Hybrid multi-model forecasting system: A case study on display market

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Hybrid multi-model forecasting system: A case study on display market

Chen-Chun Lin

a

, Chun-Ling Lin

b,⇑

, Joseph Z. Shyu

a

Institute of Management of Technology, National Chiao Tung University, No. 1001, Ta Hsueh Rd., Hsinchu 300, Taiwan b

Department of Electrical Engineering, Ming Chi University of Technology, No. 84, Gongzhuan Rd., Taishan Dist., New Taipei City 243, Taiwan

a r t i c l e

i n f o

Article history:

Received 10 January 2012

Received in revised form 5 August 2014 Accepted 5 August 2014

Available online 11 August 2014 Keywords:

Hybrid multi-model forecasting system Prediction

Display markets Mean square error (MSE)

Mean absolute percentage error (MAPE) Average square root error (ASRE)

a b s t r a c t

This paper provides a novel hybrid multi-model forecasting system, with a special focus on the changing regional market demand in the display markets. Through an intensive case study of the ups and downs of the display industry, this paper examines the panel makers suffered from low panel price and unstable market demand, then they have changed to react to the rapid demand in the market or have lower panel stock for keeping supply and demand more balanced. In addition, this paper suggests a co-evolution forecasting process of sales and market factor. It can automatically apply various combinations of both linear and nonlinear models, and which alternatives deliver the lowest statistical error and produce a good estimate for the prediction of markets.

Moreover, this article shows how the system is modeled and its accuracy is proved by means of experimental results; and judged by 3 evaluation criteria, including the mean square error (MSE), the mean absolute percentage error (MAPE), and the average square root error (ASRE) were used as the performance criteria to automatically select the optimal forecasting model. Finally, the results showed that the proposed system had considerably better predictive performance than previous and individual models. To summarize, the proposed system can reduce the user’s effort for easier obtaining the desired forecasting results and create high quality forecasts.

1. Introduction

The ﬂat-panel display (FPD) is a landmark sector all over the world in terms of technology innovation. This market is growing based on the competitiveness of three major technologies: thin-ﬁlm transistor-liquid crystal displays (TFT-LCD), plasma dis-play panels (PDP) and organic light-emitting diodes (OLED). TFT-LCD has the largest market share. This technology dominates the market, as it can be used in different types of applications, ranging from small devices including mobile phones to large applications including televisions.

However, TFT-LCD manufacture has high risk and low afﬁxa-tion. Because high-risk industry where failure for market estima-tion can lead to the eliminaestima-tion of an enterprise and where a timely, large-scale investment is essential; industry where large companies that should have the capacity to mobilize large capital are fully equipped with necessary parts and materials.

Research on ﬂat panel displays (FPD), which started in the 1960s, has ﬁnally reached the commercialization stage in the form of large plasma display panels (PDPs) and liquid crystal displays

(LCDs). Japanese companies led initial technological development in the LCD upstream industry in the 1990s. But since 2000, Korea and Taiwan have made bold investments, and they are leading the global market. In 2010 China started to join this market, global manufacturers of TFT-LCD panels have established the majority of LCD module assembly plants in China to take advantage of lower labor costs. With investment in display production facilities likely to decline in other countries, production of TFT-LCD manufacturing equipment in China will account for a greater share of the world market. Now China has become a major hub in TFT-LCD manufac-turing, and the TFT-LCD industry is one of the most dynamic industries.

Major manufacturers by country are Korea (Samsung, LG Dis-play), Taiwan (AUO, Innolux, CPT, Hannstar), Japan (Sharp, TMD, NEC, Hitachi), China (BOE-OT, CEC-Panda, CSOT, Tianma), etc. Now the industry has diverse upstream markets as following: (1) small and mid-sized products including smart phones, IT products (i.e. monitors, tablet PC, desktop PC, laptops and automotive heads-up display) and (2) large-sized products including house-hold appliances (i.e. LCD TV and monitor).

After the fall of 2008 and the European debt crisis, which began in late 2009, the shift still signiﬁcantly inﬂuences the demand ratio of the TFT-LCD regional markets in the world until now. The

http://dx.doi.org/10.1016/j.knosys.2014.08.004

E-mail address:ginnylin@mail.mcut.edu.tw(C.-L. Lin).

