Expected = 0.980334 Error = 5.065067 %Iteration NO. - 95Forecasted = 0.976696 Expected = 0.880989 Error = 10.863515 %Iteration NO. - 96Forecasted = 0.875350 Expected = 0.830910 Error = 5.348290 %Iteration NO. - 97Forecasted = 0.827684 Expected = 0.688177 Error = 20.272016 %Iteration NO. - 98Forecasted = 0.680728 Expected = 0.742365 Error = 8.302777 %

RESULTS OF AR MODEL

Means Error in Forecasted Temperature 14.889718 %RMSE in Forecasted Temperature 3.858720 %

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ARIMA MODEL

Iteration NO. - 1Forecasted = 8.989412 Expected = 7.084000 Error = 6.724350 %Iteration NO. - 2Forecasted = 6.176126 Expected = 4.523000 Error = 9.137334 %Iteration NO. - 3Forecasted = 4.218238 Expected = 2.844000 Error = 12.080147 %Iteration NO. - 4Forecasted = 2.831279 Expected = 3.576000 Error = 5.206381 %Iteration NO. - 5Forecasted = 4.865507 Expected = 6.906000 Error = 7.386667 %Iteration NO. - 6Forecasted = 8.558189 Expected = 9.295000 Error = 1.981739 %Iteration NO. - 7Forecasted = 9.147603 Expected = 12.054000 Error = 6.027869 %Iteration NO. - 8Forecasted = 12.466564 Expected = 14.145000 Error = 2.966484 %Iteration NO. - 9Forecasted = 12.881055 Expected = 15.174000 Error = 3.777752 %Iteration NO. - 10Forecasted = 13.887150 Expected = 14.377000 Error = 0.851794 %Iteration NO. - 90Forecasted = 7.558453 Expected = 9.313000 Error = 4.709940 %Iteration NO. - 91Forecasted = 9.893559 Expected = 12.312000 Error = 4.910739 %Iteration NO. - 92Forecasted = 12.287710 Expected = 14.505000 Error = 3.821596 %Iteration NO. - 93Forecasted = 13.482159 Expected = 15.051000 Error = 2.605875 %Iteration NO. - 94Forecasted = 13.416783 Expected = 14.755000 Error = 2.267396 %Iteration NO. - 95Forecasted = 13.102832 Expected = 12.999000 Error = 0.199693 %Iteration NO. - 96Forecasted = 11.205073 Expected = 10.801000 Error = 0.935268 %Iteration NO. - 97Forecasted = 9.578170 Expected = 7.433000 Error = 7.215021 %Iteration NO. - 98Forecasted = 6.354373 Expected = 5.518000 Error = 3.789294 %

RESULTS OF ARIMA MODEL

Means Error in Forecasted Temperature 4.222607 %RMSE in Forecasted Temperature 2.054898 %

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LSTM

Forecasted = -0.388320 Expected = 0.055792 Error = 5.960Forecasted = 0.139059 Expected = -0.039647 Error = 2.507Forecasted = 0.506904 Expected = -0.165015 Error = 2.072Forecasted = 0.474063 Expected = -0.304027 Error = 0.559Forecasted = 0.263254 Expected = -0.518609 Error = 0.492Forecasted = 0.140694 Expected = -0.582915 Error = 0.759Forecasted = 0.039507 Expected = -0.409169 Error = 0.903Forecasted = -0.023897 Expected = 0.282948 Error = 0.916Forecasted = -0.121186 Expected = 0.415358 Error = 0.708Forecasted = -0.223527 Expected = 0.446757 Error = 0.500Forecasted = -0.376543 Expected = 0.289116 Error = 0.302Forecasted = -0.556477 Expected = 0.141549 Error = 2.931Forecasted = -0.107204 Expected = 0.046883 Error = 1.287Forecasted = 0.136038 Expected = -0.048788 Error = 1.788Forecasted = 0.394031 Expected = -0.179228 Error = 1.198Forecasted = 0.367762 Expected = -0.325560 Error = 0.130Forecasted = 0.298924 Expected = -0.547308 Error = 0.454Forecasted = 0.177801 Expected = -0.561088 Error = 0.683Forecasted = 0.029423 Expected = -0.367726 Error = 0.920Forecasted = -0.017550 Expected = 0.246805 Error = 0.929Forecasted = -0.113975 Expected = 0.408526 Error = 0.721Forecasted = -0.248863 Expected = 0.436690 Error = 0.430Forecasted = -0.323145 Expected = 0.276639 Error = 0.168Forecasted = -0.452062 Expected = 0.131993 Error = 2.425Forecasted = -0.235712 Expected = 0.040278 Error = 4.852Forecasted = -0.064181 Expected = -0.054756 Error = 0.172Forecasted = 0.600092 Expected = -0.184701 Error = 2.249Forecasted = 0.407762 Expected = -0.334667 Error = 0.218Forecasted = 0.271651 Expected = -0.553932 Error = 0.510Forecasted = 0.130437 Expected = -0.543561 Error = 0.760Forecasted = 0.036843 Expected = -0.330946 Error = 0.889Forecasted = 0.000134 Expected = 0.220847 Error = 0.999Forecasted = -0.127757 Expected = 0.402400 Error = 0.683Forecasted = -0.236873 Expected = 0.427770 Error = 0.446Forecasted = -0.431006 Expected = 0.267579 Error = 0.611Forecasted = -0.325067 Expected = 0.128169 Error = 1.536

LSTM RESULT

Mean Error in Forecasted Temperature 1.404629 %RMSE in Forecasted Temperature 1.185170 %

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Table 7.1 Comparison of various Models

MODEL NAME RMSE

Holt’s Linear Trend Method 17.12790830144587

Holt’s Winter Model 4.427087095092175

AR 3.858720 %

MA 3.860102 %

ARIMA 2.054898 %

LSTM 1.185170 %

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