Implementation of the Data Analytics Methods for the Forecast

To predict season diseases, either statistical or structural models can be used (Hyndman and Athanasopoulos, 2018).

Statistical methods considered in this investigation include the following:

  • • Classical Poisson method.
  • • Dickson-Coles method.
Features of the decision tree

Figure 9.5 Features of the decision tree.

  • • Least squares method.
  • • Autoregressive model of variable mean.
  • • Model of simple exponential smoothing.
  • • Holt exponential smoothing model.
  • • Holt-Winters exponential smoothing model.

On the other hand, from the existing structural methods the following were selected:

  • • Neural network with nonlinear autoregressive model.
  • • Multilayer perceptron with five hidden layers.
  • • Multilayer perceptron with automatic detection of the number of hidden layers.
  • • Machine of extreme training.

Besides the methods mentioned above, another classification could be applied:

  • • Regression models and methods.
  • • Autoregressive models and methods.
  • • Models and methods of exponential smoothing.
  • • Neural network models and methods.

According to the suggested classification in the Table 9.1, there are systemized strong and weak sides of above-mentioned approaches.

For the estimation of the accuracy of prediction methods, time series forecasting error rates will be used (Hyndman and Koehler, 2006).

Table 9.1 Comparison of the Methods and Models

MODEL AND METHOD

ADVANTAGES

DISADVANTAGES

Autoregressive models and methods

Simplicity, uniformity of analysis and design; numerous application examples

The complexity of model identification; impossibility of modelling nonlinearities; low adaptability

Models and methods of exponential smoothing

Simplicity, uniformity of analysis and design

Insufficient flexibility; narrow applicability of models

Neural network models and methods

Nonlinearity of models; scalability, high adaptability; uniformity of analysis and design; large set of examples

Lack of transparency; complexity of choice of architecture; stringent training sample requirements; the complexity of choosing a learning algorithm; resource-intensive learning process

The most common time series forecasting errors are as presented below:

MAPE - mean absolute percentage error:

MAE - mean absolute error:

MSE - mean square error:

RMSE - root mean square error:

ME - mean error:

SD - standard deviation:

Forecast accuracy is an opposite concept to the prediction error. If the forecast error is large, then the accuracy is small and, conversely, if the prediction error is small, then the accuracy is large (Khair et al., 2017). In fact, the forecast error estimate is the inverse of the forecast accuracy - the dependence is simple here:

Forecast accuracy in% = 100% - MAPE (9.8)

Usually, the accuracy is not estimated, in other words, solving the task of forecasting is always evaluated, that is, determine the value of the prediction error, that is, the magnitude and the forecast error. However, it should be understood that if so, then the prediction accuracy = 95%. When talking about high accuracy, we always talk about low forecast error, and there should be no misunderstanding in this area.

In this case, the MAPE is a quantitative estimate of the error itself, and this value clearly tells us the accuracy of prediction, based on the above simple formula. Thus, when estimating the error, we always estimate the accuracy of the prediction.

According to Table 9.2, the best model is a neural network with a nonlinear autoregressive model. You can see the results for the forecast related to Figure 9.6.

Table 9.2 Comparison of Different Methods for the Colds Forecasts

METHOD

MAPE

MAE

MSE

RMSE

ME

SD

Autoregressive model of variable mean

7.1849

29.3399

2069.1879

45.48832

0.1427

45.532

Autoregressive model of variable mean (custom)

6.8860

28.6838

1930.2694

43.9348

0.5027

43.9747

Model of simple exponential smoothing

8.9315

39.2918

4190.0204

64.7303

-0.2436

64.7929

Holt exponential smoothing model

7.9362

35.6543

3899.7392

62.4478

-0.3903

62.5075

Holt-Winters exponential smoothing model

17.5070

75.3171

15462.2587

124.34

-0.9435

57.8242

Neural network with nonlinear autoregressive model

5.5145

22.4491

1135.5233

33.6975

-0.043

34.0067

Multilayer perceptron with five hidden layers

6.0216

24.7753

1425.9549

37.7618

-0.1517

37.2962

Multilayer perceptron with automatic detection of the number of hidden layers

6.8004

28.7822

2142.1202

46.2830

0.00071

46.3384

Machine of extreme training

7.3069

31.6591

2605.2752

51.0418

0.0116

51.7630

Forecast with neural network with nonlinear autoregressive model

Figure 9.6 Forecast with neural network with nonlinear autoregressive model.

Implementation of the Data Analytics Methods for the Football Matches Forecasts

For the football matches forecasts let us consider following methods (Harville, 2003):

  • • Classical Poisson method (Maher, 1982).
  • • Dickson-Coles method (Dixon and Coles, 1997).
  • • The method of time-independent least squares Ratings.
  • • “Predicting football results using a neural network based on FIFA Rating” method (Graham, 2018).

Table 9.3 Comparison of Different Methods for the Football Matches Forecasts

METHOD

MAPE

MAE

MSE

RMSE

ME

SD

Basic Poisson model

9.93

42.03

4479.00

66.9253

0.2373

67.8978

Dixon-Coles method

7.94

35.67

3900.74

62.4559

0.2451

63.1456

Mean square method

7.80

34.68

2783.43

52.7582

0.2092

52.9896

Deep neural network

6.51

27.55

2050.45

45.2819

0.1812

45.5678

According to Table 9.3, the best model is the neural network of deep learning (the lowest error rate is 6.51).

 
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