Contents lists available atScienceDirect

Knowledge-Based Systems

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TFT-LCD industry also has witnessed drastic changes in the inten-sity of competition in 2008–2010. This industry is undergoing a turbulent transformation as it becomes a mature industry as

Fig. 1. However, TFT-LCD panel manufacturers are undoubtedly

looking forward to sustainable growth, but they cannot simply wait for demand to increase and then react to that increase to gen-erate revenue. These companies should examine the various reve-nue sources in the regional markets and seek new opportunities to increase revenue, or builds a sound foundation in shaping effective output planning for the potential market. Hence, the future fore-cast should analyze historical data and forefore-cast projections to deli-ver the most detailed information and insights available.

Due to those reasons mentioned above, this research hopes to develop an efﬁcient process, and a functional tool to predict the rapid development of the TFT-LCD market. Of interest to note is forecasting is a problem that arises in many economic and mana-gerial contexts, and hundreds of forecasting procedures have been developed over the years for many different purposes, both in busi-ness enterprises and elsewhere. Previous forecasting studies relied on qualitative methods or patent analysis, which can be quite use-ful for other forecasting problems but have been shown to be inap-propriate for industrial development forecasting[5,29]. Recently, both theoretical and empirical results have suggested that combin-ing forecastcombin-ing methods can be an effective way to achieve better predictive performance over individual models[9,23]. Contribu-tions from many researchers have improved the quality of the pre-dictions and provided combined forecasting models for decision makers [1,16,26,30,35]. As a result, there have been profound changes in the forecasting ﬁeld. Combining various linear and non-linear models offers solutions in which models are combined in an optimal way and can be applied in real-world situations such as forecasting macroeconomic time series[32], tourist demand [6], and exchange rates[2].

Based on the parameters selected, the combined forecasting models can be roughly classiﬁed into three categories: (1) linear/ equally weighted combined forecasts; (2) nonlinear/unequally weighted combined forecasts; and (3) combined forecasts from lin-ear and nonlinlin-ear models. Linlin-ear methods such as the Bayesian method typically place equal weight on each of the sub-classiﬁers

in each time frame, regardless of their global or local accuracy

[4,12,15,18,38]. Nonlinear methods apply unequal weights for

the averaging of past observations (i.e., more recent observations are given more weight in forecasting than older observations); examples include neural networks, adaptive neuro-fuzzy inference systems, and fuzzy set methods[20,24,25]. Combining linear and nonlinear methods can retain the robustness while reducing the complexity considerably, such as in the combination of artiﬁcial neural networks (ANNs) and auto-regressive integrated moving average (ARIMA) methods. Among these, nonlinear combined fore-casts and combined forefore-casts from linear and nonlinear models have proven to be very effective for demand forecasting in addition to other linear or nonlinear applications[6,27,34].

Several algorithms commonly found in the literature have the potential to surpass the performance of an individual predictor by combining the outputs of a collection of complementary predic-tors. In bagging, various methods are generated by applying a learning algorithm to independent bootstrap tests of the primary training data[3,17]. Boosting is another popular ensemble algo-rithm and was originally developed for classiﬁcation problems. A sequence of models is obtained from a given dataset using an adap-tive learning algorithm and different parameters for various train-ing cases[17]. Adaptive neuro-fuzzy inference systems (ANFISs) outperform other individual methods, and the forecasting accuracy can be improved effectively using combined forecasts, as was done for a panel manufacturer[39].

Based on the forecasting performance of combined methods, Wang and Nie[41]proposed the combination of a back-propaga-tion neural network (BPNN) and support vector machines (SVMs), which have the best forecasting performance, and showed that the combined forecasting model can greatly enhance the accuracy of predictions of a stock index. Other research showed that the adap-tive neuro-fuzzy inference system method outperforms other methods in forecasting panel demand[39], automobile sales[40], and the demand for telecommunication technology[21].

However, none of these methods is a universal model that is suitable for all situations because it is difﬁcult to completely know the linear or nonlinear characteristics of the time series data in an actual problem. An important motivation to combine the forecasts Fig. 1. The global ﬂat panel display industry output (Data Resource: Photonics Industry and Technology Development Association (PIDA) in Taiwan, 2014. http:// www.pida.org.tw/usub/en/index.asp.).

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from different models is the fundamental assumption that one cannot identify the true process exactly, and thus, different models may play a complementary role in the approximation of the pro-cess that produced the data.

Hence, this paper presents a hybrid multi-model forecasting system that combines the forecasts from various linear and nonlin-ear models and compares the performance of this system with that of nonlinear combined-forecast models. The main advantage of the proposed method is that it can be used to select better forecasting modules for greater performance.

The remainder of this paper is organized as follows. In Section2, the exponential smoothing (ES) method, the ARIMA, the back-propagation neural network (BPNN), the adaptive neuro-fuzzy inference system (ANFIS), the support vector regression (SVR) method, and the combination methodology are described. Section3

describes the data source and the evaluation criteria used for com-paring the forecasting techniques. Section4compares the results obtained from the combinations of models against the nonlinear combined forecasts and discusses the forecasting system software. Finally, Section5provides concluding remarks.

2. Methodology

In this paper, we propose a systematic approach to combine dif-ferent efﬁcient methodologies for improving forecasting perfor-mance, especially focus on combined forecasting technique from linear and nonlinear models. Both the nonlinear combining fore-cast and the combining forefore-cast from linear and nonlinear models have achieved successes in their own linear or nonlinear problems

[6,11,34]. Each combining forecast method has its own advantages

and disadvantages. In order to take advantage of the strengths of each combining method to develop the best forecast possible alter-natives, we introduce a multiple forecasting system that can be used to select better combining forecasting modules for better forecasting improvement.

2.1. The combining forecasts from linear and nonlinear models Two individual linear methods (Exponential smoothing/ES and Autoregressive Integrated Moving Average/ARIMA) and other two individual nonlinear methods (Back-propagation neural network/ BPNN and Support vector regression/SVR), are selected as tech-niques for optimizing dynamic forecasting problem based on the combining forecast from linear and nonlinear models. Because a lot of work on using ES, ARIMA, BPNN and SVR as techniques for dynamic combined forecasting often have been previously reported with good predicting performance[6,14,24,33].

Then, this system is majorly proposed to provide four kinds of ‘‘combining forecasts from linear and nonlinear models’’ as follow: (1) ES_BPNN; (2) ES_SCR; (3) ARIMA_BPNN; and (4) ARIMA_SVR, which all have both linear and nonlinear modeling capabilities that can be a good strategy for practical use. Then, this study compares these results with the results from the nonlinear combining fore-cast by ANFIS and the individual forefore-cast by ANFIS.

Previous researches in combining forecasts from linear and nonlinear models believe that it may be reasonable to consider a time series to be composed of a linear autocorrelation structure and a nonlinear component[6,42]. That is:

Yt¼ Mtþ Nt ð1Þ

where Mtis the linear component and Ntis the nonlinear compo-nent of the combination models. Both Mtand Nthave to be esti-mated from the data set. First, linear model (ES and ARIMA) is used to model the linear part of data set, and then the residuals from the linear model will contain only the nonlinear relationship.

Let Etrepresent the residual at time t as obtained from the linear model, then:

Et¼ Yt bMt ð2Þ

where bMtdenotes the forecast value of the linear model at time t. In order to model the nonlinear residuals from the linear model, the nonlinear model (SVR and BPNN) can be used. In this study, the author built four various combination models with the following input layers:

Elineari ¼ f nonlinear

Elinear_i1 ;Elinear_i2 ;Elinear_i3

ð3Þ

where Elinear

i represent the residual at time t from the linear models (ES and ARIMA), fnonlinear_{a nonlinear function determined by the} nonlinear models (SVR and BPNN). Here, this study proposed four combined models, and called them as ES_BPNN, ARIMA_BPNN, ES_SVR, ARIMA_SVR. Therefore, the combined forecast will be:

b

Yi¼ bMiþ bNi ð4Þ

where bNiis the forecast value of Eq.(1).

e

i ð6Þ

where xiand eirepresent the number of visitors and random error terms at period i respectively. B is a backward shift operator deﬁned by Bxi= xi1, and related torbyr= 1 B,rd= (1 B)d, d is the order of differencing. £(B) and h(B) are autoregressive (AR) and moving averages (MA) operators of orders p and q, respectively, and are deﬁned as:

;ðBÞ ¼ 1 ;1B ;2B2 . . . ;PBP ð7Þ hðBÞ ¼ 1 h1B h2B2 . . . hqBq ð8Þ

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where £1, £2, . . . , £p are the autoregressive coefficients and h1, h2, . . . , hqare the moving average coefficients. In order to fit an ARIMA model to the raw data, the ARIMA model involves the fol-lowing four-step iterative cycles[6]: (1) Identification of the ARIMA (p, q, d) structure; (2) estimation of the unknown parameters; (3) goodness-of-fit tests on the estimated residuals; and (4) forecast future outcomes based on the known raw data. The eishould be independently and identically distributed as normal random vari-ables with mean = 0 and constant variance

r

2_{. The roots of £}

p (xi) = 0 and hq(xi) = 0 should all lie outside the unit circle.

2.1.3. Back-propagation neural network (BPNN)

BPNN is a nonlinear method. It is one of the most popular neural network models for use in business applications, especially with time series prediction problems such as sales forecasting [14]. We purpose to use BPNN as the selected nonlinear models to com-bine with the linear ones. The key motivation for doing so is due to the truth that BPNN do not make any assumption about the data. Instead, they try to learn the functional form of the true model from the data itself. For these reasons, we use BPNN to combine the linear model in forecasting the revenue trend.

Based on the algorithm of BPNN, it typically employs three or more layers of processing elements: an input layer, an output layer, and at least one hidden layer. The back propagation learning algorithm involves a forward-propagation step followed by a back-ward-propagation step. Both the forward and backward-propaga-tion steps are done for each signal presentabackward-propaga-tion during training. 2.1.3.1. Forward-propagation algorithm. This forward-propagation step is initiated when an input signal is presented to the network. Incoming connections to unit j are at the left and originate at units in the layer below. Output values from these units arrive at unit j and are summed by

Sj ¼X n

i¼1

xiwji ð9Þ

where xiis the activation level of unit i, and wjiis the weight from unit i to unit j. After the incoming sum Sjis computed, a sigmoid function F is used to compute F(Sj). After the sigmoid function is computed, the resulting value becomes the activation level of unit j. This value, the output of unit j, is sent along the output interconnections.

2.1.3.2. Backward-propagation algorithm. Here, the error (d) values are calculated for all processing elements and weight changes are calculated for all interconnections. The calculations begin at the output layer and progress backward through the network to the input layer. The error-correction step takes place after a signal is presented at the input layer and the forward-propagation step is complete. Then, the weights are adjusted for all interconnections that go into the hidden layer. The process is continued until the last layer of weights has been adjusted. If unit j is in the output layer, then its error value is

dj¼ ðtj ajÞ F0ðSjÞ ð10Þ

where tjis the target value for unit j, ajis the output value for unit j, F0_{(x) is the derivative of the sigmoid function F, and S}

j is the weighted sum of inputs to j.

2.1.4. Support vector regression (SVR)

SVR is a nonlinear method. In most real-world problems, linear function approximation is of limited practical use. The solution is to map the input data in a higher dimensional feature space, in which the training data may exhibit linearity, and then to perform linear regression in this feature space[24]. Let xibe mapped into a

feature space by a nonlinear function £(x); the decision function can be written as:

i ð Þ ¼ 0 0 6

a

i6C; i ¼ 1; 2; . . . ; l 0 6

a

i6C; i ¼ 1; 2; . . . ; 1 ð13Þ

Little knowledge may be available as a basis for selecting an appropriate nonlinear function £(xi), and further, the computation of £(xi) £(xj) in the feature space may be too complex to per-form. An advantage of SVR is that the nonlinear function £(xi) need not be used. The computation in input space can be per-formed using a ‘‘kernel’’ function K(xi, xj) = £(xi) £(xj) to yield the inner products in feature space, circumventing the problems intrinsic in evaluating the feature space. Functions that meet Mer-cer’s condition can be proven to correspond to dot products in a feature space. Therefore, any functions that satisfy Mercer’s theo-rem can be used as a kernel. In this study, we chose the radial basis function as kernel function:

Kðxi;xjÞ ¼ expð

c

jxi xjj2Þ ð14Þ

Finally, the kernel function allows the decision function of non-linear SVR to be expressed as follows.

f ðxiÞ ¼ Xl

i¼1

a

k

a

k

ð ÞKðxi;xkÞ þ b ð15Þ

The parameters that dominate the nonlinear SVR are the cost constant C, the radius of the insensitive tube

e

, and the kernel parameters. These parameters are mutually dependent so changing the value of one parameter changes other parameters. The mean-ings of parameters C and

e

can be interpreted. The parameter C controls the smoothness or ﬂatness of the approximation function. A greater C value, corresponding to a greater penalty of errors, indi-cates that the objective is only to minimize the empirical risk, which makes the learning machine more complex. In this study, determining appropriate values of C and e is often a heuristic trial-and-error process. The optimal values of SVR parameters may vary substantially among cases.

2.2. Nonlinear combining forecast by ANFIS

The ANFIS, first proposed by[19], combined the benefits of arti-ficial neural network (ANN), and fuzzy inference systems. In this study, the processing of the nonlinear combining forecast by ANFIS was same as the one of the individual forecast by ANFIS. Those two

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methods only had the difference in input data. The individual fore-cast by ANFIS adopted the training data as the inputs directly. The nonlinear combining forecast by ANFIS selected the estimated val-ues from three foresting model as the inputs to build the nonlinear combining forecasting system. The three forecasting models can be selected from three nonlinear forecasts models and four combining forecasts models which mentioned above in Section2.1. The MSE, MAPE, ASRE values of three forecasting model were the lowest of three values than other models. The first-order Sugeno fuzzy model has become a common practice on ANFIS implements in the past. Thus, we used the same model. The five steps process shows as follows: (1) In layer 1, each node is called an input lin-guistic node and corresponds to one input linlin-guistic variable. The nodes transmit input forecasts to the next layer directly. Each node function can be modeled by fuzzy membership function. Here, the generalized bell membership function and Gaussian membership function are used; (2) in layer 2, each node in this layer calculates the firing strength of a rule via multiplication; (3) in layer 3: The ith node in this layer calculates the ratio of the nth rule’s firing strength to the sum of all the rules’ firing strengths. The result would be the normalized firing strengths. For convenience, the output of this layer will be called the normalized firing strengths; (4) in layer 4: Each node in this layer is a square node with a node function. Parameters in this layer will be referred to as consequent parameters by node function; (5) in layer 5: The single node in this layer computes the final combining forecast as the summation of all incoming forecasts. Here, we assumed ANFIS as having two inputs, x and y, and one output f to delineate the regular frame-work of ANFIS inFig. 2.

2.3. The combining forecasts methodology

Both ‘‘nonlinear combining forecasts’’ and ‘‘combining fore-casts from linear and nonlinear models’’ have achieved successes in their own linear or nonlinear problems. Each combining fore-cast has its own advantages and disadvantages. In order to take advantage of the strengths of each combining method to develop the best forecast possible alternatives, we introduce a hybrid multi-Model forecasting system that can be used to select better forecasting modules for better forecasting improvement. This system is majorly proposed based on four kinds of ‘‘combining forecasts from linear and nonlinear models’’ (e.g. ES_BPNN, ES_SCR, ARIMA_BPNN, ARIMA_SVR), and ‘‘nonlinear combining model forecasting by ANFIS, which all have both linear and non-linear modeling capabilities that can be a good strategy for prac-tical use.

3. Data set and performance criteria

To test the effectiveness of this proposed system, monthly TFT-LCD revenue data for four regions (the Asia–Paciﬁc region, China, North America and Eastern Europe) were gathered as a representa-tive sampling, during this experiment and then analyzed to form a valid testing. The data were obtained between January 2008 and June 2011, from a leading global market research and consulting ﬁrm ‘‘display search’’.

The data were divided into two sets, a training set (in-sample data) and a test set (out-of-sample data), for each TFT-LCD revenue time series to assess the performance of the forecasting methods selected for this research. To achieve a more reliable and accurate result, a longer period was used for training.

Once the training stage was complete, the various methodolo-gies were applied to the test data. The ANFIS was trained using the lowest MSE and the lowest MAPE, which are deﬁned in the fol-lowing subsection, as the performance criteria.

3.1. Quantitative evaluations

There were two main categories in hybrid multi-model forecasting system. The first category included four models that combined forecasts from linear and nonlinear models (ES-BPNN, ES-SCR, ARIMA-BPNN, ARIMA-SVR), and the second category con-sisted of one nonlinear combined forecasting model (ANFIS). These five models were tested with the revenue time series data for TFT-LCD panel manufacturers in each region. We calculated the mean square error (MSE), the mean absolute percentage error (MPAE), and the average square root error (ASRE) to compare the accuracy of these five methods. Previous studies showed that the MSE, the MAPE and the ASRE are frequently used measures of the difference between actual and predicted values for a process that is being modeled [7,28]. In statistics, the MSE, the MAPE and the ASRE are used to measure the difference between actual and predicted values and can provide a measure of the level of agreement between the observed and predicted values. The lower the values of the MSE, the MAPE and the ASRE, the closer the predicted values are to the actual values. We can calculate the MSE by squaring each of the individual errors, et, and taking the average of those squared values, i.e.,

MSE ¼ Pn

i¼1e2i

n ð16Þ

The MAPE is computed by dividing the absolute errors by the corresponding true values and then averaging the deviations and multiplying by 100, i.e.,

MAPE ¼ Pn

i¼1jXt Ftj=Xt

n 100 ð17Þ

The ASRE of a model is deﬁned as the square root of the mean squared error, where Xobs are observed values and Xmodel are the predicted values at a time or place i.

ASRE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn

i¼1ðXobs;i Xmodel;iÞ2 n

s

ð18Þ

4. Results

4.1. Comparative results

Because revenues have been strongly inﬂuenced by several fac-tors such as the ﬁnancial crisis in the United States, the European debt crisis and the rapid development of the TFT-LCD industry in China, we chose the time series of revenues in the TFT-LCD markets

A1 B1 A2 B2 x y Π Ν Π Ν Σ

layer1 layer2 layer3

layer4 layer5 f w1 w2 w1 w2 w1f1 w2f2 x y x y

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in the Asia–Paciﬁc region, China, Eastern Europe and North Amer-ica for this research.Fig. 3shows the time series of revenue in the four regions.

Table 1shows the mean, the standard deviation (STD), the

conﬁ-dence interval (CI) and the correlation coefﬁcient for each of the four

regional markets[10]. The correlation coefficient was used in this study to estimate whether the data were linear or nonlinear. If the value of the correlation coefficient was between 0.3 and 0.3, the revenue was considered a nonlinear function. A common formula for calculating the correlation coefficient[8]is shown in Eq.(19). Fig. 3. The time series of revenue in the four regions.

Table 1

The statistics of the four regions.

Mean STD Confidence interval (Confidence level = 95%) Correlation coefficient

Asia 1.57E + 06 2.71E + 05 2.3852E + 006–7.6029E + 005 0.83 (Linear)

China 3.97E + 06 1.28E + 06 7.8070E + 006–1.3042E + 005 0.89 (Linear)

Eastern Europe 1.49E + 06 3.37E + 05 2.5042E + 006–4.8288E + 005 0.26 (Nonlinear)

North America 5.89E + 06 7.49E + 05 8.1374E + 006–3.6435E + 006 0.21 (Nonlinear)

Table 2.1

Prediction errors of the ten models for the China region.

China MSE MAPE ASRE

ES 1.2E + 12 22.95713 1,095,019 ARIMA 1.95E + 12 34.6286 1,396,370 SVR 9.94E + 11 21.48865 997189.3 BPNN 2.72E + 12 44.84088 1,649,544 ES_BPNN 5.43E + 12 63.23275 2,329,950 ES_SVR 6.15E + 12 68.16248 2,479,872 ARIMA_BPNN 4.68E + 10 3.795475 216426.2 ARIMA_SVR 1.05E + 12 20.88024 1,024,746 ANFIS 4.93E + 12 75.81456 2,220,437

ANFIS combination 2.76E + 12 36.27864 1,660,335 The signiﬁcance of bold values indicates the mean that the best predicating model.

Table 2.2

Prediction errors of the ten models for the Eastern Europe region.

Eastern Europe MSE MAPE ASRE

ES 1.72E + 11 28.18267 414752.2 ARIMA 2.53E + 11 35.52441 503,129 SVR 7.21E + 10 14.34171 268592.8 BPNN 4.58E + 10 12.52652 213904.2 ES_BPNN 2.55E + 11 30.93597 505157.3 ES_SVR 1.23E + 10 5.890067 110770.8 ARIMA_BPNN 5.84E + 11 55.00434 764046.3 ARIMA_SVR 1.99E + 11 22.96733 446616.2 ANFIS 1.98E + 11 22.77794 445174.1

ANFIS combination 1.09E + 12 132.4728 1,045,702 The signiﬁcance of bold values indicates the mean that the best predicating model.

Table 2.3

Prediction errors of the ten models for the North America region.

North America MSE MAPE ASRE

ES 8.52E + 11 13.16447 922961.3 ARIMA 6.57E + 11 11.46021 810648.5 SVR 2.54E + 12 29.42889 1,592,481 BPNN 8.8E + 11 14.34333 938096.5 ES_BPNN 6.43E + 11 12.56918 801913.4 ES_SVR 1.48E + 12 20.78015 1,215,228 ARIMA_BPNN 1.74E + 12 17.04229 1,320,151 ARIMA_SVR 8.91E + 11 13.59256 944057.6 ANFIS 5.44E + 10 2.995633 233204.5

ANFIS combination 2.26E + 12 27.26805 1,504,988

Table 2.4

Prediction errors of the ten models for the Asia region.

Asia MSE MAPE ASRE

ES 5.3E + 10 10.52902 230295.4 ARIMA 1.72E + 11 22.83422 415313.9 SVR 6.65E + 09 4.357999 81565.13 BPNN 1.3E + 11 22.2264 359918.1 ES_BPNN 2.41E + 10 7.533161 155244.9 ES_SVR 7.17E + 09 3.898338 84668.39 ARIMA_BPNN 7.52E + 11 54.6065 867,080 ARIMA_SVR 2.28E + 11 26.78322 477,049 ANFIS 4.44E + 11 43.9903 665994.2 ANFIS combination 4E + 10 9.811785 199905.5

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r ¼ P_XYPXPY n ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P_X2 P X ð Þ2 n _P Y2 P Y ð Þ2 n s ð19Þ 4.2. Analysis

First, we applied ﬁve single-model forecasting methods to obtain the forecasts. Two methods, ES and ARIMA, were linear, and the other three models, SCR, BPNN and ANFIS, were nonlinear. Second, we created four combined models by pairing the linear and

nonlinear models as follows: the ES and BPNN models, the ES and SCR models, the ARIMA and BPNN models and the ARIMA and SVR models. Finally, we compared and analyzed the results using the MSE, the MAPE and the ASRE. The training period was from January 2008 to June 2011 (season 1–season 10), and the test period was from July 2011 to December 2011 (season 11–season 12). In summary, 10 different forecasting models were used to predict the revenues in the four regions. Tables 2.1–2.4 compare the results of the 10 forecasting methods in the four regions.

From the results inTables 2.1–2.4, we can observe the effective-ness of the combined models, which had lower values of the MSE, the MAPE and the ASRE. The results showed the following: (1) for Actual data Database management system Database management system Step 1 Multiple forecasts

1. The combined forecasting from linear and nonlinear models (ES_BPNN, ES_SCR, ARIMA_BRNN, ARIMA_SVR) 2. Nonlinear combined forecasting (AFNIS)

Model management system Model management system

System interface System interface

Dialogue management system Dialogue management system

Step 3-2. Indicate the best model Step 3-2. Indicate the best model

Step 3-1. Compare the accuracy of combed forecasting methods

Forcasting performance test by

MSE, MAPE and ASRE Knowledge management system Knowledge management system Step 2 Step 3

Fig. 4. The multiple-model forecasting system structure and process.

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the Chinese region, the ARIMA-BPNN model was superior to the other methods; (2) for the Eastern European region, the ES-SVR model was the best; (3) for the North American region, the ANFIS was the best; and (4) for the Asia–Paciﬁc region, the ES-SVR model was the best.

The results inTables 2.1–2.4showed that the best forecasting model was different for each region. However, there is substantial evidence to demonstrate that combined forecasts from linear and nonlinear models improve the forecasting accuracy. Furthermore, combinations of linear and nonlinear models were more accurate in forecasting the revenues in the four regions than the individual linear models. Research has not yet revealed the conditions or the methods for the optimal combinations of forecasts. We infer that there were differences in the information among the four regions. It follows that the extracted data characteristics and the corre-sponding metrics should be mapped to the forecasting

perfor-mance evaluation to construct rules for selecting the forecasting method. To take advantage of the strengths of each method to develop the best forecast, we introduce a hybrid multi-model fore-casting system that can be used to select forefore-casting models to improve the forecasts.

4.3. Hybrid multi-model forecasting system (HMFS)

In this section, an operational multi-model forecasting system is designed to integrate all ﬁve combined forecasting methods into one forecasting process.Fig. 4shows the structure of hybrid model forecasting system. The main idea of the hybrid multi-model forecasting system is based on previous studies[41]. Several studies have shown multiple-model systems to be effective for software engineering, in which forecasting has become increas-ingly important[5,37]. In previous studies[22], this type of system Fig. 6. System interface – importing data.

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included information, model, knowledge and dialog management systems and combined forecasting software to obtain and analyze the data characteristics, develop the optimal forecast, and commu-nicate the forecast to the user. All of the combined forecasting functions from the two categories were implemented in the MAT-LAB programming environment (MathWorks, Natick, Massachu-setts, USA).

Fig. 5shows the interface for the forecasting system software,

which has a framework that integrates data management, moni-toring facilities and ﬁve possible combined forecasting models with a user-friendly geographic information system (GIS) platform. The system display for the initial step is shown inFig. 6. Data on TFT-LCD production by region may be imported into the system and used as the input to the various combined forecasting models. The data are stored in the database of this hybrid multi-model forecasting system. The system provides automated tools to select the most accurate and reliable forecasting model for the input time series data.Fig. 5shows that once the dataset is chosen, the system automatically attempts to load the historical data, and a separate

window allows the user to choose the forecasting mode to develop a custom combined forecasting model.

Fig. 7shows the system interface providing guidelines to the

user, typically a sales and marketing manager, in selecting suitable combined forecasting methods. The choice of the combined fore-casting method depends on the forefore-casting performance, as deter-mined by the MSE, the MAPE and the ASRE. The most important beneﬁt is that the system can automatically organize and analyze large amounts of data to indicate the forecasting performance of each combined forecasting method, allowing the manager to make the ﬁnal judgment. Additionally, this system provides forecasts based on past data, but the manager can adjust this forecast based on future events that the system did not consider.

An additional test of the system was conducted by adding noise (a random walk,[13,31]) to the revenue of one region (Eastern Eur-ope) and verifying that the hybrid multi-model forecasting system could effectively forecast the revenue of that region (Fig. 8).Fig. 9

shows the output of the hybrid multi-model forecasting system for the revenue of the Eastern European region with noise. The hybrid

0 2 4 6 8 10 12 0.8 1 1.2 1.4 1.6 1.8 2 2.2x 10 6 Period Revenue

Eastern Europe Revenue Eastern Europe Revenue with noise

Fig. 8. The revenue forecast of the Eastern European region with and without noise.

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multi-model forecasting system selected the ES-SVR model to fore-cast the revenue of the Eastern European regional market with noise in the data.

5. Conclusion and further research

In fact, this research investigated the use of combinations of lin-ear and nonlinlin-ear forecasting models to predict the revenues of the TFT-LCD industry in four regions from time series data. The results showed that the proposed models usually had better performance than the individual linear models (ES and ARIMA), the individual nonlinear models (SVR and BPNN) and the nonlinear combined forecasting model (ANFIS) in forecasting revenues in the Chinese, Eastern European and Asia–Pacific regional markets; the individual nonlinear forecasting model ANFIS had the best forecasting perfor-mance in predicting the North American market. In general, this research showed that combined forecasts from linear and nonlin-ear models had better performance compared with other methods. Chen[6]reported that there is no clear evidence in favor of combined forecasts from linear and nonlinear models over other forecasting models in terms of forecasting performance [6]. Our results indicate that combined forecasts from linear and nonlinear models are better for predicting linear or nonlinear revenue time series. However, no one method was best for all series. To do so, a powerful hybrid multi-model forecasting system to generate more accurate forecasts from empirical comparisons of alternative forecasting methods was developed in this research. This hybrid multi-model forecasting system draws on several sources for fore-casting inputs, including databases, documents, and a variety of forecasting methods. After processing the data from various sources, sophisticated forecasting systems integrate all the neces-sary data into a single spreadsheet, which the user can then manip-ulate by entering various projections such as different estimates of future revenue that the system will incorporate into a new output. It is important to note the role of this flexible and sound archi-tecture is crucial, particularly with fast-paced, rapidly developing forecasting techniques. If the base of the system is rigid or inade-quate, it can be impossible to reconfigure the system to adjust to changing market conditions. Along the same lines, in other busi-ness forecasting methods and systems, it is also important to invest in systems that will remain useful over the long term, accommodating changes in the business world.

We conclude that this system has three major beneﬁts over other forecasting systems: (1) this system has better accuracy than nonlinear combined forecasting methods or single methods; (2) this system assists in deciding which combined forecasting models are better, which alternatives are inactive, and which alternatives deliver the lowest statistical error and produce a good estimate of the variable of interest and (3) this system provides users with a graphical user interface, where the user can answer queries and can view the desired results in an integrated form. Hence, this system reduces the user’s effort in obtaining the desired forecast-ing results from the regional revenue database.

There are many types of nonlinear models and combined fore-casting methods for the prediction of markets. In this study, we considered 10 types of models and combined forecasting methods. Future work will include other types of models. Furthermore, the proposed hybrid multi-model forecasting system can be adapted to many other ﬁelds of market prediction.

Acknowledgement

This work was supported in part by National Science Council of Taiwan, Taiwan, R.O.C. under Grant NSC 103-2218-E-131-001.

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